characterized by SEM. The process is destructive, since the specimen is being sequentially milled away after each image is collected. The collected series of images is then reconstructed to a 3D volume by registering the image stack and removing artifacts.

Each analysis was carried out on three replicas with three measurements repetitions.

## Results

The RS measured in this study are not including only the residual stresses of the pure channel, but also part of the residual stresses around the channels, as indicated by the yellow circles in Fig. 2, which highlight the measurement area. Anyway, considering the intensity of the X-ray as a Gaussian distribution, the values of RS are estimated as that of the center of groove, due to the higher intensity of the X-ray around the center of the measured area. For reference, the maximum X-ray penetration depth in the RS measurement is about 10 µm, but the actual penetration depth is shallower due to the inclination of the device.

Regarding micro-EDM, due to the metallurgical changes and the action of high temperatures, compressive RS appears (Fig. 2). Specifically, micro-EDM is characterized by an increase of the temperature in a very localized area: the area surrounding the processed zone does not undergo this rapid increase in temperature and therefore the melted material tends to resolidify in a constrained area surrounded by lower temperatures which can generate compressive RS. Isotropic (bidirectional) residual stress is observed. That is associated with the uniform distribution of the individual discharges in micro-EDM. With the increment in the discharge energy (it corresponds to the increment of MRR), the residual stress also increases. This may be attributed to the increase in thickness of the defective white layer, in which the RS is a maximum. The RS measured for the 0.8 mm channels tends to be more tensile than the RS on the 0.2 mm channels (as shown in the example of Fig. 1 A and reported in literature [8]). However, observing the 0.2 mm channels measurement area, it is worth noticing that is more influenced by the surrounding surface state that has been previously machined.

<figure><img src="image_1767.png" /><figcaption>Figure 2. RS measurements at four degrees on the micro-EDM processed samples.</figcaption></figure>
<figure><img src="image_1770.png" /><figcaption>Figure 3. RS measurements at four degrees on the MM processed samples.</figcaption></figure>

Regarding MM, in which the relative movement between the tool edges and the workpiece determines the chip formation, the mechanical effect highly influences the RS. Observing the results of Fig. 3, the size of the tool seems to have a significant effect. Specifically, the surface machined with D0.8 mm micro tool exhibits compressive residual stress in feed direction (0°) almost two-times higher than the traversal axis direction (perpendicular to the feed direction). This effect is confirmed in literature [9] demonstrating that in conventional size milling, the RS on the machined surface in feed direction are higher than the RS along the traversal axis direction (90°). On the other hand, the surface machined with D0.2 mm micro tool shows more uniform residual stress, as visible in Fig. 3.

<figure><img src="image_1771.png" /><figcaption>Figure 4. FIB cross section of micro-EDM and MM samples showing the differences between the tool diameters used and the measurement direction in relation to the traversal axis and feed direction. Yellow circles referring to the 0.8 mm features indicate examples of the different grain structure (micro-EDM) and white layer (MM).</figcaption></figure>
<figure><img src="image_1768.png" /><figcaption>Figure 3. RS measurements at four degrees on the MM processed samples.</figcaption></figure>

Regarding MM, in which the relative movement between the tool edges and the workpiece determines the chip formation, the mechanical effect highly influences the RS. Observing the results of Fig. 3, the size of the tool seems to have a significant effect. Specifically, the surface machined with D0.8 mm micro tool exhibits compressive residual stress in feed direction (0°) almost two-times higher than the traversal axis direction (perpendicular to the feed direction). This effect is confirmed in literature [9] demonstrating that in conventional size milling, the RS on the machined surface in feed direction are higher than the RS along the traversal axis direction (90°). On the other hand, the surface machined with D0.2 mm micro tool shows more uniform residual stress, as visible in Fig. 3.

<figure><img src="image_1769.png" /><figcaption>Figure 4. FIB cross section of micro-EDM and MM samples showing the differences between the tool diameters used and the measurement direction in relation to the traversal axis and feed direction. Yellow circles referring to the 0.8 mm features indicate examples of the different grain structure (micro-EDM) and white layer (MM).</figcaption></figure>
Figure 4 shows the results of FIB-SEM analysis. It allows comparing the microstructure of the surface of unprocessed samples with the post-machined surfaces, both in feed and traversal axis directions. About micro-EDM sample, the larger electrode allows for observing greater thermal effects in the region immediately below the machined surface: a different grain structure is distinguishable between the two rows of images, specifically, along the feed direction. This can be related to the higher amount of energy transferred to the machined surfaces by the use of a bigger electrode which generates more sparks. Moreover, a white layer, due to the resolidified material typical of EDM processes, can be observed, with a thickness proportional to the electrode diameter. From the analysis, it is possible to exclude the presence of micro-cracks.

About MM, a superficial white layer is also visible regardless of the tool size. Its thickness appears proportional to the tool diameter. The formation of this brittle and hard white layer consisting of martensite is typical in machining of hard materials when the frictional heating is followed by the subsequent cooling process [10].

## Conclusions

This work shows a preliminary analysis of the residual stresses caused by the post-processing of 3D printed metal samples with different Micromachining techniques. Considering the up-to-date literature and the related promising applications, micro-EDM and Micro-Milling have been taken into account for this analysis. It is worth remembering that tensile residual stresses are usually considered more damaging than compressive residual stresses.

* A few differences between tensile and compressive stresses can be observed and need to be highlighted. Specifically, it can be noticed that micro-EDM samples show lower compressive RS compared to the MM ones, probably due to the residual stresses caused by the LPBF technique combined with the stresses appeared during micro-EDM local melting and subsequent solidification [11].

* Micro-EDM was carried out on pre-machined samples, therefore, it would be reasonable to conclude that the typical tensile stresses on the surface of LPBF parts have been balanced with compressive stresses introduced by the pre-machining step and subsequently, further tensile stresses have been caused by micro-EDM.

* MM induced stresses, are purely compressive and dependent on the feed direction. Moreover, the compressive MM stresses seem dependent on the tool size. In MM, a tensile state of pre-stress can be detrimental in terms of burr formation and the occurrence of the ploughing phenomenon [12].

These results can be further analysed to understand which type of post-processing treatments are necessary for 3D printed metals, especially in the case of laser-powder bed fusion parts. Moreover, the analysis of residual stresses, especially on the surface, can support the mechanical characterization of machined 3D structures for bespoke and load bearing applications. Furthermore, different 3D printing techniques can cause severe and diverse residual stresses on metal samples, highlighting the need for residual stresses evaluation on as-built, treated, and machined parts.

## Funding

Financed by the European Union - NextGenerationEU (National Sustainable Mobility Center CN00000023, Italian Ministry of University and Research Decree n. 1033 - 17/06/2022, Spoke 11 - Innovative Materials & Lightweighting - CUP: D83C22000690001). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission's official position. Neither the European Union nor the European Commission can be held responsible for them.
Figure 4 shows the results of FIB-SEM analysis. It allows comparing the microstructure of the surface of unprocessed samples with the post-machined surfaces, both in feed and traversal axis directions. About micro-EDM sample, the larger electrode allows for observing greater thermal effects in the region immediately below the machined surface: a different grain structure is distinguishable between the two rows of images, specifically, along the feed direction. This can be related to the higher amount of energy transferred to the machined surfaces by the use of a bigger electrode which generates more sparks. Moreover, a white layer, due to the resolidified material typical of EDM processes, can be observed, with a thickness proportional to the electrode diameter. From the analysis, it is possible to exclude the presence of micro-cracks.

About MM, a superficial white layer is also visible regardless of the tool size. Its thickness appears proportional to the tool diameter. The formation of this brittle and hard white layer consisting of martensite is typical in machining of hard materials when the frictional heating is followed by the subsequent cooling process [10].

## Conclusions

This work shows a preliminary analysis of the residual stresses caused by the post-processing of 3D printed metal samples with different Micromachining techniques. Considering the up-to-date literature and the related promising applications, micro-EDM and Micro-Milling have been taken into account for this analysis. It is worth remembering that tensile residual stresses are usually considered more damaging than compressive residual stresses.

* A few differences between tensile and compressive stresses can be observed and need to be highlighted. Specifically, it can be noticed that micro-EDM samples show lower compressive RS compared to the MM ones, probably due to the residual stresses caused by the LPBF technique combined with the stresses appeared during micro-EDM local melting and subsequent solidification [11].

* Micro-EDM was carried out on pre-machined samples, therefore, it would be reasonable to conclude that the typical tensile stresses on the surface of LPBF parts have been balanced with compressive stresses introduced by the pre-machining step and subsequently, further tensile stresses have been caused by micro-EDM.

* MM induced stresses, are purely compressive and dependent on the feed direction. Moreover, the compressive MM stresses seem dependent on the tool size. In MM, a tensile state of pre-stress can be detrimental in terms of burr formation and the occurrence of the ploughing phenomenon [12].

These results can be further analysed to understand which type of post-processing treatments are necessary for 3D printed metals, especially in the case of laser-powder bed fusion parts. Moreover, the analysis of residual stresses, especially on the surface, can support the mechanical characterization of machined 3D structures for bespoke and load bearing applications. Furthermore, different 3D printing techniques can cause severe and diverse residual stresses on metal samples, highlighting the need for residual stresses evaluation on as-built, treated, and machined parts.

## Funding

Financed by the European Union - NextGenerationEU (National Sustainable Mobility Center CN00000023, Italian Ministry of University and Research Decree n. 1033 - 17/06/2022, Spoke 11 - Innovative Materials & Lightweighting - CUP: D83C22000690001). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission's official position. Neither the European Union nor the European Commission can be held responsible for them.
## References

[1] A., Abeni, P.S., Ginestra, A. Attanasio. Micro-milling of Selective Laser Melted Stainless Steel. In: Ceretti, E., Tolio, T. (eds) Selected Topics in Manufacturing. Lecture Notes in Mechanical Engineering. (2021) Springer, Cham. https://doi.org/10.1007/978-3-030-57729-2_1

[2] M., Quarto, G. Maccarini. Surface Quality Improvement Techniques for 3D Printed Metal Samples. In: Carrino, L., Galantucci, L.M., Settineri, L. (eds) Selected Topics in Manufacturing. Lecture Notes in Mechanical Engineering. (2024) Springer, Cham. https://doi.org/10.1007/978-3-031-41163-2_3

[3] C. Li, Z.Y. Liu, X.Y. Fang, Y.B. Guo, Residual Stress in Metal Additive Manufacturing, Procedia CIRP, Volume 71, (2018) Pages 348-353, ISSN 2212-8271, https://doi.org/10.1016/j.procir.2018.05.039

[4] E.S.; Statnik, F.; Uzun, S.A.; Lipovskikh, Y.V.; Kan, S.I.; Eleonsky, V.S.; Pisarev, P.A.; Somov, A.I.; Salimon, Y.V.; Malakhova, A.G.; Seferyan, et al. Comparative Multi-Modal, Multi-Scale Residual Stress Evaluation in SLM 3D-Printed Al-Si-Mg Alloy (RS-300) Parts. Metals (2021) 11, 2064. https://doi.org/10.3390/met11122064

[5] QP Ma, J Mesicek, F Fojtik, J Hajnys, P Krpec, M Pagac, J Petru. Residual Stress Build-Up in Aluminum Parts Fabricated with SLM Technology Using the Bridge Curvature Method. Materials (Basel). (2022) Sep 1;15(17):6057. doi: 10.3390/ma15176057. PMID: 36079438; PMCID: PMC9457910

[6] A., Abeni, M. Quarto, & P.S Ginestra. Post-processing of powder bed fused stainless steel: micro-machining and micro-electrical discharge machining. J Intell Manuf (2023). https://doi.org/10.1007/s10845-023-02277-z

[7] S. Tamura, A. Ezura, and T. Matsumura, "Cutting Force in Peripheral Milling of Additively Manufactured Maraging Steel," Int. J. Automation Technol., (2022) Vol.16 No.6, pp. 897-905,

[8] S. Schneider, J. Vorspohl, F. Frerichs, A. Klink, M. Meinke, W. Schröder, T. Lübben, Investigation on residual stress induced by multiple EDM discharges, Procedia CIRP, Volume 102, (2021), Pages 482-487, ISSN 2212-8271, https://doi.org/10.1016/j.procir.2021.09.082.

[9] H., Liu, D.Schraknepper, T. Bergs. Investigation of residual stresses and workpiece distortion during high-feed milling of slender stainless steel components. Procedia CIRP, 108, (2022). 495-500.

[10] S. K.,Rajbongshi, D. K., Sarma, M. A. Singh. (A Brief Review of White Layer Formation in Hard Machining with a Case Study. In Advances in Mechanical Engineering: Select Proceedings of ICRIDME (2020). pp. 407-417. Springer Singapore.

[11] R. Acevedo, P. Sedlak, R. Kolman, M. Fredel, Residual stress analysis of additive manufacturing of metallic parts using ultrasonic waves: State of the art review, Journal of Materials Research and Technology, Volume 9, Issue 4, (2020), Pages 9457-9477, ISSN 2238-7854, https://doi.org/10.1016/j.jmrt.2020.05.092

[12] R., Yadav, N.D. Chakladar, S. Paul. Effects of tailored residual stress on micro-end milling: numerical modelling and validation. Int J Adv Manuf Technol 127, 5449-5470 (2023). https://doi.org/10.1007/s00170-023-11780-9
## References

[1] A., Abeni, P.S., Ginestra, A. Attanasio. Micro-milling of Selective Laser Melted Stainless Steel. In: Ceretti, E., Tolio, T. (eds) Selected Topics in Manufacturing. Lecture Notes in Mechanical Engineering. (2021) Springer, Cham. https://doi.org/10.1007/978-3-030-57729-2_1

[2] M., Quarto, G. Maccarini. Surface Quality Improvement Techniques for 3D Printed Metal Samples. In: Carrino, L., Galantucci, L.M., Settineri, L. (eds) Selected Topics in Manufacturing. Lecture Notes in Mechanical Engineering. (2024) Springer, Cham. https://doi.org/10.1007/978-3-031-41163-2_3

[3] C. Li, Z.Y. Liu, X.Y. Fang, Y.B. Guo, Residual Stress in Metal Additive Manufacturing, Procedia CIRP, Volume 71, (2018) Pages 348-353, ISSN 2212-8271, https://doi.org/10.1016/j.procir.2018.05.039

[4] E.S.; Statnik, F.; Uzun, S.A.; Lipovskikh, Y.V.; Kan, S.I.; Eleonsky, V.S.; Pisarev, P.A.; Somov, A.I.; Salimon, Y.V.; Malakhova, A.G.; Seferyan, et al. Comparative Multi-Modal, Multi-Scale Residual Stress Evaluation in SLM 3D-Printed Al-Si-Mg Alloy (RS-300) Parts. Metals (2021) 11, 2064. https://doi.org/10.3390/met11122064

[5] QP Ma, J Mesicek, F Fojtik, J Hajnys, P Krpec, M Pagac, J Petru. Residual Stress Build-Up in Aluminum Parts Fabricated with SLM Technology Using the Bridge Curvature Method. Materials (Basel). (2022) Sep 1;15(17):6057. doi: 10.3390/ma15176057. PMID: 36079438; PMCID: PMC9457910

[6] A., Abeni, M. Quarto, & P.S Ginestra. Post-processing of powder bed fused stainless steel: micro-machining and micro-electrical discharge machining. J Intell Manuf (2023). https://doi.org/10.1007/s10845-023-02277-z

[7] S. Tamura, A. Ezura, and T. Matsumura, "Cutting Force in Peripheral Milling of Additively Manufactured Maraging Steel," Int. J. Automation Technol., (2022) Vol.16 No.6, pp. 897-905,

[8] S. Schneider, J. Vorspohl, F. Frerichs, A. Klink, M. Meinke, W. Schröder, T. Lübben, Investigation on residual stress induced by multiple EDM discharges, Procedia CIRP, Volume 102, (2021), Pages 482-487, ISSN 2212-8271, https://doi.org/10.1016/j.procir.2021.09.082.

[9] H., Liu, D.Schraknepper, T. Bergs. Investigation of residual stresses and workpiece distortion during high-feed milling of slender stainless steel components. Procedia CIRP, 108, (2022). 495-500.

[10] S. K.,Rajbongshi, D. K., Sarma, M. A. Singh. (A Brief Review of White Layer Formation in Hard Machining with a Case Study. In Advances in Mechanical Engineering: Select Proceedings of ICRIDME (2020). pp. 407-417. Springer Singapore.

[11] R. Acevedo, P. Sedlak, R. Kolman, M. Fredel, Residual stress analysis of additive manufacturing of metallic parts using ultrasonic waves: State of the art review, Journal of Materials Research and Technology, Volume 9, Issue 4, (2020), Pages 9457-9477, ISSN 2238-7854, https://doi.org/10.1016/j.jmrt.2020.05.092

[12] R., Yadav, N.D. Chakladar, S. Paul. Effects of tailored residual stress on micro-end milling: numerical modelling and validation. Int J Adv Manuf Technol 127, 5449-5470 (2023). https://doi.org/10.1007/s00170-023-11780-9
# An innovative method to model run-out phenomena in micro-milling by using cutting force signal

SENECI Greta<fnref n="1" />,ª, PANCERA Pierpaolo Vincenzo<fnref n="1" />,ᵇ, CAPPELLINI Cristian<fnref n="2" />,ᶜ, ABENI Andrea<fnref n="1" />,ᵈ* and ATTANASIO Aldo<fnref n="1" />,ᵉ

**Keywords:** Tool Run-Out, Micro-Milling, Al-Si-10mg, Analytical Modeling, Additive Manufacturing

**Abstract.** This work deals with the modeling of micro-milling processes by considering the phenomena generated by the transition from conventional size to the micro-scale machining. The concomitant effects of different cutting regimes, and the deviation of the cutting edges from their theoretical trajectories due to tool run-out, are important aspects to be considered during the process modeling. Several models are available in literature to describe how ploughing and shearing regimes influence cutting forces and how the tool run-out impacts on the actual chip thickness. In a previous authors research, a comprehensive model was published achieving a good agreement with the experimental data, but its calibration requires the measurement of the width of the micro-milled slots. This practice is time consuming and subjected to experimental errors, while a calibration of the model based only on the elaboration of the cutting force signal appears a promising strategy. Starting from the mathematical description of the geometrical model, a new equation to compute the tool run-out parameters was found. The parameters depend on eight variables that must be calculated from tool geometry, material composition, cutting parameters and the cutting force signal. An experimental procedure was developed to compare the prediction achieved by the new method and the conventional technique.

**Introduction**

Micro-milling is a machining operation concerning the employment of cutting tools with a diameter lower than 1 mm. At this scale level, critical issues, usually neglectable when dealing with the same process on conventional scale, rise up. These issues are size effect, burr formation, high cutting forces, rapid tool wear, different cutting regimes (*ploughing* and *shearing*) and tool run-out [1, 2]. Ploughing regime is an undesired cutting condition in which uncut chip thickness is not sufficient to completely remove the chip and a not-neglectable elastic deformation is induced in the workpiece. This phenomenon implicates the increase of cutting forces as well as a poor surface quality on the machined features [3]. On the contrary, when chip thickness is higher than a threshold value, i.e. Minimum Uncut Chip Thickness (MUCT), shearing regime occurs. The uncut chip thickness depends on the instantaneous trajectories of the tool cutting edges, which are strongly influenced by tool run-out. This latter is defined as the deviation of the effective tool's rotational axis from the theoretical one. The phenomenon implicates different uncut chip thickness in relation of each cutting edge. Therefore, different cutting forces are applied on each tool flute, with a resulting non-homogeneous tool wear. So that, many researchers focused on considering tool run-out and cutting regimes when modelling micro-milling [4, 5].

<figure><img src="image_1772.png" /></figure>

<footnote n="1">¹Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy</footnote>

<footnote n="2">²Department of Management, Information and Production Engineering, University of Bergamo, Via Pasubio 7/b, 24044 Dalmine, Italy</footnote>

<footnote>ªgreta.seneci@unibs.it, ᵇp.pancera001@studenti.unibs.it, ᶜcristian.cappellini@unibg.it,</footnote>

<footnote>ᵈandrea.abeni@unibs.it, ᵈaldo.attanasio@unibs.it</footnote>
# An innovative method to model run-out phenomena in micro-milling by using cutting force signal

SENECI Greta<fnref n="1" />,ª, PANCERA Pierpaolo Vincenzo<fnref n="1" />,ᵇ, CAPPELLINI Cristian<fnref n="2" />,ᶜ, ABENI Andrea<fnref n="1" />,ᵈ* and ATTANASIO Aldo<fnref n="1" />,ᵉ

**Keywords:** Tool Run-Out, Micro-Milling, Al-Si-10mg, Analytical Modeling, Additive Manufacturing

**Abstract.** This work deals with the modeling of micro-milling processes by considering the phenomena generated by the transition from conventional size to the micro-scale machining. The concomitant effects of different cutting regimes, and the deviation of the cutting edges from their theoretical trajectories due to tool run-out, are important aspects to be considered during the process modeling. Several models are available in literature to describe how ploughing and shearing regimes influence cutting forces and how the tool run-out impacts on the actual chip thickness. In a previous authors research, a comprehensive model was published achieving a good agreement with the experimental data, but its calibration requires the measurement of the width of the micro-milled slots. This practice is time consuming and subjected to experimental errors, while a calibration of the model based only on the elaboration of the cutting force signal appears a promising strategy. Starting from the mathematical description of the geometrical model, a new equation to compute the tool run-out parameters was found. The parameters depend on eight variables that must be calculated from tool geometry, material composition, cutting parameters and the cutting force signal. An experimental procedure was developed to compare the prediction achieved by the new method and the conventional technique.

**Introduction**

Micro-milling is a machining operation concerning the employment of cutting tools with a diameter lower than 1 mm. At this scale level, critical issues, usually neglectable when dealing with the same process on conventional scale, rise up. These issues are size effect, burr formation, high cutting forces, rapid tool wear, different cutting regimes (*ploughing* and *shearing*) and tool run-out [1, 2]. Ploughing regime is an undesired cutting condition in which uncut chip thickness is not sufficient to completely remove the chip and a not-neglectable elastic deformation is induced in the workpiece. This phenomenon implicates the increase of cutting forces as well as a poor surface quality on the machined features [3]. On the contrary, when chip thickness is higher than a threshold value, i.e. Minimum Uncut Chip Thickness (MUCT), shearing regime occurs. The uncut chip thickness depends on the instantaneous trajectories of the tool cutting edges, which are strongly influenced by tool run-out. This latter is defined as the deviation of the effective tool's rotational axis from the theoretical one. The phenomenon implicates different uncut chip thickness in relation of each cutting edge. Therefore, different cutting forces are applied on each tool flute, with a resulting non-homogeneous tool wear. So that, many researchers focused on considering tool run-out and cutting regimes when modelling micro-milling [4, 5].

<figure><img src="image_1770.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.

<footnote n="1">¹Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy</footnote>

<footnote n="2">²Department of Management, Information and Production Engineering, University of Bergamo, Via Pasubio 7/b, 24044 Dalmine, Italy</footnote>

<footnote>ªgreta.seneci@unibs.it, ᵇp.pancera001@studenti.unibs.it, ᶜcristian.cappellini@unibg.it,</footnote>

<footnote>ᵈandrea.abeni@unibs.it, ᵈaldo.attanasio@unibs.it</footnote>
Bissacco et al. [6] proposed an analytical model to estimate the unbalancing of cutting forces due to tool run-out. In this model, different force profiles for each cutting edge are considered as a function of tool run-out. Rodriguez & Labarga [7] elaborated an analytical force model through a set of linear equations considering the run-out deviation, the tool deflection and the size effect. Chen et al. [8] proposed an analytical model that considers both ploughing and shearing conditions depending on the value of uncut chip thickness. The instantaneous uncut chip thickness was calculated by considering tool run-out and the machine tool systems vibrations. Many experimental tests confirmed the capability of the model to provide an accurate force prediction. A similar model was elaborated by Zhang et al. [9]. This model was validated by performing a series of micro end milling experiments on Al6061 workpieces under different conditions.

The purpose of this paper is to verify a novel procedure to quantify tool run-out through the model described in [5], by only exploiting the cutting force signal as model input. An experimental method was defined to compute the unknown parameters of the geometrical model of run-out. Firstly, micro-channels were realized on AlSi10Mg samples fabricated with different production technologies (i.e., additive manufacturing and casting). The tests were performed by varying the feed rates in order to change the chip cross section to investigate the cutting regime transition. During the process, the cutting force was acquired using a load cell. After the process, channel's width was measured with a profilometer laser probe and data were used to calibrate the model described in [5]. Finally, the experimental outputs were compared with the results of the innovative calibration procedure to assess its reliability.

## Tool run-out model

Fig. 1a represents the run-out effect on the tool flutes trajectories and the related geometric parameters. The analysis considers for simplicity a two cutting edges tool, which is sectioned in a plane normal to the theoretical tool rotation axis. Tool run-out has three main effects on the cutting process:

1. The effective radius of one of the cutting edges, in this investigation the first one ($r_{CE1}$), increases.

2. The radius of the other cutting edge, in this study the second one ($r_{CE2}$), decreases.

3. The phase angle $\alpha$ [rad] between the two cutting edges is not constantly equal to $\pi$ [rad].

The run-out can be evaluated using two geometric parameters: the run-out length $r_0$, defined as the distance between the theoretical spindle rotational centre $O$ and the effective one $O'$; and the run-out angle $\gamma$ as represented in Fig. 1. Even though these parameters cannot be directly measured, it is demonstrated [10] that they can be estimated assessing the tool diameter $d$ [mm], the cutting-edge phase angle $\alpha$ [rad] and the rotational radius of the main cutting edge $r_{CE1}$ [mm], by applying Eq. 1 and Eq. 2:
Bissacco et al. [6] proposed an analytical model to estimate the unbalancing of cutting forces due to tool run-out. In this model, different force profiles for each cutting edge are considered as a function of tool run-out. Rodriguez & Labarga [7] elaborated an analytical force model through a set of linear equations considering the run-out deviation, the tool deflection and the size effect. Chen et al. [8] proposed an analytical model that considers both ploughing and shearing conditions depending on the value of uncut chip thickness. The instantaneous uncut chip thickness was calculated by considering tool run-out and the machine tool systems vibrations. Many experimental tests confirmed the capability of the model to provide an accurate force prediction. A similar model was elaborated by Zhang et al. [9]. This model was validated by performing a series of micro end milling experiments on Al6061 workpieces under different conditions.

The purpose of this paper is to verify a novel procedure to quantify tool run-out through the model described in [5], by only exploiting the cutting force signal as model input. An experimental method was defined to compute the unknown parameters of the geometrical model of run-out. Firstly, micro-channels were realized on AlSi10Mg samples fabricated with different production technologies (i.e., additive manufacturing and casting). The tests were performed by varying the feed rates in order to change the chip cross section to investigate the cutting regime transition. During the process, the cutting force was acquired using a load cell. After the process, channel's width was measured with a profilometer laser probe and data were used to calibrate the model described in [5]. Finally, the experimental outputs were compared with the results of the innovative calibration procedure to assess its reliability.

## Tool run-out model

Fig. 1a represents the run-out effect on the tool flutes trajectories and the related geometric parameters. The analysis considers for simplicity a two cutting edges tool, which is sectioned in a plane normal to the theoretical tool rotation axis. Tool run-out has three main effects on the cutting process:

1. The effective radius of one of the cutting edges, in this investigation the first one ($r_{CE1}$), increases.

2. The radius of the other cutting edge, in this study the second one ($r_{CE2}$), decreases.

3. The phase angle $\alpha$ [rad] between the two cutting edges is not constantly equal to $\pi$ [rad].

The run-out can be evaluated using two geometric parameters: the run-out length $r_0$, defined as the distance between the theoretical spindle rotational centre $O$ and the effective one $O'$; and the run-out angle $\gamma$ as represented in Fig. 1. Even though these parameters cannot be directly measured, it is demonstrated [10] that they can be estimated assessing the tool diameter $d$ [mm], the cutting-edge phase angle $\alpha$ [rad] and the rotational radius of the main cutting edge $r_{CE1}$ [mm], by applying Eq. 1 and Eq. 2:
<figure><img src="image_1773.png" /><figcaption>Figure 1 – (a) Geometrical representation of tool run-out (b) and representation of tool edge trajectories and force components.</figcaption></figure>

$$r_0 = \sqrt{r_{CE2}^2 + \left(\frac{d}{2}\right)^2 - 2 \cdot r_{CE2} \cdot \frac{d}{2} \cdot \cos \delta} \quad (1)$$

$$\gamma = \arcsin \left( \frac{r_{CE2}}{r_0} \cdot \sin \delta \right) \quad (2)$$

where angle $\delta$ and $r_{CE2}$ are again expressed as a function of the previously reported measurable parameters (Eq. 3 and Eq. 4) [10]:

$$\delta = \arcsin \left( \frac{r_{CE1}}{d} \cdot \sin \alpha \right) \quad (3)$$

$$r_{CE1} = \sqrt{r_{CE1}^2 + d^2 - 2r_{CE1}d \cos(\pi - \alpha - \delta)} \quad (4)$$

In [10] the whole procedure for determining the phase angle $\alpha$, using the cutting period derived from the force signal, and for measuring $d$ and $r_{CE1}$ is clearly explained.

In Fig. 1b it is possible to see how the run-out influence the trajectories of the tool flutes and its effect on the instantaneous uncut chip thickness $h$.

The total cutting force $F_C$ is the combination of its spatial components $F_x$, $F_y$, and $F_z$. In turn, the $F_C$ component in the section plane can be subdivided in its tangential $F_t$ and radial $F_r$ components as demonstrated in [5]. They depend on tool rotational angle $\theta$ and they can be decomposed along x-axis and y-axis by using the set of Eqs. 5, where the subscripted number is related to the considered cutting edge.

$$\left\{ \begin{array}{l} F_{x1} = F_{t1} \cdot \cos \theta + F_{r1} \cdot \sin \theta \\ F_{y1} = -F_{t1} \cdot \sin \theta + F_{r1} \cdot \cos \theta \\ F_{x2} = F_{t2} \cdot \cos \theta + F_{r2} \cdot \sin \theta \\ F_{y2} = -F_{t2} \cdot \sin \theta + F_{r2} \cdot \cos \theta \end{array} \right. \quad (5)$$

As developed in [5], for each cutting edge, tangential and radial force components can be estimated by the set of Eqs. 6 as follows:
<figure><img src="image_1771.png" /><figcaption>Figure 1 – (a) Geometrical representation of tool run-out (b) and representation of tool edge trajectories and force components.</figcaption></figure>

$$r_0 = \sqrt{r_{CE2}^2 + \left(\frac{d}{2}\right)^2 - 2 \cdot r_{CE2} \cdot \frac{d}{2} \cdot \cos \delta} \quad (1)$$

$$\gamma = \arcsin \left( \frac{r_{CE2}}{r_0} \cdot \sin \delta \right) \quad (2)$$

where angle $\delta$ and $r_{CE2}$ are again expressed as a function of the previously reported measurable parameters (Eq. 3 and Eq. 4) [10]:

$$\delta = \arcsin \left( \frac{r_{CE1}}{d} \cdot \sin \alpha \right) \quad (3)$$

$$r_{CE1} = \sqrt{r_{CE1}^2 + d^2 - 2r_{CE1}d \cos(\pi - \alpha - \delta)} \quad (4)$$

In [10] the whole procedure for determining the phase angle $\alpha$, using the cutting period derived from the force signal, and for measuring $d$ and $r_{CE1}$ is clearly explained.

In Fig. 1b it is possible to see how the run-out influence the trajectories of the tool flutes and its effect on the instantaneous uncut chip thickness $h$.

The total cutting force $F_C$ is the combination of its spatial components $F_x$, $F_y$, and $F_z$. In turn, the $F_C$ component in the section plane can be subdivided in its tangential $F_t$ and radial $F_r$ components as demonstrated in [5]. They depend on tool rotational angle $\theta$ and they can be decomposed along x-axis and y-axis by using the set of Eqs. 5, where the subscripted number is related to the considered cutting edge.

$$\left\{ \begin{array}{l} F_{x1} = F_{t1} \cdot \cos \theta + F_{r1} \cdot \sin \theta \\ F_{y1} = -F_{t1} \cdot \sin \theta + F_{r1} \cdot \cos \theta \\ F_{x2} = F_{t2} \cdot \cos \theta + F_{r2} \cdot \sin \theta \\ F_{y2} = -F_{t2} \cdot \sin \theta + F_{r2} \cdot \cos \theta \end{array} \right. \quad (5)$$

As developed in [5], for each cutting edge, tangential and radial force components can be estimated by the set of Eqs. 6 as follows:
$$ \left\{ \begin{aligned} F_{t1}(\theta) &= (K_{ts} \cdot h_{CE1}(\theta) + K_{tp} \cdot A_{p1}(\theta)) \cdot a_p \\ F_{r1}(\theta) &= (K_{rs} \cdot h_{CE1}(\theta) + K_{rp} \cdot A_{p1}(\theta)) \cdot a_p \\ F_{t2}(\theta) &= (K_{ts} \cdot h_{CE2}(\theta) + K_{tp} \cdot A_{p2}(\theta)) \cdot a_p \\ F_{r2}(\theta) &= (K_{rs} \cdot h_{CE2}(\theta) + K_{rp} \cdot A_{p2}(\theta)) \cdot a_p \end{aligned} \right. \qquad (6) $$

where $K_{ts}$ [N/mm²], $K_{tp}$ [N/mm³], $K_{rs}$ [N/mm²], and $K_{rp}$ [N/mm³] are tangential and radial specific cutting force coefficients for shearing and ploughing regime respectively, and they depend on workpiece material; $h_{CE1}(\theta)$ [mm] and $h_{CE2}(\theta)$ [mm] are the chip thicknesses, as a function of the tool rotational angle, for the first and the second cutting edge respectively; $a_p$ [mm] is the axial depth of cut; and $A_p$ [mm²] is the ploughed area, computed as the portion of the cut material which remain in ploughing regime due to the low value of chip thickness.

Considering that the peaks force of each cutting edge will be in correspondence of maximum chip cross-sectional area, for the first Cutting Edge (CE1) the peak occurs when $\theta \approx 90^\circ$, while for the second Cutting Edge (CE2) the peak will appear at $\theta \approx 270^\circ$. Fig. 2a shows an example of the force trend in the direction orthogonal to the feed direction ($F_y$) during angle $\theta$ variation. The difference between the peaks of the force amongst the two cutting edges ($\Delta F_y$) is visible. Substituting Eqs. 6 in Eqs. 5, and introducing the values of $\theta$ in the correspondence of the peaks of the forces, it is possible to define a new equation (Eq. 7) to calculate the force difference in the y-axis between the two cutting edges $\Delta F_y$.

$$ \frac{\Delta F_y(\theta)}{a_p} = K_{ts}(h_{CE1}(\theta) - h_{CE2}(\theta)) + K_{tp}(A_{pCE1}(\theta) - A_{pCE2}(\theta)) \qquad (7) $$

<figure><img src="image_1774.png" /><figcaption>Figure 2 – (a) Trend of cutting force ($F_y$) vs tool rotational angle ($\theta$) and (b) Measure of $r_{CE1}$.</figcaption></figure>

If the maximum values of $h_{CE1}$ and $h_{CE2}$ are higher than Minimum Uncut Chip Thickness (MUCT), the transition between ploughing and shearing is completely occurred and the ploughing area $A_p$ of the two cutting edges are approximately the same ($A_{pCE1} = A_{pCE2}$). For this reason, Eq. 7 can be simplified in Eq. 8:

$$ \frac{\Delta F_y}{a_p} = K_{ts}(h_{CE1}(\theta) - h_{CE2}(\theta)) \qquad (8) $$

Referring to Fig. 1b, as reported in [5], $h_{CE1}$ and $h_{CE2}$ are calculated by the set of Eqs. 9:
$$ \left\{ \begin{aligned} F_{t1}(\theta) &= (K_{ts} \cdot h_{CE1}(\theta) + K_{tp} \cdot A_{p1}(\theta)) \cdot a_p \\ F_{r1}(\theta) &= (K_{rs} \cdot h_{CE1}(\theta) + K_{rp} \cdot A_{p1}(\theta)) \cdot a_p \\ F_{t2}(\theta) &= (K_{ts} \cdot h_{CE2}(\theta) + K_{tp} \cdot A_{p2}(\theta)) \cdot a_p \\ F_{r2}(\theta) &= (K_{rs} \cdot h_{CE2}(\theta) + K_{rp} \cdot A_{p2}(\theta)) \cdot a_p \end{aligned} \right. \qquad (6) $$

where $K_{ts}$ [N/mm²], $K_{tp}$ [N/mm³], $K_{rs}$ [N/mm²], and $K_{rp}$ [N/mm³] are tangential and radial specific cutting force coefficients for shearing and ploughing regime respectively, and they depend on workpiece material; $h_{CE1}(\theta)$ [mm] and $h_{CE2}(\theta)$ [mm] are the chip thicknesses, as a function of the tool rotational angle, for the first and the second cutting edge respectively; $a_p$ [mm] is the axial depth of cut; and $A_p$ [mm²] is the ploughed area, computed as the portion of the cut material which remain in ploughing regime due to the low value of chip thickness.

Considering that the peaks force of each cutting edge will be in correspondence of maximum chip cross-sectional area, for the first Cutting Edge (CE1) the peak occurs when $\theta \approx 90^{\circ}$, while for the second Cutting Edge (CE2) the peak will appear at $\theta \approx 270^{\circ}$. Fig. 2a shows an example of the force trend in the direction orthogonal to the feed direction ($F_y$) during angle $\theta$ variation. The difference between the peaks of the force amongst the two cutting edges ($\Delta F_y$) is visible. Substituting Eqs. 6 in Eqs. 5, and introducing the values of $\theta$ in the correspondence of the peaks of the forces, it is possible to define a new equation (Eq. 7) to calculate the force difference in the y-axis between the two cutting edges $\Delta F_y$.

$$ \frac{\Delta F_y(\theta)}{a_p} = K_{ts}(h_{CE1}(\theta) - h_{CE2}(\theta)) + K_{tp}(A_{pCE1}(\theta) - A_{pCE2}(\theta)) \qquad (7) $$

<figure><img src="image_1772.png" /><figcaption>Figure 2 – (a) Trend of cutting force ($F_y$) vs tool rotational angle ($\theta$) and (b) Measure of $r_{CE1}$.</figcaption></figure>

If the maximum values of $h_{CE1}$ and $h_{CE2}$ are higher than Minimum Uncut Chip Thickness (MUCT), the transition between ploughing and shearing is completely occurred and the ploughing area $A_p$ of the two cutting edges are approximately the same ($A_{pCE1} = A_{pCE2}$). For this reason, Eq. 7 can be simplified in Eq. 8:

$$ \frac{\Delta F_y}{a_p} = K_{ts}(h_{CE1}(\theta) - h_{CE2}(\theta)) \qquad (8) $$

Referring to Fig. 1b, as reported in [5], $h_{CE1}$ and $h_{CE2}$ are calculated by the set of Eqs. 9:
$$ \begin{cases} h_{CE1}(\theta) = \sqrt{(r_{CE1} \sin \theta + \Delta s_{CE1})^2 + (r_{CE1} \cos \theta)^2} - r_{CE2} \\ h_{CE2}(\theta) = \sqrt{(r_{CE2} \sin \theta + \Delta s_{CE2})^2 + (r_{CE2} \cos \theta)^2} - r_{CE1} \end{cases} \qquad (9) $$

where $\Delta s_{CE1}$ is defined as the distance crossed by the rotational axis between the passage of the second cutting edge CE2 and the consecutive passage of the first one CE1 in the instantaneous angular position $\theta$, while $\Delta s_{CE2}$ is the distance crossed between the passage of CE1 and the consecutive passage of CE2 (expressed by the set of Eqs. 10).

$$ \begin{cases} \Delta s_{CE1} = \frac{f}{60} \cdot \frac{\alpha}{\omega} \\ \Delta s_{CE2} = \frac{f}{60} \cdot \frac{2\pi - \alpha}{\omega} \end{cases} \qquad (10) $$

When $\theta \approx 90^\circ$ and $\theta \approx 270^\circ$, substituting the set of Eqs. 9 in Eq. 8, this latter can be rewritten as Eq. 11:

$$ \frac{\Delta Fy}{K_{ts} \cdot a_p} = 2 \cdot (r_{CE1} - r_{CE2}) + \Delta s_{CE1} - \Delta s_{CE2} \qquad (11) $$

Considering then the set of Eqs. 10, Eq. 11 can be simplified in Eq. 12:

$$ r_{CE1} - r_{CE2} = \frac{\Delta Fy}{2 \cdot K_{ts} \cdot a_p} - \frac{f}{60 \cdot \omega} (\alpha - \pi) = I \qquad (12) $$

The difference between the two cutting radii is named as $I$. Substituting in Eq. 12 the values of $r_{CE2}$ and $\beta$ (i.e. $\pi-\alpha-\delta$), a 4th grade equation to estimate $r_{CE1}$ is found (Eq. 13):

$$ a \cdot r_{CE1}^4 + b \cdot r_{CE1}^3 + c \cdot r_{CE1}^2 + e \cdot r_{CE1} + g = 0 \qquad (13) $$

Where the parameters $a, b, c, e$, and $g$ are computed with Eqs. 14-18:

$$ a = \sin^4(\alpha) + \cos^2(\alpha) \cdot \sin^2(\alpha) \qquad (14) $$

$$ b = -2 \cdot I \cdot \sin^2(\alpha) \qquad (15) $$

$$ c = I^2 + I^2 \cdot \sin^2(\alpha) - d^2 \cdot \sin^2(\alpha) - d^2 \cdot \cos^2(\alpha) \qquad (16) $$

$$ e = I \cdot d^2 - I^3 \qquad (17) $$

$$ g = \left( \frac{I^2}{2} - \frac{d^2}{2} \right)^2 \qquad (18) $$

All the variables of Eq. 13 can be experimentally determined. The conventional calibration method of the model, described in [5], requires the direct measurement of the micro-slots widths to establish the experimental value of $r_{CE1}$, assuming that their widths are equal to the double of $r_{CE1}$ (see Fig. 1 and Fig. 2b). The resolution of the Eq. 13 would allow to estimate the value of $r_{CE1}$ only by measuring the difference between the force peaks with the undirect method. Once $r_{CE1}$ is known, all the other geometrical parameters, including $r_0$ and $\gamma$, can be calculated without any dimensional measurement of the micro-slots. If the value of $r_{CE1}$ obtained by solving the equation would be coherent with the experimental one, the model could be employed to estimate tool run-out. This would consent to avoid channels measurements in the experimental procedure and
$$ \begin{cases} h_{CE1}(\theta) = \sqrt{(r_{CE1} \sin \theta + \Delta s_{CE1})^2 + (r_{CE1} \cos \theta)^2} - r_{CE2} \\ h_{CE2}(\theta) = \sqrt{(r_{CE2} \sin \theta + \Delta s_{CE2})^2 + (r_{CE2} \cos \theta)^2} - r_{CE1} \end{cases} \quad (9) $$

where $\Delta s_{CE1}$ is defined as the distance crossed by the rotational axis between the passage of the second cutting edge CE2 and the consecutive passage of the first one CE1 in the instantaneous angular position $\theta$, while $\Delta s_{CE2}$ is the distance crossed between the passage of CE1 and the consecutive passage of CE2 (expressed by the set of Eqs. 10).

$$ \begin{cases} \Delta s_{CE1} = \frac{f}{60} \cdot \frac{\alpha}{\omega} \\ \Delta s_{CE2} = \frac{f}{60} \cdot \frac{2\pi - \alpha}{\omega} \end{cases} \quad (10) $$

When $\theta \approx 90^\circ$ and $\theta \approx 270^\circ$, substituting the set of Eqs. 9 in Eq. 8, this latter can be rewritten as Eq. 11:

$$ \frac{\Delta Fy}{K_{ts} \cdot a_p} = 2 \cdot (r_{CE1} - r_{CE2}) + \Delta s_{CE1} - \Delta s_{CE2} \quad (11) $$

Considering then the set of Eqs. 10, Eq. 11 can be simplified in Eq. 12:

$$ r_{CE1} - r_{CE2} = \frac{\Delta Fy}{2 \cdot K_{ts} \cdot a_p} - \frac{f}{60 \cdot \omega} (\alpha - \pi) = I \quad (12) $$

The difference between the two cutting radii is named as $I$. Substituting in Eq. 12 the values of $r_{CE2}$ and $\beta$ (i.e. $\pi-\alpha-\delta$), a 4th grade equation to estimate $r_{CE1}$ is found (Eq. 13):

$$ a \cdot r_{CE1}^4 + b \cdot r_{CE1}^3 + c \cdot r_{CE1}^2 + e \cdot r_{CE1} + g = 0 \quad (13) $$

Where the parameters $a, b, c, e$, and $g$ are computed with Eqs. 14-18:

$$ a = \sin^4(\alpha) + \cos^2(\alpha) \cdot \sin^2(\alpha) \quad (14) $$

$$ b = -2 \cdot I \cdot \sin^2(\alpha) \quad (15) $$

$$ c = I^2 + I^2 \cdot \sin^2(\alpha) - d^2 \cdot \sin^2(\alpha) - d^2 \cdot \cos^2(\alpha) \quad (16) $$

$$ e = I \cdot d^2 - I^3 \quad (17) $$

$$ g = \left( \frac{I^2}{2} - \frac{d^2}{2} \right)^2 \quad (18) $$

All the variables of Eq. 13 can be experimentally determined. The conventional calibration method of the model, described in [5], requires the direct measurement of the micro-slots widths to establish the experimental value of $r_{CE1}$, assuming that their widths are equal to the double of $r_{CE1}$ (see Fig. 1 and Fig. 2b). The resolution of the Eq. 13 would allow to estimate the value of $r_{CE1}$ only by measuring the difference between the force peaks with the undirect method. Once $r_{CE1}$ is known, all the other geometrical parameters, including $r_0$ and $\gamma$, can be calculated without any dimensional measurement of the micro-slots. If the value of $r_{CE1}$ obtained by solving the equation would be coherent with the experimental one, the model could be employed to estimate tool run-out. This would consent to avoid channels measurements in the experimental procedure and
conclude that the determination of tool run-out would be possible only basing on cutting forces analysis.

## Material and methods

The experimental validation of the new method was performed by micro-milling of AlSi10Mg prismatic specimens in two different furnishing conditions. The first one was fabricated by Laser Based Powder Bed Fusion (LB-PBF) and treated with HIP and T6. The LB-PBF samples were produced using the laser-based powder bed fusion machine EOSM290 machine. The process parameters were: a laser power of 370 W, a scanning speed of 1300 mm/s, a hatching distance of 190 µm, a layer thickness of 30 µm, a temperature of the building platform equal to 80 °C. The second one was obtained by Gravity Casting (GC) and treated with T6. Table 1 summarizes the chemical composition of the alloys.

<table><caption>Table 1– Chemical composition (wt.%) of AlSi10Mg aluminium produced via GC and LB-PBF.</caption><thead><tr><th>AlSi10Mg</th><th>Si</th><th>Fe</th><th>Mn</th><th>Mg</th><th>Cu</th><th>Al</th></tr></thead><tbody><tr><td>GC</td><td>9.89</td><td>0.51</td><td>0.40</td><td>0.38</td><td>0.21</td><td>balance</td></tr><tr><td>LB-PBF</td><td>10.2</td><td>0.21</td><td>&lt; 0.02</td><td>0.40</td><td>&lt; 0.002</td><td>balance</td></tr></tbody></table>

The T6 heat-treatment consists of a solution treatment at 540 °C for 7 h, followed by quench in water and artificial aging at 160 °C for 4 h, while HIP mechano-thermal treatment consists of a Hot Isostatic Pressing (HIP) treatment at 520 °C for 2 h. These samples were machined by using a Ø 0.8 mm flat-bottom two-flutes micro-mill to realize micro-slots. The actual diameter of the micro-mill was measured with three repetitions with a multifocal microscope Hirox RH-2000 and its value is $d = 789 \pm 2$ µm. Fourteen micro-slots were realized on each sample changing the feed per tooth $f_z$ between two consecutive slots, from a minimum value of 0.5 µm/tooth to a maximum value 7 µm/tooth, while cutting speed $v_c = 80$ m/min and axial depth $a_p = 0.25$ mm were kept constant. Moreover, the specimens were bounded to a load cell Kistler 9317C to measure cutting forces. A laser profilometer probe Mitaka PF60 was employed to measure the widths of micro-slots; in Table 2 its main properties are listed.

<table><caption>Table 2 – Laser profilometer properties.</caption><thead><tr><th>Property</th><th>Value</th></tr></thead><tbody><tr><td>Range measurement [mm]</td><td>60x60x10</td></tr><tr><td>x, y resolution [µm]</td><td>0.1</td></tr><tr><td>z resolution [µm]</td><td>0.01</td></tr><tr><td>Laser spot diameter [µm]</td><td>1</td></tr><tr><td>Laser wavelength [nm]</td><td>635</td></tr></tbody></table>

The laser scanning speed was 20 µm/s and the measuring software was MitakaMap. As the mean micro-slot length is about 4500 µm, a measure has been made every 1125 µm to estimate the width. Therefore, the laser probe was employed to execute five profile scans for each micro-slot. In some cases, the excessive burr does not allow to measure the width properly. For this reason, the novel procedure to estimate run-out was tested only on the micro-slots with an average width $W_{av}$ higher than $d = 789$ µm. The values of $r_{CEI}$ are calculated as half of the $W_{av}$. A Matlab script was defined to estimate the difference between the two cutting force peaks detected during
conclude that the determination of tool run-out would be possible only basing on cutting forces analysis.

## Material and methods

The experimental validation of the new method was performed by micro-milling of AlSi10Mg prismatic specimens in two different furnishing conditions. The first one was fabricated by Laser Based Powder Bed Fusion (LB-PBF) and treated with HIP and T6. The LB-PBF samples were produced using the laser-based powder bed fusion machine EOSM290 machine. The process parameters were: a laser power of 370 W, a scanning speed of 1300 mm/s, a hatching distance of 190 µm, a layer thickness of 30 µm, a temperature of the building platform equal to 80 °C. The second one was obtained by Gravity Casting (GC) and treated with T6. Table 1 summarizes the chemical composition of the alloys.

<table><caption>Table 1– Chemical composition (wt.%) of AlSi10Mg aluminium produced via GC and LB-PBF.</caption><thead><tr><th>AlSi10Mg</th><th>Si</th><th>Fe</th><th>Mn</th><th>Mg</th><th>Cu</th><th>Al</th></tr></thead><tbody><tr><td>GC</td><td>9.89</td><td>0.51</td><td>0.40</td><td>0.38</td><td>0.21</td><td>balance</td></tr><tr><td>LB-PBF</td><td>10.2</td><td>0.21</td><td>&lt; 0.02</td><td>0.40</td><td>&lt; 0.002</td><td>balance</td></tr></tbody></table>

The T6 heat-treatment consists of a solution treatment at 540 °C for 7 h, followed by quench in water and artificial aging at 160 °C for 4 h, while HIP mechano-thermal treatment consists of a Hot Isostatic Pressing (HIP) treatment at 520 °C for 2 h. These samples were machined by using a Ø 0.8 mm flat-bottom two-flutes micro-mill to realize micro-slots. The actual diameter of the micro-mill was measured with three repetitions with a multifocal microscope Hirox RH-2000 and its value is $d = 789 \pm 2$ µm. Fourteen micro-slots were realized on each sample changing the feed per tooth $f_z$ between two consecutive slots, from a minimum value of 0.5 µm/tooth to a maximum value 7 µm/tooth, while cutting speed $v_c = 80$ m/min and axial depth $a_p = 0.25$ mm were kept constant. Moreover, the specimens were bounded to a load cell Kistler 9317C to measure cutting forces. A laser profilometer probe Mitaka PF60 was employed to measure the widths of micro-slots; in Table 2 its main properties are listed.

<table><caption>Table 2 – Laser profilometer properties.</caption><thead><tr><th>Property</th><th>Value</th></tr></thead><tbody><tr><td>Range measurement [mm]</td><td>60x60x10</td></tr><tr><td>x, y resolution [µm]</td><td>0.1</td></tr><tr><td>z resolution [µm]</td><td>0.01</td></tr><tr><td>Laser spot diameter [µm]</td><td>1</td></tr><tr><td>Laser wavelength [nm]</td><td>635</td></tr></tbody></table>

The laser scanning speed was 20 µm/s and the measuring software was MitakaMap. As the mean micro-slot length is about 4500 µm, a measure has been made every 1125 µm to estimate the width. Therefore, the laser probe was employed to execute five profile scans for each micro-slot. In some cases, the excessive burr does not allow to measure the width properly. For this reason, the novel procedure to estimate run-out was tested only on the micro-slots with an average width $W_{av}$ higher than $d = 789$ µm. The values of $r_{CEI}$ are calculated as half of the $W_{av}$. A Matlab script was defined to estimate the difference between the two cutting force peaks detected during
the process in the y-direction. The cutting-edge phase angle $\alpha$ can be calculated from cutting force signal as reported in [10].

## Results and discussion

In the first part of this section the experimental results are presented together with the calculation of the run-out parameters. In the second part, a simplification of Eq. 13 from a 4th grade equation to a 2nd grade equation is carried out. In the last part of the chapter, the simplified analytical model proposed in this work is applied to the case study and a comparison between the values of $r_{CEI}$ experimentally determined and computed through analytical model is proposed.

This section collects the experimental values of $r_{CEI}$, the computed values of $\Delta F_y$ and $\alpha$, and the run-out parameters $r_0$ and $\gamma$ computed by using equations Eq. 1 and Eq. 2. Table 3 lists the parameters for GC specimen, while Table 4 refers to LB-PBF specimen.

<table><caption>Table 3 – Measures of $r_{CEI}$, $\Delta F_y$ and $\alpha$ on GC specimen.</caption><thead><tr><th>TEST</th><th>f<sub>z</sub><br>[mm/tooth]</th><th>Exp r<sub>CEI</sub><br>[mm]</th><th>Dev.St. r<sub>CEI</sub><br>[mm]</th><th>ΔF<sub>y</sub><br>[N]</th><th>α<br>[°]</th><th>Dev.St. α<br>[°]</th><th>Exp r<sub>0</sub><br>[mm]</th><th>γ<br>[rad]</th></tr></thead><tbody><tr><td>1</td><td>0,0030</td><td>0,3985</td><td>0,0398</td><td>0,43</td><td>177,47</td><td>1,01</td><td>0,010</td><td>1,147</td></tr><tr><td>2</td><td>0,0035</td><td>0,4040</td><td>0,0104</td><td>0,37</td><td>172,26</td><td>1,57</td><td>0,028</td><td>1,257</td></tr><tr><td>3</td><td>0,0005</td><td>0,4133</td><td>0,0084</td><td>0,35</td><td>168,44</td><td>1,56</td><td>0,043</td><td>1,171</td></tr><tr><td>4</td><td>0,0065</td><td>0,4053</td><td>0,0214</td><td>0,31</td><td>175,37</td><td>3,54</td><td>0,019</td><td>0,990</td></tr><tr><td>5</td><td>0,0055</td><td>0,4108</td><td>0,0286</td><td>0,35</td><td>170,33</td><td>2,42</td><td>0,037</td><td>1,151</td></tr><tr><td>6</td><td>0,0050</td><td>0,4176</td><td>0,0290</td><td>0,38</td><td>174,55</td><td>4,50</td><td>0,029</td><td>0,690</td></tr></tbody></table>

<table><caption>Table 4 – Measures of $r_{CEI}$, $\Delta F_y$ and $\alpha$ on LB-PBF specimen.</caption><thead><tr><th>TEST</th><th>f<sub>z</sub><br>[mm/tooth]</th><th>Exp<br>r<sub>CEI</sub><br>[mm]</th><th>Dev.St.<br>r<sub>CEI</sub><br>[mm]</th><th>ΔF<sub>y</sub><br>[N]</th><th>α<br>[°]</th><th>Dev.St.<br>α<br>[°]</th><th>Exp r<sub>0</sub><br>[mm]</th><th>γ<br>[rad]</th></tr></thead><tbody><tr><td>1</td><td>0,0030</td><td>0,3980</td><td>0,0242</td><td>0,11</td><td>176,74</td><td>1,56</td><td>0,012</td><td>1,281</td></tr><tr><td>2</td><td>0,0035</td><td>0,3948</td><td>0,0174</td><td>0,11</td><td>178,09</td><td>2,48</td><td>0,007</td><td>1,535</td></tr><tr><td>3</td><td>0,0005</td><td>0,3945</td><td>0,0171</td><td>0,06</td><td>178,78</td><td>2,32</td><td>0,004</td><td>1,440</td></tr><tr><td>4</td><td>0,0065</td><td>0,4010</td><td>0,0055</td><td>0,07</td><td>179,74</td><td>3,81</td><td>0,007</td><td>0,136</td></tr><tr><td>5</td><td>0,0050</td><td>0,3975</td><td>0,0198</td><td>0,08</td><td>177,82</td><td>2,49</td><td>0,008</td><td>1,195</td></tr><tr><td>6</td><td>0,0070</td><td>0,3998</td><td>0,0272</td><td>0,09</td><td>177,42</td><td>5,78</td><td>0,010</td><td>1,038</td></tr></tbody></table>

The standard deviation of $r_{CEI}$ ranges between the 2% and the 10% of the nominal value. It is a not-neglectable variability due to the impact of the tool run-out phenomenon on of $r_{CEI}$, which is equal to few micrometres. It is a confirmation about the necessity to determine the run-out by avoiding direct measurements on the machined features, especially during the machining of soft materials where the burrs are higher and lead to a difficult measurement of the width, even if after deburring. The run-out parameter $r_0$ ranged between 4 and 43 micrometres, which can not be considered as reliable values due to the guarantee of the tool holder manufacturer of a maximum value of run-out equal to 3 micrometres. The low differences about the cutting force peaks $\Delta F_y$ related to the tool flutes is a further demonstration of the not-reliability of the experimental determination of $r_{CEI}$.

The experimental values of $r_{CEI}$ resulted average higher for GC sample than LB-PBF sample. In GC specimen the $\Delta F_y$ is higher while angle $\alpha$ is lower; both the results demonstrate that GC specimen is more subjected to run-out phenomenon instead of the LB-PBF sample. Run-out is a
the process in the y-direction. The cutting-edge phase angle $\alpha$ can be calculated from cutting force signal as reported in [10].

## Results and discussion

In the first part of this section the experimental results are presented together with the calculation of the run-out parameters. In the second part, a simplification of Eq. 13 from a 4th grade equation to a 2nd grade equation is carried out. In the last part of the chapter, the simplified analytical model proposed in this work is applied to the case study and a comparison between the values of $r_{CEI}$ experimentally determined and computed through analytical model is proposed.

This section collects the experimental values of $r_{CEI}$, the computed values of $\Delta F_y$ and $\alpha$, and the run-out parameters $r_0$ and $\gamma$ computed by using equations Eq. 1 and Eq. 2. Table 3 lists the parameters for GC specimen, while Table 4 refers to LB-PBF specimen.

<table><caption>Table 3 – Measures of $r_{CEI}$, $\Delta F_y$ and $\alpha$ on GC specimen.</caption><thead><tr><th>TEST</th><th>f<sub>z</sub><br>[mm/tooth]</th><th>Exp r<sub>CEI</sub><br>[mm]</th><th>Dev.St. r<sub>CEI</sub><br>[mm]</th><th>ΔF<sub>y</sub><br>[N]</th><th>α<br>[°]</th><th>Dev.St. α<br>[°]</th><th>Exp r<sub>0</sub><br>[mm]</th><th>γ<br>[rad]</th></tr></thead><tbody><tr><td>1</td><td>0,0030</td><td>0,3985</td><td>0,0398</td><td>0,43</td><td>177,47</td><td>1,01</td><td>0,010</td><td>1,147</td></tr><tr><td>2</td><td>0,0035</td><td>0,4040</td><td>0,0104</td><td>0,37</td><td>172,26</td><td>1,57</td><td>0,028</td><td>1,257</td></tr><tr><td>3</td><td>0,0005</td><td>0,4133</td><td>0,0084</td><td>0,35</td><td>168,44</td><td>1,56</td><td>0,043</td><td>1,171</td></tr><tr><td>4</td><td>0,0065</td><td>0,4053</td><td>0,0214</td><td>0,31</td><td>175,37</td><td>3,54</td><td>0,019</td><td>0,990</td></tr><tr><td>5</td><td>0,0055</td><td>0,4108</td><td>0,0286</td><td>0,35</td><td>170,33</td><td>2,42</td><td>0,037</td><td>1,151</td></tr><tr><td>6</td><td>0,0050</td><td>0,4176</td><td>0,0290</td><td>0,38</td><td>174,55</td><td>4,50</td><td>0,029</td><td>0,690</td></tr></tbody></table>

<table><caption>Table 4 – Measures of $r_{CEI}$, $\Delta F_y$ and $\alpha$ on LB-PBF specimen.</caption><thead><tr><th>TEST</th><th>f<sub>z</sub><br>[mm/tooth]</th><th>Exp<br>r<sub>CEI</sub><br>[mm]</th><th>Dev.St.<br>r<sub>CEI</sub><br>[mm]</th><th>ΔF<sub>y</sub><br>[N]</th><th>α<br>[°]</th><th>Dev.St.<br>α<br>[°]</th><th>Exp r<sub>0</sub><br>[mm]</th><th>γ<br>[rad]</th></tr></thead><tbody><tr><td>1</td><td>0,0030</td><td>0,3980</td><td>0,0242</td><td>0,11</td><td>176,74</td><td>1,56</td><td>0,012</td><td>1,281</td></tr><tr><td>2</td><td>0,0035</td><td>0,3948</td><td>0,0174</td><td>0,11</td><td>178,09</td><td>2,48</td><td>0,007</td><td>1,535</td></tr><tr><td>3</td><td>0,0005</td><td>0,3945</td><td>0,0171</td><td>0,06</td><td>178,78</td><td>2,32</td><td>0,004</td><td>1,440</td></tr><tr><td>4</td><td>0,0065</td><td>0,4010</td><td>0,0055</td><td>0,07</td><td>179,74</td><td>3,81</td><td>0,007</td><td>0,136</td></tr><tr><td>5</td><td>0,0050</td><td>0,3975</td><td>0,0198</td><td>0,08</td><td>177,82</td><td>2,49</td><td>0,008</td><td>1,195</td></tr><tr><td>6</td><td>0,0070</td><td>0,3998</td><td>0,0272</td><td>0,09</td><td>177,42</td><td>5,78</td><td>0,010</td><td>1,038</td></tr></tbody></table>

The standard deviation of $r_{CEI}$ ranges between the 2% and the 10% of the nominal value. It is a not-neglectable variability due to the impact of the tool run-out phenomenon on of $r_{CEI}$, which is equal to few micrometres. It is a confirmation about the necessity to determine the run-out by avoiding direct measurements on the machined features, especially during the machining of soft materials where the burrs are higher and lead to a difficult measurement of the width, even if after deburring. The run-out parameter $r_0$ ranged between 4 and 43 micrometres, which can not be considered as reliable values due to the guarantee of the tool holder manufacturer of a maximum value of run-out equal to 3 micrometres. The low differences about the cutting force peaks $\Delta F_y$ related to the tool flutes is a further demonstration of the not-reliability of the experimental determination of $r_{CEI}$.

The experimental values of $r_{CEI}$ resulted average higher for GC sample than LB-PBF sample. In GC specimen the $\Delta F_y$ is higher while angle $\alpha$ is lower; both the results demonstrate that GC specimen is more subjected to run-out phenomenon instead of the LB-PBF sample. Run-out is a
random phenomenon determined by the elastic clamping of the tool in the tool holder and it does not depend on the material properties. Consequently, the novel procedure of calibration of the model was applied on two different geometrical configurations of run-out.

The implementation of the model (Eq. 13) needs the calibration of the $K_{ts}$ variable for the AlSi10Mg alloy before the calculation of $r_{CEI}$ values. In Table 5 the sensitivity analysis on the influence of $K_{ts}$ value on the other terms described in Eq. 13 is presented. The analysis is presented for the data obtained with GC specimen, but analogue consideration can be exploited with the data referred to the LB-PBF sample.

<table><caption>Table 5 – Sensitivity analysis on $K_{ts}$ referred to GC.</caption><thead><tr><th>K<sub>ts</sub> [N/mm<sup>2</sup>]</th><th>a·(r<sub>CEI</sub>)<sup>4</sup> [mm<sup>4</sup>]</th><th>b·(r<sub>CEI</sub>)<sup>3</sup> [mm<sup>4</sup>]</th><th>c·(r<sub>CEI</sub>)<sup>2</sup> [mm<sup>4</sup>]</th><th>e·(r<sub>CEI</sub>) [mm<sup>4</sup>]</th><th>g [mm<sup>4</sup>]</th></tr></thead><tbody><tr><td>1</td><td>4,92E-05</td><td>-2,03E-04</td><td>9,36E-03</td><td>-1,89E-02</td><td>8,29E-04</td></tr><tr><td>10</td><td>4,92E-05</td><td>-2,04E-05</td><td>-9,78E-02</td><td>2,02E-02</td><td>9,48E-02</td></tr><tr><td>100</td><td>4,92E-05</td><td>-2,04E-06</td><td>-9,89E-02</td><td>2,06E-03</td><td>9,69E-02</td></tr><tr><td>1000</td><td>4,92E-05</td><td>-2,14E-07</td><td>-9,89E-02</td><td>2,15E-04</td><td>9,69E-02</td></tr><tr><td>10000</td><td>4,92E-05</td><td>-3,07E-08</td><td>-9,89E-02</td><td>3,09E-05</td><td>9,69E-02</td></tr><tr><td>100000</td><td>4,92E-05</td><td>-1,24E-08</td><td>-9,89E-02</td><td>1,25E-05</td><td>9,69E-02</td></tr><tr><td>1000000</td><td>4,92E-05</td><td>-1,06E-08</td><td>-9,89E-02</td><td>1,07E-05</td><td>9,69E-02</td></tr></tbody></table>

As visible, the terms which assumes highest value are $g$ and $c·(r_{CEI})^2$. Common values of $K_{ts}$ for metallic alloys are higher than $10^3$ N/mm² thus, and in [11] it is reported a $K_{ts}$ for AlSi10Mg alloy ranging between $10^3$ N/mm² and $10^4$ N/mm². Assuming this hypothesis, the order of magnitude of $g$ and $c·(r_{CEI})^2$ is $10^{-2}$, while the other terms range between $10^{-4}$ and $10^{-8}$. As conclusion, the terms of Eq. 13 $a·(r_{CEI})^4$, $b·(r_{CEI})^3$ and $e·(r_{CEI})$ are approximated to zero. The following results were obtained supposing $K_{ts}$ equal to 10000 N/mm² and simplifying the Eq. 13 from 4th to 2nd order. The result is visible in Eq. 19.

$$c \cdot r_{CE1}^2 + g = 0 \qquad (19)$$

This 2nd grade equation leads to a simplified equation to predict $r_{CEI}$ (Eq. 20).

$$r_{CE1} = \pm \sqrt{-\frac{g}{c}} \qquad (20)$$

Where $c$ and $g$ can be computed with Eq. 12, Eq. 16 and Eq. 18. In Table 6 and Table 7 there is a comparison between experimental values and the data computed from the analytical model. The simplified equation (Eq. 19) is applied to predict $r_{CEI}$ by using experimentally measured $d$, $\alpha$, $\Delta F_y$ parameters and $c$, $g$ constants. The error considered (i.e. % error) is calculated according to the equation Eq. 21.

$$\% \text{ error} = \frac{|\Delta r_{CE1}|}{\text{Analytical } r_{CE1}} \cdot 100 \qquad (21)$$
random phenomenon determined by the elastic clamping of the tool in the tool holder and it does not depend on the material properties. Consequently, the novel procedure of calibration of the model was applied on two different geometrical configurations of run-out.

The implementation of the model (Eq. 13) needs the calibration of the $K_{ts}$ variable for the AlSi10Mg alloy before the calculation of $r_{CEI}$ values. In Table 5 the sensitivity analysis on the influence of $K_{ts}$ value on the other terms described in Eq. 13 is presented. The analysis is presented for the data obtained with GC specimen, but analogue consideration can be exploited with the data referred to the LB-PBF sample.

<table><caption>Table 5 – Sensitivity analysis on $K_{ts}$ referred to GC.</caption><thead><tr><th>K<sub>ts</sub> [N/mm<sup>2</sup>]</th><th>a·(r<sub>CEI</sub>)<sup>4</sup> [mm<sup>4</sup>]</th><th>b·(r<sub>CEI</sub>)<sup>3</sup> [mm<sup>4</sup>]</th><th>c·(r<sub>CEI</sub>)<sup>2</sup> [mm<sup>4</sup>]</th><th>e·(r<sub>CEI</sub>) [mm<sup>4</sup>]</th><th>g [mm<sup>4</sup>]</th></tr></thead><tbody><tr><td>1</td><td>4,92E-05</td><td>-2,03E-04</td><td>9,36E-03</td><td>-1,89E-02</td><td>8,29E-04</td></tr><tr><td>10</td><td>4,92E-05</td><td>-2,04E-05</td><td>-9,78E-02</td><td>2,02E-02</td><td>9,48E-02</td></tr><tr><td>100</td><td>4,92E-05</td><td>-2,04E-06</td><td>-9,89E-02</td><td>2,06E-03</td><td>9,69E-02</td></tr><tr><td>1000</td><td>4,92E-05</td><td>-2,14E-07</td><td>-9,89E-02</td><td>2,15E-04</td><td>9,69E-02</td></tr><tr><td>10000</td><td>4,92E-05</td><td>-3,07E-08</td><td>-9,89E-02</td><td>3,09E-05</td><td>9,69E-02</td></tr><tr><td>100000</td><td>4,92E-05</td><td>-1,24E-08</td><td>-9,89E-02</td><td>1,25E-05</td><td>9,69E-02</td></tr><tr><td>1000000</td><td>4,92E-05</td><td>-1,06E-08</td><td>-9,89E-02</td><td>1,07E-05</td><td>9,69E-02</td></tr></tbody></table>

As visible, the terms which assumes highest value are g and $c·(r_{CEI})^2$. Common values of $K_{ts}$ for metallic alloys are higher than $10^3$ N/mm² thus, and in [11] it is reported a $K_{ts}$ for AlSi10Mg alloy ranging between $10^3$ N/mm² and $10^4$ N/mm². Assuming this hypothesis, the order of magnitude of g and $c·(r_{CEI})^2$ is $10^{-2}$, while the other terms range between $10^{-4}$ and $10^{-8}$. As conclusion, the terms of Eq. 13 $a·(r_{CEI})^4$, $b·(r_{CEI})^3$ and $e·(r_{CEI})$ are approximated to zero. The following results were obtained supposing $K_{ts}$ equal to 10000 N/mm² and simplifying the Eq. 13 from 4th to 2nd order. The result is visible in Eq. 19.

$$c \cdot r_{CE1}^2 + g = 0 \qquad (19)$$

This 2nd grade equation leads to a simplified equation to predict $r_{CEI}$ (Eq. 20).

$$r_{CE1} = \pm \sqrt{-\frac{g}{c}} \qquad (20)$$

Where c and g can be computed with Eq. 12, Eq. 16 and Eq. 18. In Table 6 and Table 7 there is a comparison between experimental values and the data computed from the analytical model. The simplified equation (Eq. 19) is applied to predict $r_{CEI}$ by using experimentally measured d, $\alpha$, $\Delta F_y$ parameters and c, g constants. The error considered (i.e. % error) is calculated according to the equation Eq. 21.

$$\% \text{ error} = \frac{|\Delta r_{CE1}|}{\text{Analytical } r_{CE1}} \cdot 100 \qquad (21)$$
<table><caption>Table 6 – Comparison between experimental $r_{CEI}$ values for GC machining tests and the computed ones.</caption><thead><tr><td>TEST</td><td>Exp r<sub>CEI</sub>[mm]</td><td>Computed r<sub>CEI</sub>[mm]</td><td>Δr<sub>CEI</sub> variation [mm]</td><td>% error</td></tr></thead><tbody><tr><td>1</td><td>0,3985</td><td>0,3945</td><td>0,0040</td><td>1,02%</td></tr><tr><td>2</td><td>0,4040</td><td>0,3945</td><td>0,0095</td><td>2,42%</td></tr><tr><td>3</td><td>0,4133</td><td>0,3945</td><td>0,0188</td><td>4,76%</td></tr><tr><td>4</td><td>0,4053</td><td>0,3945</td><td>0,0108</td><td>2,73%</td></tr><tr><td>5</td><td>0,4108</td><td>0,3945</td><td>0,0163</td><td>4,12%</td></tr><tr><td>6</td><td>0,4176</td><td>0,3945</td><td>0,0231</td><td>5,86%</td></tr></tbody></table>

<table><caption>Table 7 – Comparison between experimental $r_{CEI}$ values for LB-PBF machining tests and the computed ones.</caption><thead><tr><td>TEST</td><td>Exp r<sub>CEI</sub>[mm]</td><td>Computed r<sub>CEI</sub>[mm]</td><td>Δr<sub>CEI</sub> variation [mm]</td><td>% error</td></tr></thead><tbody><tr><td>1</td><td>0,3980</td><td>0,3945</td><td>0,0035</td><td>0,89%</td></tr><tr><td>2</td><td>0,3948</td><td>0,3945</td><td>0,0003</td><td>0,07%</td></tr><tr><td>3</td><td>0,3945</td><td>0,3945</td><td>0,0000</td><td>0,00%</td></tr><tr><td>4</td><td>0,4010</td><td>0,3945</td><td>0,0065</td><td>1,66%</td></tr><tr><td>5</td><td>0,3975</td><td>0,3945</td><td>0,0030</td><td>0,77%</td></tr><tr><td>6</td><td>0,3998</td><td>0,3945</td><td>0,0053</td><td>1,35%</td></tr></tbody></table>

The value of $r_{CEI}$ calculated for all the experimental tests resulted constant up to the fourth decimal place and equal to the half of the actual tool diameter (i.e., $d/2$), regardless the sample and the process parameter. The computed values of $r_{CEI}$ changed only after the fourth decimal place. This result does not agree with the experimental measurement of $r_{CEI}$, but the experimental values of $r_{CEI}$ can not be considered reliable as previously discussed.

## Conclusions

The application of Eq. 19 to the experimental tests demonstrates that the procedure computes values of run-out lower than the values determined with the classic methodology. The experimental determination through the direct measurement of the channel width led in this study case to an overestimation of run-out, while the value of the computed $r_{CEI}$ is always equal to half the tool diameter up to the 4th decimal place. As consequence, the new procedure predicts an almost null run-out in both the specimens (LB-PBF and GC). On the other hand, the differences about cutting force peaks on the two tool flutes demonstrates that tool run-out phenomenon was not completely neglectable. As a matter of fact, micro-milling of GC specimen was more affected by tool run-out. Based on those evidence, it can be stated that the estimation of tool-run parameters is still not possible by using only the cutting force signal (i.e., $ΔF_y$ and $α$). Nevertheless, the obtained results have been found from a restricted dataset, due to the exclusion of the tests more affected by the presence of excessive burrs. Furthermore, the estimation of $r_{CEI}$ could be performed by solving the 4th grade equation without doing any approximation. Future research should expand the experimental campaign to analyse more specimens, realized from different production techniques. Moreover, the specimens realized by the same production technology should be compared as a function of the heat treatment they were subjected to. It would give a larger dataset to elaborate more general conclusions on the reliability of the analytical model presented. A direct comparison between the cutting force signal predicted by the model and experimental acquired will be performed to assess the estimation of the tool run out by the new methodology.

## Acknowledgment

Financed by the European Union - NextGenerationEU (National Sustainable Mobility Center CN00000023, Italian Ministry of University and Research Decree n. 1033 - 17/06/2022, Spoke 11
<table><caption>Table 6 – Comparison between experimental $r_{CEI}$ values for GC machining tests and the computed ones.</caption><thead><tr><td>TEST</td><td>Exp r<sub>CEI</sub>[mm]</td><td>Computed r<sub>CEI</sub>[mm]</td><td>Δr<sub>CEI</sub> variation [mm]</td><td>% error</td></tr></thead><tbody><tr><td>1</td><td>0,3985</td><td>0,3945</td><td>0,0040</td><td>1,02%</td></tr><tr><td>2</td><td>0,4040</td><td>0,3945</td><td>0,0095</td><td>2,42%</td></tr><tr><td>3</td><td>0,4133</td><td>0,3945</td><td>0,0188</td><td>4,76%</td></tr><tr><td>4</td><td>0,4053</td><td>0,3945</td><td>0,0108</td><td>2,73%</td></tr><tr><td>5</td><td>0,4108</td><td>0,3945</td><td>0,0163</td><td>4,12%</td></tr><tr><td>6</td><td>0,4176</td><td>0,3945</td><td>0,0231</td><td>5,86%</td></tr></tbody></table>

<table><caption>Table 7 – Comparison between experimental $r_{CEI}$ values for LB-PBF machining tests and the computed ones.</caption><thead><tr><td>TEST</td><td>Exp r<sub>CEI</sub>[mm]</td><td>Computed r<sub>CEI</sub>[mm]</td><td>Δr<sub>CEI</sub> variation [mm]</td><td>% error</td></tr></thead><tbody><tr><td>1</td><td>0,3980</td><td>0,3945</td><td>0,0035</td><td>0,89%</td></tr><tr><td>2</td><td>0,3948</td><td>0,3945</td><td>0,0003</td><td>0,07%</td></tr><tr><td>3</td><td>0,3945</td><td>0,3945</td><td>0,0000</td><td>0,00%</td></tr><tr><td>4</td><td>0,4010</td><td>0,3945</td><td>0,0065</td><td>1,66%</td></tr><tr><td>5</td><td>0,3975</td><td>0,3945</td><td>0,0030</td><td>0,77%</td></tr><tr><td>6</td><td>0,3998</td><td>0,3945</td><td>0,0053</td><td>1,35%</td></tr></tbody></table>

The value of $r_{CEI}$ calculated for all the experimental tests resulted constant up to the fourth decimal place and equal to the half of the actual tool diameter (i.e., $d/2$), regardless the sample and the process parameter. The computed values of $r_{CEI}$ changed only after the fourth decimal place. This result does not agree with the experimental measurement of $r_{CEI}$, but the experimental values of $r_{CEI}$ can not be considered reliable as previously discussed.

## Conclusions

The application of Eq. 19 to the experimental tests demonstrates that the procedure computes values of run-out lower than the values determined with the classic methodology. The experimental determination through the direct measurement of the channel width led in this study case to an overestimation of run-out, while the value of the computed $r_{CEI}$ is always equal to half the tool diameter up to the 4th decimal place. As consequence, the new procedure predicts an almost null run-out in both the specimens (LB-PBF and GC). On the other hand, the differences about cutting force peaks on the two tool flutes demonstrates that tool run-out phenomenon was not completely neglectable. As a matter of fact, micro-milling of GC specimen was more affected by tool run-out. Based on those evidence, it can be stated that the estimation of tool-run parameters is still not possible by using only the cutting force signal (i.e., $\Delta F_y$ and $\alpha$). Nevertheless, the obtained results have been found from a restricted dataset, due to the exclusion of the tests more affected by the presence of excessive burrs. Furthermore, the estimation of $r_{CEI}$ could be performed by solving the 4th grade equation without doing any approximation. Future research should expand the experimental campaign to analyse more specimens, realized from different production techniques. Moreover, the specimens realized by the same production technology should be compared as a function of the heat treatment they were subjected to. It would give a larger dataset to elaborate more general conclusions on the reliability of the analytical model presented. A direct comparison between the cutting force signal predicted by the model and experimental acquired will be performed to assess the estimation of the tool run out by the new methodology.

## Acknowledgment

Financed by the European Union - NextGenerationEU (National Sustainable Mobility Center CN00000023, Italian Ministry of University and Research Decree n. 1033 - 17/06/2022, Spoke 11
- Innovative Materials & Lightweighting). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission's official position. Neither the European Union nor the European Commission can be held responsible for them. CUP D83C22000690001.

## References

[1] R. Yadav, N. D. Chakladar, S. Paul, A dynamic recrystallization based constitutive flow model for micro-machining of Ti-6Al-4V, J. Manuf. Process. 77 (2022) 463-484.
https://doi.org/10.1016/j.jmapro.2022.03.040

[2] D. Wang, L. Penter, A. Hänel, Y. Yang, S. Ihlenfeldt, Investigation on dynamic tool deflection and run out-dependent analysis of the micro-milling process, Mech. Syst. Signal Process. 178 (2022) 109282.
https://doi.org/10.1016/j.ymssp.2022.109282

[3] C. Cappellini, A. Malandruccolo, A. Abeni, A. Attanasio, A feasibility study of promoting osseointegration surface roughness by micro-milling of Ti-6Al-4V biomedical alloy, Int. J. Adv. Manuf. Technol. 126 (7-8) (2020) 3053-3067.
https://doi.org/10.1007/s00170-023-11318-z

[4] A. Abeni, D. Loda, T. Özel, A. Attanasio, Analytical force modelling for micro milling additively fabricated Inconel 625, Prod. Eng. 14 (2020) 613-627.
https://doi.org/10.1007/s11740-020-00980-x

[5] C. Cappellini, A. Abeni, A. Attanasio, Modelling of micro-milling by considering tool run-out and ploughing regime, Procedia CIRP, 118 (2023) 402-407.
https://doi.org/10.1016/j.procir.2023.06.069

[6] G. Bissacco, H.N. Hansen, J. Slunsky, Modelling the cutting edge radius size effect for force prediction in micro milling, CIRP Ann. Manuf. Technol. 58 (2009) 49-52.
https://doi.org/10.1016/j.cirp.2008.03.085

[7] P. Rodríguez, J.E. Labarga, A new model for the prediction of cutting forces in micro end-milling operations, J. Mater. Process. Technol. 213 (2013) 261-268.
https://doi.org/10.1016/j.jmatprotec.2012.09.009

[8] W. Chen, X. Teng, D. Huo, Q. Wang, An improved cutting force model for micro milling considering machining dynamics, Int. J. Adv. Manuf. Technol. 93 (2017) 3005-3016.
https://doi.org/10.1007/s00170-017-0706-2

[9] X. Zhang, T. Yu, W. Wang, Prediction of cutting forces and instantaneous tool deflection in micro end milling by considering tool run-out, Int. J. Mech. Sci. 136 (2018) 124-133.
https://doi.org/10.1016/j.ijmecsci.2017.12.019

[10] A. Attanasio, Tool Run-Out Measurement in Micro Milling, Micromachines 8 (2017) 221.
https://doi.org/10.3390/mi8070221

[11] F.O. Campos, A.L. Mougo, A.C. Araujo. Modeling micromilling cutting force on machining aluminum alloy, 22nd International Congress of Mechanical Engineering COBEM (2013).
- Innovative Materials & Lightweighting). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission's official position. Neither the European Union nor the European Commission can be held responsible for them. CUP D83C22000690001.

## References

[1] R. Yadav, N. D. Chakladar, S. Paul, A dynamic recrystallization based constitutive flow model for micro-machining of Ti-6Al-4V, J. Manuf. Process. 77 (2022) 463-484.
https://doi.org/10.1016/j.jmapro.2022.03.040

[2] D. Wang, L. Penter, A. Hänel, Y. Yang, S. Ihlenfeldt, Investigation on dynamic tool deflection and run out-dependent analysis of the micro-milling process, Mech. Syst. Signal Process. 178 (2022) 109282.
https://doi.org/10.1016/j.ymssp.2022.109282

[3] C. Cappellini, A. Malandruccolo, A. Abeni, A. Attanasio, A feasibility study of promoting osseointegration surface roughness by micro-milling of Ti-6Al-4V biomedical alloy, Int. J. Adv. Manuf. Technol. 126 (7-8) (2020) 3053-3067.
https://doi.org/10.1007/s00170-023-11318-z

[4] A. Abeni, D. Loda, T. Özel, A. Attanasio, Analytical force modelling for micro milling additively fabricated Inconel 625, Prod. Eng. 14 (2020) 613-627.
https://doi.org/10.1007/s11740-020-00980-x

[5] C. Cappellini, A. Abeni, A. Attanasio, Modelling of micro-milling by considering tool run-out and ploughing regime, Procedia CIRP, 118 (2023) 402-407.
https://doi.org/10.1016/j.procir.2023.06.069

[6] G. Bissacco, H.N. Hansen, J. Slunsky, Modelling the cutting edge radius size effect for force prediction in micro milling, CIRP Ann. Manuf. Technol. 58 (2009) 49-52.
https://doi.org/10.1016/j.cirp.2008.03.085

[7] P. Rodríguez, J.E. Labarga, A new model for the prediction of cutting forces in micro end-milling operations, J. Mater. Process. Technol. 213 (2013) 261-268.
https://doi.org/10.1016/j.jmatprotec.2012.09.009

[8] W. Chen, X. Teng, D. Huo, Q. Wang, An improved cutting force model for micro milling considering machining dynamics, Int. J. Adv. Manuf. Technol. 93 (2017) 3005-3016.
https://doi.org/10.1007/s00170-017-0706-2

[9] X. Zhang, T. Yu, W. Wang, Prediction of cutting forces and instantaneous tool deflection in micro end milling by considering tool run-out, Int. J. Mech. Sci. 136 (2018) 124-133.
https://doi.org/10.1016/j.ijmecsci.2017.12.019

[10] A. Attanasio, Tool Run-Out Measurement in Micro Milling, Micromachines 8 (2017) 221.
https://doi.org/10.3390/mi8070221

[11] F.O. Campos, A.L. Mougo, A.C. Araujo. Modeling micromilling cutting force on machining aluminum alloy, 22nd International Congress of Mechanical Engineering COBEM (2013).
# Machinability of PLA obtained by injection molding under a dry milling process

CLOËZ Liam¹,²,a, FONTAINE Michaël¹,ᵇ, GILBIN Alexandre¹,ᶜ and BARRIÈRE Thierry²,ᵈ

¹ SUPMICROTECH, CNRS, Institut FEMTO-ST, F-25000 Besançon, France

² Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France

a liam.cloez@femto-st.fr, b michael fontaine@ens2m.fr, c alexandre.gilbin@ens2m.fr, d thierry.barriere@univ-fcomte.fr

**Keywords:** Poly Lactic Acid, Injection Molding, Machining, Dry Milling

**Abstract.** This paper is part of a study focusing on the elaboration of accurate component with complex geometries using bio-sourced as an alternative to petrochemical polymer. The bio-sourced and biodegradable in this study is composed of a Poly Lactic Acid (PLA) matrix and hemp fibers. The final component is obtained by injection followed by a machining operation. The final component is obtained by injection followed by a machining finishing operation. Injection molding will be carried out to be compared with 3D printing on economic, environmental, production and workpiece quality criteria. This paper focuses only on the combination of two processes, injection molding followed by machining on poly (L-lactic acid) or PLLA which is biobased and biodegradable. After injecting the workpiece, thermo-physical characterization tests are realized on PLLA polymer. Rheology, thermal and mechanical tests are carried out in order to study thermomechanical behavior and to understand material flow phenomena at different temperatures and shear rates. The objective of this paper is to overcome the technical challenges of milling this material without any lubricant. In an upcoming project, various machining operations will be carried out such as turning to study continuous cutting, or milling to study discontinuous cutting on workpieces reinforced with bio-sourced fibers as hemp.

**Introduction**

Over the decades, the growing use of polymer materials has changed our everyday lives, and they are now omnipresent, such as in medicine [1] or in civil construction [2]. However, this widespread popularity of polymers has often come at the expense of careful consideration of their ecological impact. While the versatility and durability of these materials make them ideal candidates for a variety of applications, it is becoming imperative to question our indiscriminate use of polymers. This exploration raises essential questions about the need to modify our approach to more ecofriendly materials, at a time when ecological concerns are taking center stage in our collective consciousness. It is in this context that biosourced polymer materials, derived from renewable sources such as corn, sugarcane or algae, are emerging as promising solutions [3].

These polymers, often referred to as "bioplastics", offer the possibility of reducing dependence on non-renewable petrochemical resources, while limiting the greenhouse gas emissions associated with their production. Belboom et al. [4] shows that by carefully selecting the location and type of crops for the production of bio-based polymers, greenhouse gas emissions could be reduced for equivalent volumes of similar polymers derived from petrochemicals. Some have focused on recyclability of these materials and their performance throughout their various life cycles as Schäfer et al. [5].

Injection molding is now a well-known and mature process to realize complex components in large scale and the machining of polymers has been studied, in turning or drilling processes.

<figure><img src="image_1775.png" /></figure>
# Machinability of PLA obtained by injection molding under a dry milling process

CLOËZ Liam¹,²,a, FONTAINE Michaël¹,ᵇ, GILBIN Alexandre¹,ᶜ and BARRIÈRE Thierry²,ᵈ

¹ SUPMICROTECH, CNRS, Institut FEMTO-ST, F-25000 Besançon, France

² Université de Franche-Comté, CNRS, Institut FEMTO-ST, F-25000 Besançon, France

a.liam.cloez@femto-st.fr, b.michael fontaine@ens2m.fr, c.alexandre.gilbin@ens2m.fr,

d.thierry.barriere@univ-fcomte.fr

**Keywords:** Poly Lactic Acid, Injection Molding, Machining, Dry Milling

**Abstract.** This paper is part of a study focusing on the elaboration of accurate component with complex geometries using bio-sourced as an alternative to petrochemical polymer. The bio-sourced and biodegradable in this study is composed of a Poly Lactic Acid (PLA) matrix and hemp fibers. The final component is obtained by injection followed by a machining operation. The final component is obtained by injection followed by a machining finishing operation. Injection molding will be carried out to be compared with 3D printing on economic, environmental, production and workpiece quality criteria. This paper focuses only on the combination of two processes, injection molding followed by machining on poly (L-lactic acid) or PLLA which is biobased and biodegradable. After injecting the workpiece, thermo-physical characterization tests are realized on PLLA polymer. Rheology, thermal and mechanical tests are carried out in order to study thermomechanical behavior and to understand material flow phenomena at different temperatures and shear rates. The objective of this paper is to overcome the technical challenges of milling this material without any lubricant. In an upcoming project, various machining operations will be carried out such as turning to study continuous cutting, or milling to study discontinuous cutting on workpieces reinforced with bio-sourced fibers as hemp.

**Introduction**

Over the decades, the growing use of polymer materials has changed our everyday lives, and they are now omnipresent, such as in medicine [1] or in civil construction [2]. However, this widespread popularity of polymers has often come at the expense of careful consideration of their ecological impact. While the versatility and durability of these materials make them ideal candidates for a variety of applications, it is becoming imperative to question our indiscriminate use of polymers. This exploration raises essential questions about the need to modify our approach to more ecofriendly materials, at a time when ecological concerns are taking center stage in our collective consciousness. It is in this context that biosourced polymer materials, derived from renewable sources such as corn, sugarcane or algae, are emerging as promising solutions [3].

These polymers, often referred to as "bioplastics", offer the possibility of reducing dependence on non-renewable petrochemical resources, while limiting the greenhouse gas emissions associated with their production. Belboom et al. [4] shows that by carefully selecting the location and type of crops for the production of bio-based polymers, greenhouse gas emissions could be reduced for equivalent volumes of similar polymers derived from petrochemicals. Some have focused on recyclability of these materials and their performance throughout their various life cycles as Schäfer et al. [5].

Injection molding is now a well-known and mature process to realize complex components in large scale and the machining of polymers has been studied, in turning or drilling processes.

<figure><img src="image_1773.png" /></figure>
Milling of polymer parts is less investigated, especially for PLA. Rawal *et al.* [6] presents the various factors influencing the cutting of these materials, such as cutting parameters, cutting tool, polymer type, manufacturing method, and composite polymer properties. This is the reason why a characterization study on this material is necessary to analyze its thermal, mechanical and rheological behaviors before machining the injected parts. The correct parameters for molding components through injection will be selected based on results of the thermal and rheological study.

## Materials and methods

### Material

The material selected in this study is poly (L-lactic acid) or PLLA with D-lactide content of 0.5%, a density of 1.25 g.cm⁻³, a melting temperature (T<sub>m</sub>) between 170 °C and 180 °C and a glass transition temperature (T<sub>g</sub>) of 58°C. It is provided by NaturePlast by the name PLI005 in pellet form. They recommend drying the material at 60 °C for 3 hours before any manufacturing process. However, according to a parametric study performed in our laboratory, the ideal drying parameters for PLI005 are 80 °C for a minimum of 5 hours, to minimize degradation caused by humidity during processing.

### Differential Scanning Calorimetry (DSC)

Tests were carried out on SETARAM DSC131EVO to study the thermal behavior of the material. Only temperatures of transition phases such as melting (T<sub>m</sub>), crystallization (T<sub>c</sub>) and glass transition (T<sub>g</sub>) were recorded. Pellets (for a mass of 25.4 g) taken from the PLA feedstock were placed into an aluminum crucible with a heating rate of 1 °C.min<sup>-1</sup> from 25 °C to 195 °C and then was cooled with air to 25 °C.

### Cone-and-plate rheometer

Two different rheometers were employed to analyze the rheological behavior of the material. The first rheometer HAAKE MARS is a cone-and-plate system, enabling the examination of the polymer's shear viscosity across shear rates ranging from 10<sup>-5</sup> s<sup>-1</sup> to 10<sup>2</sup> s<sup>-1</sup> at different temperatures. The sample is placed on the 35 mm diameter plate and the cone positioned above with an air gap angle (β) of 2 ° will rotate at a certain angular viscosity (ω) and then heated at the required temperature.

### Capillary rheometer

The second rheometer is a capillary rheometer ROSAND RH2000. The polymer flows through a shear die with a diameter of 1 mm and a length of 16 mm. Pressures at the entrance and exit of the die are measured to determine the shear viscosity values. This system enables the measurement of polymer viscosity at higher shear rates ranging from 10<sup>2</sup> s<sup>-1</sup> to 10<sup>4</sup> s<sup>-1</sup>.

### Tensile test

Tensile strength, elongation at break and Young's modulus were measured on injected-molded PLA specimens following the ISO 527-2 standard (Figure 1). Before the tensile test, specimens were stored in a climatic chamber at 23 °C and 50% RH (relative humidity) for 7 days. The tensile testing press performed the C45 model from MTS. Tests were conducted with a crosshead speed of 2 mm.min<sup>-1</sup> and a load cell of 12 kN.
Milling of polymer parts is less investigated, especially for PLA. Rawal *et al.* [6] presents the various factors influencing the cutting of these materials, such as cutting parameters, cutting tool, polymer type, manufacturing method, and composite polymer properties. This is the reason why a characterization study on this material is necessary to analyze its thermal, mechanical and rheological behaviors before machining the injected parts. The correct parameters for molding components through injection will be selected based on results of the thermal and rheological study.

# Materials and methods

## Material

The material selected in this study is poly (L-lactic acid) or PLLA with D-lactide content of 0.5%, a density of 1.25 g.cm⁻³, a melting temperature (T<sub>m</sub>) between 170 °C and 180 °C and a glass transition temperature (T<sub>g</sub>) of 58°C. It is provided by NaturePlast by the name PLI005 in pellet form. They recommend drying the material at 60 °C for 3 hours before any manufacturing process. However, according to a parametric study performed in our laboratory, the ideal drying parameters for PLI005 are 80 °C for a minimum of 5 hours, to minimize degradation caused by humidity during processing.

## Differential Scanning Calorimetry (DSC)

Tests were carried out on SETARAM DSC131EVO to study the thermal behavior of the material. Only temperatures of transition phases such as melting (T<sub>m</sub>), crystallization (T<sub>c</sub>) and glass transition (T<sub>g</sub>) were recorded. Pellets (for a mass of 25.4 g) taken from the PLA feedstock were placed into an aluminum crucible with a heating rate of 1 °C.min<sup>-1</sup> from 25 °C to 195 °C and then was cooled with air to 25 °C.

## Cone-and-plate rheometer

Two different rheometers were employed to analyze the rheological behavior of the material. The first rheometer HAAKE MARS is a cone-and-plate system, enabling the examination of the polymer's shear viscosity across shear rates ranging from 10<sup>-5</sup> s<sup>-1</sup> to 10<sup>2</sup> s<sup>-1</sup> at different temperatures. The sample is placed on the 35 mm diameter plate and the cone positioned above with an air gap angle (β) of 2 ° will rotate at a certain angular viscosity (ω) and then heated at the required temperature.

## Capillary rheometer

The second rheometer is a capillary rheometer ROSAND RH2000. The polymer flows through a shear die with a diameter of 1 mm and a length of 16 mm. Pressures at the entrance and exit of the die are measured to determine the shear viscosity values. This system enables the measurement of polymer viscosity at higher shear rates ranging from 10<sup>2</sup> s<sup>-1</sup> to 10<sup>4</sup> s<sup>-1</sup>.

## Tensile test

Tensile strength, elongation at break and Young's modulus were measured on injected-molded PLA specimens following the ISO 527-2 standard (Figure 1). Before the tensile test, specimens were stored in a climatic chamber at 23 °C and 50% RH (relative humidity) for 7 days. The tensile testing press performed the C45 model from MTS. Tests were conducted with a crosshead speed of 2 mm.min<sup>-1</sup> and a load cell of 12 kN.
<figure><img src="image_1776.png" /><figcaption>Figure 1: Dimensions (mm) of tensile test specimens (ISO 527-2)</figcaption></figure>

### Injection molding

The injection molding was carried out using a BOY 22M with a clamping force of 220 kN. The materials were introduced into the injection molding press (Figure 2) in pellet form and injected to tensile test specimen with dimensions detailed in Figure 1 or milling block (Figure 3.C). The injection molding parameters are outlined in Table 1.

<table><caption>Table 1: Injection molding parameters</caption><thead><tr><th>Material</th><th>Feed zone<br/>[°C]</th><th>Transition zone<br/>[°C]</th><th>Transition zone<br/>[°C]</th><th>Metering zone<br/>[°C]</th><th>Mold temperature<br/>[°C]</th><th>Injection flow<br/>[g.s<sup>-1</sup>]</th><th>Injection pressure<br/>[MPa]</th><th>Cooling time<br/>[s]</th></tr></thead><tbody><tr><td>PLA</td><td>195</td><td>190</td><td>190</td><td>190</td><td>45</td><td>41</td><td>14</td><td>25</td></tr></tbody></table>

<figure><img src="image_1777.png" /><figcaption>Figure 2: Injection molding process</figcaption></figure>

### Machining

Dry machining tests were conducted on a DECKEL MAHO DMU35M milling machine. The specimen dimensions are detailed in Figure 3. In order to overcome technical challenges related to the machinability of PLA in dry conditions, slotting was chosen as initial machining operation. To optimize samples, six slots were made per piece (Figure 3). The cutting tool used for slotting was a 2-tooth end mill with a diameter of 6 mm, referenced as ELCO K0750.060. To measure
<figure><img src="image_1774.png" /><figcaption>Figure 1: Dimensions (mm) of tensile test specimens (ISO 527-2)</figcaption></figure>

### Injection molding

The injection molding was carried out using a BOY 22M with a clamping force of 220 kN. The materials were introduced into the injection molding press (Figure 2) in pellet form and injected to tensile test specimen with dimensions detailed in Figure 1 or milling block (Figure 3.C). The injection molding parameters are outlined in Table 1.

<table><caption>Table 1: Injection molding parameters</caption><thead><tr><th>Material</th><th>Feed zone<br/>[°C]</th><th>Transition zone<br/>[°C]</th><th>Transition zone<br/>[°C]</th><th>Metering zone<br/>[°C]</th><th>Mold temperature<br/>[°C]</th><th>Injection flow<br/>[g.s<sup>-1</sup>]</th><th>Injection pressure<br/>[MPa]</th><th>Cooling time<br/>[s]</th></tr></thead><tbody><tr><td>PLA</td><td>195</td><td>190</td><td>190</td><td>190</td><td>45</td><td>41</td><td>14</td><td>25</td></tr></tbody></table>

<figure><img src="image_1775.png" /><figcaption>Figure 2: Injection molding process</figcaption></figure>

### Machining

Dry machining tests were conducted on a DECKEL MAHO DMU35M milling machine. The specimen dimensions are detailed in Figure 3. In order to overcome technical challenges related to the machinability of PLA in dry conditions, slotting was chosen as initial machining operation. To optimize samples, six slots were made per piece (Figure 3). The cutting tool used for slotting was a 2-tooth end mill with a diameter of 6 mm, referenced as ELCO K0750.060. To measure
cutting forces, PLA blocks were clamped onto the KISTLER 9129AA force sensor. For each measurement acquisition, the sampling frequency was set at 50 points per tooth pass, ranging from a minimum frequency of 1768 Hz to a maximum frequency of 8842 Hz.

### Optical 3D measuring instrument / digital microscope

The microscope ALICONA InfiniteFocus was used to measure the surface roughness of the machined parts. Measurements (9 × 3 mm) were taken at the center of the groove in the longitudinal direction relative to the feed direction. Then the data analysis was processed using Digital Surf's MountainsMap software. Evaluation lengths and cut-off were chosen according to the ISO 21920 standard. Values of these two parameters vary depending on the measurement.

<figure><img src="image_1778.png" /><figcaption>Figure 3: CAD diagram of a PLA milling block fixed on the KISTLER sensor (A), photograph of the PLA block on the cutting forces sensor (B), geometry of a block after machining with 8 slots (C)</figcaption></figure>

## Results and discussion

### Thermal properties

On the figure 4, the DSC thermogram is observed, showing various temperature peaks representing phase transitions of PLA. The first endothermic phase transition corresponds to the material's glass transition at a temperature ($T_g$) of 58 ± 1 °C. Then, the second phase transition is exothermic and corresponds to the crystallization of the material at a temperature ($T_c$) of 107 ± 1 °C and finally, a last endothermic phase transition is observable at a temperature ($T_m$) of 176 ± 1 °C. Temperature values for the various phase transitions of our PLA are consistent with those provided by NaturePlast. The values may vary depending on the isomeric composition of PLA, but similar values are found as reported by Kasmi et al. [7], who also employed a semi-crystalline PLA.
cutting forces, PLA blocks were clamped onto the KISTLER 9129AA force sensor. For each measurement acquisition, the sampling frequency was set at 50 points per tooth pass, ranging from a minimum frequency of 1768 Hz to a maximum frequency of 8842 Hz.

### Optical 3D measuring instrument / digital microscope

The microscope ALICONA InfiniteFocus was used to measure the surface roughness of the machined parts. Measurements (9 × 3 mm) were taken at the center of the groove in the longitudinal direction relative to the feed direction. Then the data analysis was processed using Digital Surf's MountainsMap software. Evaluation lengths and cut-off were chosen according to the ISO 21920 standard. Values of these two parameters vary depending on the measurement.

<figure><img src="image_1776.png" /><figcaption>Figure 3: CAD diagram of a PLA milling block fixed on the KISTLER sensor (A), photograph of the PLA block on the cutting forces sensor (B), geometry of a block after machining with 8 slots (C)</figcaption></figure>

## Results and discussion

### Thermal properties

On the figure 4, the DSC thermogram is observed, showing various temperature peaks representing phase transitions of PLA. The first endothermic phase transition corresponds to the material's glass transition at a temperature ($T_g$) of 58 ± 1 °C. Then, the second phase transition is exothermic and corresponds to the crystallization of the material at a temperature ($T_c$) of 107 ± 1 °C and finally, a last endothermic phase transition is observable at a temperature ($T_m$) of 176 ± 1 °C. Temperature values for the various phase transitions of our PLA are consistent with those provided by NaturePlast. The values may vary depending on the isomeric composition of PLA, but similar values are found as reported by Kasmi et al. [7], who also employed a semi-crystalline PLA.
<figure><img src="image_1779.png" /><figcaption>Figure 4: DSC thermogram of PLA</figcaption></figure>

### Rheological properties

In Figure 5, a Newtonian plateau is observed at low shear rates (up to 1 s⁻¹). Subsequently, the shear viscosity decreases with increasing of the shear rate, showing a pseudoplastic behavior of PLA. Moreover, the shear viscosity decreases with the rising temperature, indicating a thermo-dependent response. These trend curves are similar to other rheological studies on PLA. Lacambra-Andreu *et al.* observes the same behaviors [8] but with higher values. Indeed, they studied an amorphous PLA with a different isomer composition, altering the physico-chemical parameters of the material and consequently the rheological behavior.

<figure><img src="image_1780.png" /><figcaption>Figure 5: Shear viscosity depending on shear rate for tested PLA at 190°C and 200°C and associated theoretical curves (eq. 1)</figcaption></figure>

The displayed temperatures were chosen based on the manufacturing process used. Indeed, as indicated in Table 1, the injection temperatures range from 190 °C to 200 °C.

Curves has been plotted according to the Carreau-Yasuda model (Eq. 1) to theoretically describe the rheological behavior based on the shear rate and model parameters ($η_∞$, $η_0$, $λ$, $n$, $a$). Model parameters has been fitted [9] based on the work of Ou :
<figure><img src="image_1777.png" /><figcaption>Figure 4: DSC thermogram of PLA</figcaption></figure>

### Rheological properties

In Figure 5, a Newtonian plateau is observed at low shear rates (up to 1 s⁻¹). Subsequently, the shear viscosity decreases with increasing of the shear rate, showing a pseudoplastic behavior of PLA. Moreover, the shear viscosity decreases with the rising temperature, indicating a thermo-dependent response. These trend curves are similar to other rheological studies on PLA. Lacambra-Andreu *et al.* observes the same behaviors [8] but with higher values. Indeed, they studied an amorphous PLA with a different isomer composition, altering the physico-chemical parameters of the material and consequently the rheological behavior.

<figure><img src="image_1778.png" /><figcaption>Figure 5: Shear viscosity depending on shear rate for tested PLA at 190°C and 200°C and associated theoretical curves (eq. 1)</figcaption></figure>

The displayed temperatures were chosen based on the manufacturing process used. Indeed, as indicated in Table 1, the injection temperatures range from 190 °C to 200 °C.

Curves has been plotted according to the Carreau-Yasuda model (Eq. 1) to theoretically describe the rheological behavior based on the shear rate and model parameters ($η_∞$, $η_0$, $λ$, $n$, $a$). Model parameters has been fitted [9] based on the work of Ou :
$$ \eta = \eta_{\infty} + (\eta_{0} - \eta_{\infty})(1 + (\lambda\dot{\gamma})^{a})^{\frac{n-1}{a}} \quad (1) $$

$\dot{\gamma}$ is the shear rate and at 190 °C, $a=2$, $n=0.48$, $\eta_{\infty}=0$ Pa.s, $\eta_{0}=383.45$ Pa.s, $\lambda=0.04$ s. The shear rate in 3D printing at the nozzle at this temperature is about 600 s⁻¹ [8], and thus the shear viscosity would be approximately 80 Pa.s. For injection molding, the shear rate exceeds 1000 s⁻¹, and therefore, the shear viscosity would be less than 30 Pa.s.

## Mechanical properties

The figure 6 illustrates the mechanical properties of the injected PLA using parameters stated in Table 1. In order to measure the longitudinal deformation, an MTS axial extensometer was attached to the effective section of the specimen. This curve indicates a brittle polymer by breaking without showing necking. The average values across several injected specimens for mechanical properties are as follows: elongation at break of 1.74 ± 0.19%, Young modulus of 2.91 ± 0.15 GPa and ultimate stress of 46 ± 2 MPa.

<figure><img src="image_1781.png" /><figcaption>Figure 6: Tensile curve of injected specimen of PLA</figcaption></figure>

These values diverge from those available in the literature; indeed, Lay et al. or Lacambra-Andreu et al. presents the same ultimate stress [4,6], but the tensile modulus is divided by two and the elongation at break is multiplied by three compared to values in this study. Once again, the properties of PLA can vary from one grade to another. Thus, the studied PLA is more brittle than those presented by these authors. An explanation could be that differences arise from the prior conditioning cycle of the specimens.
$$ \eta = \eta_{\infty} + (\eta_{0} - \eta_{\infty})(1 + (\lambda\dot{\gamma})^{a})^{\frac{n-1}{a}} \quad (1) $$

$\dot{\gamma}$ is the shear rate and at 190 °C, $a=2$, $n=0.48$, $\eta_{\infty}=0$ Pa.s, $\eta_{0}=383.45$ Pa.s, $\lambda=0.04$ s. The shear rate in 3D printing at the nozzle at this temperature is about 600 s⁻¹ [8], and thus the shear viscosity would be approximately 80 Pa.s. For injection molding, the shear rate exceeds 1000 s⁻¹, and therefore, the shear viscosity would be less than 30 Pa.s.

## Mechanical properties

The figure 6 illustrates the mechanical properties of the injected PLA using parameters stated in Table 1. In order to measure the longitudinal deformation, an MTS axial extensometer was attached to the effective section of the specimen. This curve indicates a brittle polymer by breaking without showing necking. The average values across several injected specimens for mechanical properties are as follows: elongation at break of 1.74 ± 0.19%, Young modulus of 2.91 ± 0.15 GPa and ultimate stress of 46 ± 2 MPa.

<figure><img src="image_1779.png" /><figcaption>Figure 6: Tensile curve of injected specimen of PLA</figcaption></figure>

These values diverge from those available in the literature; indeed, Lay et al. or Lacambra-Andreu et al. presents the same ultimate stress [4,6], but the tensile modulus is divided by two and the elongation at break is multiplied by three compared to values in this study. Once again, the properties of PLA can vary from one grade to another. Thus, the studied PLA is more brittle than those presented by these authors. An explanation could be that differences arise from the prior conditioning cycle of the specimens.
<figure><img src="image_1782.png" /><figcaption>Figure 7: Images of the six first slots captured by the microscope InfiniteFocus depending on the cutting parameters (for $a_p = 2$ mm)</figcaption></figure>

<figure><img src="image_1783.png" /><figcaption>Figure 8: Images of the six following slots captured by the microscope InfiniteFocus depending on the cutting parameters (for $a_p = 2$ mm)</figcaption></figure>
<figure><img src="image_1780.png" /><figcaption>Figure 7: Images of the six first slots captured by the microscope InfiniteFocus depending on the cutting parameters (for $a_p = 2$ mm)</figcaption></figure>

<figure><img src="image_1781.png" /><figcaption>Figure 8: Images of the six following slots captured by the microscope InfiniteFocus depending on the cutting parameters (for $a_p = 2$ mm)</figcaption></figure>
Forces

For each of the machining tests conducted, the chip was discontinuous. In order to overcome technical barriers regarding PLA machining in dry conditions, tests were performed according to the NF E66-520 standard to study the tool-workpiece combination. Various tests were implemented to determine the cutting parameters ($V_c$, $f_z$, $a_p$ and $a_e$). Tests at cutting speeds of 30, 40 and 50 m.min⁻¹ were repeated three times. As for the other tests, they were not replicated and would therefore need to be reproduced to validate results. The specific cutting coefficient is calculated (Eq. 2) for the position of the cutting tool where material removal is equal to the feed per tooth. Thus, it is assumed that the cutting force is the maximal force along the X-axis, considering that $F_y$ is significantly lower than $F_x$. These forces are averaged peak-to-peak with a measurement uncertainty around 5%. This assumption remains acceptable given that this is a comparative study between cutting parameters. The curve in Figure 9.A represents the average specific cutting coefficient ($K_c$) as function of the cutting speed ($V_c$). The specific cutting coefficient can be determined by the equation 2, where $F_c$ is the cutting force.

$$K_c = \frac{F_c}{f_z \cdot a_p} \quad (2)$$

Limited by the machine used, the maximum cutting speed applied is here of 100 m.min⁻¹. It can be concluded based on the standard that the minimum cutting speed in our configuration lies between 50 m.min⁻¹ and 60 m.min⁻¹ by limiting variation. Similarly, the feed per tooth is determined by the specific cutting coefficient (Figure 9.B). Thus, it can be concluded that the minimum feed rate is 0.4 mm/rev, and the maximum is 0.8 mm/rev, with the occurrence of catastrophic phenomena on the slot edge, such as large material removal. Next, a test campaign was conducted for the depth of cutting with no significant change in the cutting coefficient, ranging from 0.25 mm to 3 mm, limited by the geometric dimensions of the workpiece.

<figure><img src="image_1784.png" /><figcaption>Figure 9: Effect of cutting speed ($a_p$ = 2 mm, $f$ = 0.4 mm/rev) on the average specific cutting coefficient ($K_c$) in dry milling of PLA (A). Effect of feed rate ($a_p$ = 2 mm, $V_c$ = 75 m.min⁻¹) on the average specific cutting coefficient ($K_c$) in dry milling of PLA (B).</figcaption></figure>
Forces

For each of the machining tests conducted, the chip was discontinuous. In order to overcome technical barriers regarding PLA machining in dry conditions, tests were performed according to the NF E66-520 standard to study the tool-workpiece combination. Various tests were implemented to determine the cutting parameters ($V_c$, $f_z$, $a_p$ and $a_e$). Tests at cutting speeds of 30, 40 and 50 m.min⁻¹ were repeated three times. As for the other tests, they were not replicated and would therefore need to be reproduced to validate results. The specific cutting coefficient is calculated (Eq. 2) for the position of the cutting tool where material removal is equal to the feed per tooth. Thus, it is assumed that the cutting force is the maximal force along the X-axis, considering that $F_y$ is significantly lower than $F_x$. These forces are averaged peak-to-peak with a measurement uncertainty around 5%. This assumption remains acceptable given that this is a comparative study between cutting parameters. The curve in Figure 9.A represents the average specific cutting coefficient ($K_c$) as function of the cutting speed ($V_c$). The specific cutting coefficient can be determined by the equation 2, where $F_c$ is the cutting force.

$$K_c = \frac{F_c}{f_z \cdot a_p} \quad (2)$$

Limited by the machine used, the maximum cutting speed applied is here of 100 m.min⁻¹. It can be concluded based on the standard that the minimum cutting speed in our configuration lies between 50 m.min⁻¹ and 60 m.min⁻¹ by limiting variation. Similarly, the feed per tooth is determined by the specific cutting coefficient (Figure 9.B). Thus, it can be concluded that the minimum feed rate is 0.4 mm/rev, and the maximum is 0.8 mm/rev, with the occurrence of catastrophic phenomena on the slot edge, such as large material removal. Next, a test campaign was conducted for the depth of cutting with no significant change in the cutting coefficient, ranging from 0.25 mm to 3 mm, limited by the geometric dimensions of the workpiece.

<figure><img src="image_1782.png" /><figcaption>Figure 9: Effect of cutting speed ($a_p$ = 2 mm, $f$ = 0.4 mm/rev) on the average specific cutting coefficient ($K_c$) in dry milling of PLA (A). Effect of feed rate ($a_p$ = 2 mm, $V_c$ = 75 m.min⁻¹) on the average specific cutting coefficient ($K_c$) in dry milling of PLA (B).</figcaption></figure>
## Surface roughness

A study was conducted to compare surface roughness within the slots for different cutting speeds and feed per tooth for a depth of cut of 2 mm. The various captures taken by the digital microscope are shown in figure 7 and figure 8 as a function of these cutting parameters. Figure 10 shows the average surface roughness on both surface and linear parameters as a function of cutting speed and feed per revolution. Similar trends are observed between the two roughness measures. Beyond a feed of 0.4 mm/rev, an increase in roughness is observed at various cutting speeds. An increase in cutting speed can lead to partial melting or local deformation of the polymer, resulting in a rougher surface. Surface roughness increases linearly with feed, which is less the case for linear roughness. Indeed, Ra values remain constant from a feed of 0.5 mm/rev up to 1 mm/rev. These curves highlight limitations of linear criteria for milled surfaces.

<figure><img src="image_1785.png" /><figcaption>Figure 10: Effect of cutting speed and feed per tooth on the surface roughness ($a_p = 2$ mm)</figcaption></figure>

## Conclusions and prospects

This paper presents preliminary results on PLA machining in dry conditions, and allows us to select injection molding (Table 1) and cutting parameters (a minimum cutting speed of 60 m.min⁻¹, and a feed per revolution between 0.2 and 0.4 mm/rev) potentially suitable for this material, especially when it will be reinforced with bio-sourced fibers such as hemp. For the dry machining of the polymer, it is about finding a compromise in cutting parameters between surface quality and cutting quality. At a cutting speed of 20 m.min⁻¹, the surface roughness of the slot is approximately 6.5 µm, and the cutting force is 58 N. For a test with a higher cutting speed (75 m.min⁻¹), the surface roughness is multiplied by 2 (~ 12 µm), and the cutting force decreases slightly (~ 43 N). It is necessary to avoid agglomeration of molten chips on the tool, burrs, and surface degradation. Thus, additional tests will be conducted to find this balance point for dry milling, by studying burrs and thermal aspects for values of cutting parameters that will be extended. Further studies are underway on the same process sequence, considering different factors for the machining of these materials such as the process (turning, milling, drilling), the lubricant (air flow, water) or the cutting tool. The final purpose is also to compare machinability of reinforced PLA pre-formed by injection molding and 3D printing (Pellet Additive Manufacturing). Several studies will be necessary to achieve machining of the printed polymer composite. Once these samples have been obtained, the same type of machining tests will be carried out.
## Surface roughness

A study was conducted to compare surface roughness within the slots for different cutting speeds and feed per tooth for a depth of cut of 2 mm. The various captures taken by the digital microscope are shown in figure 7 and figure 8 as a function of these cutting parameters. Figure 10 shows the average surface roughness on both surface and linear parameters as a function of cutting speed and feed per revolution. Similar trends are observed between the two roughness measures. Beyond a feed of 0.4 mm/rev, an increase in roughness is observed at various cutting speeds. An increase in cutting speed can lead to partial melting or local deformation of the polymer, resulting in a rougher surface. Surface roughness increases linearly with feed, which is less the case for linear roughness. Indeed, Ra values remain constant from a feed of 0.5 mm/rev up to 1 mm/rev. These curves highlight limitations of linear criteria for milled surfaces.

<figure><img src="image_1783.png" /><figcaption>Figure 10: Effect of cutting speed and feed per tooth on the surface roughness ($a_p = 2$ mm)</figcaption></figure>

## Conclusions and prospects

This paper presents preliminary results on PLA machining in dry conditions, and allows us to select injection molding (Table 1) and cutting parameters (a minimum cutting speed of 60 m.min⁻¹, and a feed per revolution between 0.2 and 0.4 mm/rev) potentially suitable for this material, especially when it will be reinforced with bio-sourced fibers such as hemp. For the dry machining of the polymer, it is about finding a compromise in cutting parameters between surface quality and cutting quality. At a cutting speed of 20 m.min⁻¹, the surface roughness of the slot is approximately 6.5 µm, and the cutting force is 58 N. For a test with a higher cutting speed (75 m.min⁻¹), the surface roughness is multiplied by 2 (~ 12 µm), and the cutting force decreases slightly (~ 43 N). It is necessary to avoid agglomeration of molten chips on the tool, burrs, and surface degradation. Thus, additional tests will be conducted to find this balance point for dry milling, by studying burrs and thermal aspects for values of cutting parameters that will be extended. Further studies are underway on the same process sequence, considering different factors for the machining of these materials such as the process (turning, milling, drilling), the lubricant (air flow, water) or the cutting tool. The final purpose is also to compare machinability of reinforced PLA pre-formed by injection molding and 3D printing (Pellet Additive Manufacturing). Several studies will be necessary to achieve machining of the printed polymer composite. Once these samples have been obtained, the same type of machining tests will be carried out.
## Acknowledgments

This work was carried out within the Manufacturing 21 working group, which gathers about 20 French research laboratories. The covered topics are manufacturing processes optimization, tool-workpiece interaction, and emerging manufacturing methods. The authors would like to thank the French Ministry of Higher Education and Research for funding the thesis grant, and the MIFHYSTO and AMETISTE platforms of the Applied Mechanics Department of the FEMTO-ST Institute for access to experimental facilities.

## References

[1] S. Ramakrishna, J. Mayer, E. Wintermantel, and K. W. Leong, "Biomedical applications of polymer-composite materials: a review," *Compos. Sci. Technol.*, vol. 61, no. 9, pp. 1189-1224, Jul. 2001. https://doi.org/10.1016/S0266-3538(00)00241-4

[2] S. S. Pendhari, T. Kant, and Y. M. Desai, "Application of polymer composites in civil construction: A general review," *Compos. Struct.*, vol. 84, no. 2, pp. 114-124, Jul. 2008. https://doi.org/10.1016/j.compstruct.2007.06.007

[3] I. Vroman and L. Tighzert, "Biodegradable Polymers," *Materials*, vol. 2, no. 2, pp. 307-344, Apr. 2009. https://doi.org/10.3390/ma2020307

[4] S. Belboom and A. Léonard, "Does biobased polymer achieve better environmental impacts than fossil polymer? Comparison of fossil HDPE and biobased HDPE produced from sugar beet and wheat," *Biomass Bioenergy*, vol. 85, pp. 159-167, Feb. 2016. https://doi.org/10.1016/j.biombioe.2015.12.014

[5] H. Schäfer, C. Pretschuh, and O. Brüggemann, "Reduction of cycle times in injection molding of PLA through bio-based nucleating agents," *Eur. Polym. J.*, vol. 115, pp. 6-11, Jun. 2019. https://doi.org/10.1016/j.eurpolymj.2019.03.011

[6] S. Rawal, A. M. Sidpara, and J. Paul, "A review on micro machining of polymer composites," *J. Manuf. Process.*, vol. 77, pp. 87-113, May 2022. https://doi.org/10.1016/j.jmapro.2022.03.014

[7] S. Kasmi, J. Cayuela, B. D. Backer, E. Labbé, and S. Alix, "Modified Polylactic Acid with Improved Impact Resistance in the Presence of a Thermoplastic Elastomer and the Influence of Fused Filament Fabrication on Its Physical Properties," *J. Compos. Sci.*, vol. 5, no. 9, p. 232, Sep. 2021. https://doi.org/10.3390/jcs5090232

[8] X. Lacambra-Andreu, X. P. Morelle, A. Maazouz, J.-M. Chenal, and K. Lamnawar, "Rheological investigation and modeling of healing properties during extrusion-based 3D printing of poly(lactic-acid)," *Rheol. Acta*, vol. 62, no. 1, pp. 31-44, Jan. 2023. https://doi.org/10.1007/s00397-022-01377-6

[9] H. Ou, "Modélisation multi-physiques et simulations numériques du moulage par injection mono et bi-matières thermoplastique / silicone liquide," *Matériaux, Université de Franche-Comté*, 2015.

[10] M. Lay, N. L. N. Thajudin, Z. A. A. Hamid, A. Rusli, M. K. Abdullah, and R. K. Shuib, "Comparison of physical and mechanical properties of PLA, ABS and nylon 6 fabricated using fused deposition modeling and injection molding," *Compos. Part B Eng.*, vol. 176, p. 107341, Nov. 2019. https://doi.org/10.1016/j.compositesb.2019.107341
## Acknowledgments

This work was carried out within the Manufacturing 21 working group, which gathers about 20 French research laboratories. The covered topics are manufacturing processes optimization, tool-workpiece interaction, and emerging manufacturing methods. The authors would like to thank the French Ministry of Higher Education and Research for funding the thesis grant, and the MIFHYSTO and AMETISTE platforms of the Applied Mechanics Department of the FEMTO-ST Institute for access to experimental facilities.

## References

[1] S. Ramakrishna, J. Mayer, E. Wintermantel, and K. W. Leong, "Biomedical applications of polymer-composite materials: a review," *Compos. Sci. Technol.*, vol. 61, no. 9, pp. 1189-1224, Jul. 2001. https://doi.org/10.1016/S0266-3538(00)00241-4

[2] S. S. Pendhari, T. Kant, and Y. M. Desai, "Application of polymer composites in civil construction: A general review," *Compos. Struct.*, vol. 84, no. 2, pp. 114-124, Jul. 2008. https://doi.org/10.1016/j.compstruct.2007.06.007

[3] I. Vroman and L. Tighzert, "Biodegradable Polymers," *Materials*, vol. 2, no. 2, pp. 307-344, Apr. 2009. https://doi.org/10.3390/ma2020307

[4] S. Belboom and A. Léonard, "Does biobased polymer achieve better environmental impacts than fossil polymer? Comparison of fossil HDPE and biobased HDPE produced from sugar beet and wheat," *Biomass Bioenergy*, vol. 85, pp. 159-167, Feb. 2016. https://doi.org/10.1016/j.biombioe.2015.12.014

[5] H. Schäfer, C. Pretschuh, and O. Brüggemann, "Reduction of cycle times in injection molding of PLA through bio-based nucleating agents," *Eur. Polym. J.*, vol. 115, pp. 6-11, Jun. 2019. https://doi.org/10.1016/j.eurpolymj.2019.03.011

[6] S. Rawal, A. M. Sidpara, and J. Paul, "A review on micro machining of polymer composites," *J. Manuf. Process.*, vol. 77, pp. 87-113, May 2022. https://doi.org/10.1016/j.jmapro.2022.03.014

[7] S. Kasmi, J. Cayuela, B. D. Backer, E. Labbé, and S. Alix, "Modified Polylactic Acid with Improved Impact Resistance in the Presence of a Thermoplastic Elastomer and the Influence of Fused Filament Fabrication on Its Physical Properties," *J. Compos. Sci.*, vol. 5, no. 9, p. 232, Sep. 2021. https://doi.org/10.3390/jcs5090232

[8] X. Lacambra-Andreu, X. P. Morelle, A. Maazouz, J.-M. Chenal, and K. Lamnawar, "Rheological investigation and modeling of healing properties during extrusion-based 3D printing of poly(lactic-acid)," *Rheol. Acta*, vol. 62, no. 1, pp. 31-44, Jan. 2023. https://doi.org/10.1007/s00397-022-01377-6

[9] H. Ou, "Modélisation multi-physiques et simulations numériques du moulage par injection mono et bi-matières thermoplastique / silicone liquide," *Matériaux, Université de Franche-Comté*, 2015.

[10] M. Lay, N. L. N. Thajudin, Z. A. A. Hamid, A. Rusli, M. K. Abdullah, and R. K. Shuib, "Comparison of physical and mechanical properties of PLA, ABS and nylon 6 fabricated using fused deposition modeling and injection molding," *Compos. Part B Eng.*, vol. 176, p. 107341, Nov. 2019. https://doi.org/10.1016/j.compositesb.2019.107341
# Using the particle finite element method for predicting optimum shear cutting clearance

SANDIN Olle¹,ª*, LAROUR Patrick²,ᵇ, RODRÍGUEZ Juan Manuel¹,³,ᶜ, KAJBERG Jörgen¹,ᵈ and CASELLAS Daniel¹,⁴,ᵉ

¹Department of Engineering Sciences and Mathematics, Division of Solid Mechanics, Luleå University of Technology, Luleå, 971 87, Sweden

²Voestalpine Stahl GmbH, voestalpine-Straße 3, Linz, A-4020, Austria

³School of Applied Sciences and Engineering, EAFIT University, Medellin, Colombia

⁴Unit of Metallic and Ceramic Materials, Eurecat, Centre Tecnològic de Catalunya, Placa de la Ciència, 2, Manresa, 08243, Spain

ªolle.sandin@ltu.se, ᵇpatrick.larour@voestalpine.com, ᶜjmrodrigup@eafit.edu.co,

ᵈjorgen.kajberg@ltu.se, ᶜdaniel.casellas@eurecat.org

**Keywords:** Shear Cutting, AHSS, PFEM

**Abstract.** The shear cutting process, which is the most common cutting technique in the sheet forming industry, is known for introducing damage to the cut edges of high strength metal. This damage may impair the forming- or fatigue properties of the material and can cause edge-cracking during forming or in-service part failure. The edge formability of a sheared edge is strongly linked with the appearance of large notches arising due to unfavorable process parameters. By numerical modelling of the shear cutting process with the possibility to vary important process parameters, the sheared edge damage can be detected and avoided in the manufacturing process. This work present numerical modelling of shear cutting in Advanced High Strength Steel using a novel Particle Finite Element Method approach. Numerical modelling of shear cutting processes over a large range of cutting clearances were conducted and validated against laboratory experiment results. The results showed that the PFEM modelling could detect the cut edge damages with the largest negative impact on formability, thus narrowing the feasible cutting clearance range.

**Introduction**

The shear cutting process is a common cutting technique in the sheet metal forming industry due to its cost-effectiveness and automation possibilities. However, the shear cutting process is known for inducing damage to the sheared edges that affect the formability and fatigue properties, especially for high strength metal sheets. Such damages may appear as micro-cracks, notches and residual stresses and are shown to be the driving cause of edge-cracking [1–5] and reduced fatigue life [6–11]. Larour et al. [12] showed that sharp geometrical notches such as secondary burnish, excessive burr or rough fracture surfaces have a strong negative influence on the sheared edge formability. The appearance of such geometrical defects is controlled by the cutting clearance, which accordingly is considered an influential cutting process parameter with regards to edge formability. Numerical modelling of the shear cutting process can furthermore be an efficient tool for predicting defects along the cut edge, enabling cutting process optimization, and preventing edge-cracking. However, numerical modelling of shear cutting requires robust numerical handling of large material deformation, which is challenging using conventional Finite Element Methods as element distortion during excessive deformation impair the numerical accuracy. Therefore, the Particle Finite Element Model (PFEM) is applied in this work for the numerical modelling of the shear cutting process, as it efficiently handles the large deformation involved in cutting processes [13–16]. In this work, an axisymmetric PFEM formulation is used for modelling of hole punching

<figure><img src="image_1786.png" /></figure>
# Using the particle finite element method for predicting optimum shear cutting clearance

SANDIN Olle¹,ª*, LAROUR Patrick²,ᵇ, RODRÍGUEZ Juan Manuel¹,³,ᶜ, KAJBERG Jörgen¹,ᵈ and CASELLAS Daniel¹,⁴,ᵉ

¹Department of Engineering Sciences and Mathematics, Division of Solid Mechanics, Luleå University of Technology, Luleå, 971 87, Sweden

²Voestalpine Stahl GmbH, voestalpine-Straße 3, Linz, A-4020, Austria

³School of Applied Sciences and Engineering, EAFIT University, Medellin, Colombia

⁴Unit of Metallic and Ceramic Materials, Eurecat, Centre Tecnològic de Catalunya, Placa de la Ciència, 2, Manresa, 08243, Spain

ªolle.sandin@ltu.se, ᵇpatrick.larour@voestalpine.com, ᶜjmrodrigup@eafit.edu.co, ᵈjorgen.kajberg@ltu.se, ᵉdaniel.casellas@eurecat.org

**Keywords:** Shear Cutting, AHSS, PFEM

**Abstract.** The shear cutting process, which is the most common cutting technique in the sheet forming industry, is known for introducing damage to the cut edges of high strength metal. This damage may impair the forming- or fatigue properties of the material and can cause edge-cracking during forming or in-service part failure. The edge formability of a sheared edge is strongly linked with the appearance of large notches arising due to unfavorable process parameters. By numerical modelling of the shear cutting process with the possibility to vary important process parameters, the sheared edge damage can be detected and avoided in the manufacturing process. This work present numerical modelling of shear cutting in Advanced High Strength Steel using a novel Particle Finite Element Method approach. Numerical modelling of shear cutting processes over a large range of cutting clearances were conducted and validated against laboratory experiment results. The results showed that the PFEM modelling could detect the cut edge damages with the largest negative impact on formability, thus narrowing the feasible cutting clearance range.

**Introduction**

The shear cutting process is a common cutting technique in the sheet metal forming industry due to its cost-effectiveness and automation possibilities. However, the shear cutting process is known for inducing damage to the sheared edges that affect the formability and fatigue properties, especially for high strength metal sheets. Such damages may appear as micro-cracks, notches and residual stresses and are shown to be the driving cause of edge-cracking [1–5] and reduced fatigue life [6–11]. Larour et al. [12] showed that sharp geometrical notches such as secondary burnish, excessive burr or rough fracture surfaces have a strong negative influence on the sheared edge formability. The appearance of such geometrical defects is controlled by the cutting clearance, which accordingly is considered an influential cutting process parameter with regards to edge formability. Numerical modelling of the shear cutting process can furthermore be an efficient tool for predicting defects along the cut edge, enabling cutting process optimization, and preventing edge-cracking. However, numerical modelling of shear cutting requires robust numerical handling of large material deformation, which is challenging using conventional Finite Element Methods as element distortion during excessive deformation impair the numerical accuracy. Therefore, the Particle Finite Element Model (PFEM) is applied in this work for the numerical modelling of the shear cutting process, as it efficiently handles the large deformation involved in cutting processes [13–16]. In this work, an axisymmetric PFEM formulation is used for modelling of hole punching

<figure><img src="image_1784.png" /></figure>
processes that predicts the cut edge morphologies over a large range of cutting clearances. By numerically predicting the appearance of secondary burnish and burr, the model determines the feasible cutting clearance range for a complex-phase AHSS grade of 1.5 mm thickness. The experimental work used for validation of the numerical modelling was presented by Larour et al. [12] and gives the average cut edge zone distribution of punched holes for varying cutting clearances and the corresponding hole expansion ratio (HER) that describes the formability of the punched hole. By predicting the experimental cut edge shapes, including notches such as burr or secondary burnish, and the clear trend between cut edge shape and experimental HER values state the applicability of the PFEM model as an effective tool for predicting the optimum range of cutting clearances for the studied AHSS grade.

## The Particle Finite Element Method

PFEM was originally developed by Idelsohn et al. [17] for modelling of incompressible free-flowing surfaces and fluid structure interactions. However, its efficiency in large material deformation and predicting new boundaries makes it suitable for non-linear solid mechanics. This was shown by Rodriguez et al. [15,18–21] for modelling of orthogonal cutting using thermo-mechanical material modelling. Similarly, Oñate et al. [16] showcased numerous examples of non-linear solid mechanics application for PFEM. A recent publication by Sandin et al. [13] applies PFEM for shear cutting of AHSS, where the accuracy and robustness of PFEM for this process is highlighted.

Even though PFEM can be applied on various mechanical problems, the following modelling steps are fundamental [22]:

* Define a volume with a particle distribution.

* Connect the particles using Delaunay triangulation.

* Solve the governing equations using a Lagrangian framework.

* Perform re-connectivity of the particles continuously to prevent element distortion. Transfer results variables.

* The α-shape method, or constrained α-shape method [23] as in this work, defines the internal and external boundaries.

Fig. 1 shows the schematic steps of PFEM in a shear cutting context from initial configuration and over a set of time steps.
processes that predicts the cut edge morphologies over a large range of cutting clearances. By numerically predicting the appearance of secondary burnish and burr, the model determines the feasible cutting clearance range for a complex-phase AHSS grade of 1.5 mm thickness. The experimental work used for validation of the numerical modelling was presented by Larour et al. [12] and gives the average cut edge zone distribution of punched holes for varying cutting clearances and the corresponding hole expansion ratio (HER) that describes the formability of the punched hole. By predicting the experimental cut edge shapes, including notches such as burr or secondary burnish, and the clear trend between cut edge shape and experimental HER values state the applicability of the PFEM model as an effective tool for predicting the optimum range of cutting clearances for the studied AHSS grade.

## The Particle Finite Element Method

PFEM was originally developed by Idelsohn et al. [17] for modelling of incompressible free-flowing surfaces and fluid structure interactions. However, its efficiency in large material deformation and predicting new boundaries makes it suitable for non-linear solid mechanics. This was shown by Rodriguez et al. [15,18–21] for modelling of orthogonal cutting using thermo-mechanical material modelling. Similarly, Oñate et al. [16] showcased numerous examples of non-linear solid mechanics application for PFEM. A recent publication by Sandin et al. [13] applies PFEM for shear cutting of AHSS, where the accuracy and robustness of PFEM for this process is highlighted.

Even though PFEM can be applied on various mechanical problems, the following modelling steps are fundamental [22]:

* Define a volume with a particle distribution.

* Connect the particles using Delaunay triangulation.

* Solve the governing equations using a Lagrangian framework.

* Perform re-connectivity of the particles continuously to prevent element distortion. Transfer results variables.

* The α-shape method, or constrained α-shape method [23] as in this work, defines the internal and external boundaries.

Fig. 1 shows the schematic steps of PFEM in a shear cutting context from initial configuration and over a set of time steps.
<figure><img src="image_1787.png" /><figcaption>Fig. 1: Schematic steps of the PFEM procedure for shear cutting. Starting from initial time step $t_0$ to time step $t_{n+x}$.</figcaption></figure>

The benefits of using PFEM in large deformation solid mechanics are discussed in [13], which in short describes the efficient re-meshing algorithm and computational robustness in large deformations as the main advantages over the conventional Finite Element Method. Meanwhile, the computational efficiency of PFEM is an advantage when comparing it to various mesh-less or particle methods that are developed for large deformation mechanical analysis. The PFEM scheme can insert particles in localized areas for increasing accuracy and can remove particles in redundant areas for reducing the computational cost. However, such operations should be done sparingly as extensive introduction or removal of particles may cause results smoothing or diffusion. Therefore, a fine initial discretization of the problem is suggested.

## Constitutive modelling

This work investigates a Complex Phase steel grade with high ductility, named as CP1000HD. It is an AHSS grade commonly used in the automotive industry for structural components. Its loading response was described using an elasto-plastic material model, combined with a ductile damage model for prediction of material failure. The elasto-plastic material behavior was calculated by an iterative radial return method using a Stiebler et al. [24] model, shown in Eq. (1), for defining the plastic response. The Stiebler model was calibrated by experimental data from hydraulic bulge testing according to ISO 16808 [25]. The experimental bulge data and the model fitting is shown in Fig. 2 and the Stiebler parameters $c_1$ to $c_4$ are shown in Table 1 and a Young's modulus of 210 GPa was assumed. The tensile mechanical properties of the material are presented in Table 2.

$$ \hat{\sigma}(\varepsilon_p) = c_1 + c_2 \cdot \varepsilon_p + c_3 \cdot (1 - e^{c_4 \cdot \varepsilon_p}) \quad (1) $$
<figure><img src="image_1785.png" /><figcaption>Fig. 1: Schematic steps of the PFEM procedure for shear cutting. Starting from initial time step $t_0$ to time step $t_{n+x}$.</figcaption></figure>

The benefits of using PFEM in large deformation solid mechanics are discussed in [13], which in short describes the efficient re-meshing algorithm and computational robustness in large deformations as the main advantages over the conventional Finite Element Method. Meanwhile, the computational efficiency of PFEM is an advantage when comparing it to various mesh-less or particle methods that are developed for large deformation mechanical analysis. The PFEM scheme can insert particles in localized areas for increasing accuracy and can remove particles in redundant areas for reducing the computational cost. However, such operations should be done sparingly as extensive introduction or removal of particles may cause results smoothing or diffusion. Therefore, a fine initial discretization of the problem is suggested.

## Constitutive modelling

This work investigates a Complex Phase steel grade with high ductility, named as CP1000HD. It is an AHSS grade commonly used in the automotive industry for structural components. Its loading response was described using an elasto-plastic material model, combined with a ductile damage model for prediction of material failure. The elasto-plastic material behavior was calculated by an iterative radial return method using a Stiebler et al. [24] model, shown in Eq. (1), for defining the plastic response. The Stiebler model was calibrated by experimental data from hydraulic bulge testing according to ISO 16808 [25]. The experimental bulge data and the model fitting is shown in Fig. 2 and the Stiebler parameters $c_1$ to $c_4$ are shown in Table 1 and a Young's modulus of 210 GPa was assumed. The tensile mechanical properties of the material are presented in Table 2.

$$ \hat{\sigma}(\varepsilon_p) = c_1 + c_2 \cdot \varepsilon_p + c_3 \cdot (1 - e^{c_4 \cdot \varepsilon_p}) \quad (1) $$
<figure><img src="image_1788.png" /><figcaption>Fig. 2: Plastic hardening response from hydraulic bulge experiment and the fitted Stiebler plasticity model.</figcaption></figure>

<table><caption>Table 1: Stiebler plasticity model parameters after curve fitting to experimental hydraulic bulge testing.</caption><thead><tr><th>c<sub>1</sub><br>[MPa]</th><th>c<sub>2</sub><br>[MPa]</th><th>c<sub>3</sub><br>[MPa]</th><th>c<sub>4</sub></th></tr></thead><tbody><tr><td>909.5</td><td>296.6</td><td>229.3</td><td>31.1</td></tr></tbody></table>

<table><caption>Table 2: Tensile mechanical properties of the CP1000HD grade, stating the rolling direction (RD), yield strength (Rp02), tensile strength (Rm), uniform elongation (Ag), total elongation (A80), n-value (nAg), r-value (r) and fracture toughness measured by the essential work of fracture method (EWF) transverse to RD.</caption><thead><tr><th>RD</th><th>Rp02 [MPa]</th><th>Rm [MPa]</th><th>Ag [%]</th><th>A80 [%]</th><th>nAg</th><th>r</th><th>EWF [kJ/m²]</th></tr></thead><tbody><tr><td>0°</td><td>893</td><td>1052</td><td>7.3</td><td>11.1</td><td>0.071</td><td>0.91</td><td>-</td></tr><tr><td>45°</td><td>905</td><td>1052</td><td>7.0</td><td>10.6</td><td>0.068</td><td>1.02</td><td>-</td></tr><tr><td>90°</td><td>909</td><td>1062</td><td>7.1</td><td>10.7</td><td>0.068</td><td>0.96</td><td>282</td></tr></tbody></table>

The damage- and failure modelling implemented in the PFEM scheme was based on the Generalized Incremental Stress State Dependent Damage Model (GISSMO), developed by Neukamm et al. [26] and provides a stress-state dependent damage- and failure behavior. The stress-state was defined by the stress triaxiality $\eta$ and Lode angle parameter $\bar{\theta}$, expressed in Eq. (2) and Eq. (3) respectively, where $\sigma$ is the Cauchy stress tensor and $s$ is the deviatoric stress tensor.

$$ \eta = \frac{\mathrm{tr}(\boldsymbol{\sigma})}{3\sqrt{\frac{3}{2}\boldsymbol{s} \cdot \boldsymbol{s}}} \qquad (2) $$

$$ \bar{\theta} = \frac{1}{3} \arccos \left( \frac{3\sqrt{3} \det(\boldsymbol{s})}{2 \left( \frac{1}{2} \boldsymbol{s} \cdot \boldsymbol{s} \right)^{\frac{3}{2}}} \right) \qquad (3) $$
<figure><img src="image_1786.png" /><figcaption>Fig. 2: Plastic hardening response from hydraulic bulge experiment and the fitted Stiebler plasticity model.</figcaption></figure>

<table><caption>Table 1: Stiebler plasticity model parameters after curve fitting to experimental hydraulic bulge testing.</caption><thead><tr><th>c<sub>1</sub><br>[MPa]</th><th>c<sub>2</sub><br>[MPa]</th><th>c<sub>3</sub><br>[MPa]</th><th>c<sub>4</sub></th></tr></thead><tbody><tr><td>909.5</td><td>296.6</td><td>229.3</td><td>31.1</td></tr></tbody></table>

<table><caption>Table 2: Tensile mechanical properties of the CP1000HD grade, stating the rolling direction (RD), yield strength (Rp02), tensile strength (Rm), uniform elongation (Ag), total elongation (A80), n-value (nAg), r-value (r) and fracture toughness measured by the essential work of fracture method (EWF) transverse to RD.</caption><thead><tr><th>RD</th><th>Rp02 [MPa]</th><th>Rm [MPa]</th><th>Ag [%]</th><th>A80 [%]</th><th>nAg</th><th>r</th><th>EWF [kJ/m²]</th></tr></thead><tbody><tr><td>0°</td><td>893</td><td>1052</td><td>7.3</td><td>11.1</td><td>0.071</td><td>0.91</td><td>-</td></tr><tr><td>45°</td><td>905</td><td>1052</td><td>7.0</td><td>10.6</td><td>0.068</td><td>1.02</td><td>-</td></tr><tr><td>90°</td><td>909</td><td>1062</td><td>7.1</td><td>10.7</td><td>0.068</td><td>0.96</td><td>282</td></tr></tbody></table>

The damage- and failure modelling implemented in the PFEM scheme was based on the Generalized Incremental Stress State Dependent Damage Model (GISSMO), developed by Neukamm et al. [26] and provides a stress-state dependent damage- and failure behavior. The stress-state was defined by the stress triaxiality $\eta$ and Lode angle parameter $\bar{\theta}$, expressed in Eq. (2) and Eq. (3) respectively, where $\sigma$ is the Cauchy stress tensor and $s$ is the deviatoric stress tensor.

$$ \eta = \frac{\mathrm{tr}(\boldsymbol{\sigma})}{3\sqrt{\frac{3}{2}\boldsymbol{s} \cdot \boldsymbol{s}}} \qquad (2) $$

$$ \bar{\theta} = \frac{1}{3} \arccos \left( \frac{3\sqrt{3} \det(\boldsymbol{s})}{2 \left( \frac{1}{2} \boldsymbol{s} \cdot \boldsymbol{s} \right)^{\frac{3}{2}}} \right) \qquad (3) $$
The damage- and failure model accumulates a damage parameter $D$ according to Eq. (4), where $n$ is the rate of damage accumulation, $\varepsilon_f(\eta, \bar{\theta})$ is the effective plastic failure strain, and $\dot{\varepsilon}_p$ is the effective plastic strain increment.

$$ \dot{D} = \frac{n}{\varepsilon_f(\eta, \bar{\theta})} D^{(1-\frac{1}{n})} \dot{\varepsilon}_p \quad (4) $$

Similarly, an instability parameter $F$ accumulates according to Eq. (5), where $e_i(\eta)$ is the effective plastic instability strain and $m$ is the material degradation rate.

$$ \dot{F} = \frac{m}{\varepsilon_i(\eta)} F^{(1-\frac{1}{m})} \dot{\varepsilon}_p \quad (5) $$

When $F = 1$, damage coupling to the stress tensor is activated to account for the loss of load bearing capacity due to void growth. This reduction of material strength is common in ductile metals, such as CP1000HD or similar AHSS grades. The damage related coupling to the load bearing capacity is defined according to Eq. (6), where $D_c$ is the accumulated value of $D$ when $F = 1$.

$$ \tilde{\sigma} = \sigma(1 - \tilde{D}) \text{ where } \tilde{D} = \left( \frac{D - D_c}{1 - D_c} \right)^m \quad (6) $$

When the damage parameter $D$ reaches a critical threshold value of $D = 0.99$, the stiffness of the element is lost, and the element is removed from the post-processing for clearer visualization of the material failure.

Experimental values of effective plastic failure strain were obtained using Digital Image Correlation (DIC) according to the work by [27]. This method extracted the strain field with a square 0.1 mm grids continuously during tensile testing of various tensile specimen and the effective plastic failure strain and the corresponding stress-state was calculated for each specimen. The specimens were designed to deform and failed at designated stress-states, thus cover a wide range of stress-states. This procedure enabled calibration of a failure locus, providing $\varepsilon_f(\eta, \bar{\theta})$ for the complete stress-state space. In this work, the Modified Mohr-Coulomb (MMC) locus developed by [28,29] was calibrated due to its renowned accuracy in failure modelling of ductile AHSS grades. Eq. (7) states the MMC equation, reduced to von Mises plasticity, where parameters $C_1$ to $C_3$ were calibrated with a least-squares fitting to the experimentally obtained values of the stress-state dependent effective plastic failure strains.

$$ \varepsilon_f(\eta, \bar{\theta}) = \left( C_2 \left( \sqrt{\frac{1+C_1^2}{3}} \cos\left(\frac{\bar{\theta}\pi}{6}\right) + C_1 \left( \eta + \frac{1}{3}\sin\left(\frac{\bar{\theta}\pi}{6}\right) \right) \right) \right)^{-\frac{1}{C_3}} \quad (7) $$

Eq. (8) relates the Lode angle parameter $\bar{\theta}$ to the stress triaxiality for plane stress assumption, which is considered during the tensile testing of the thin tensile specimen. Table 3 states the values of the calibrated parameters $C_1$ to $C_3$ for the CP1000HD MMC failure locus.
The damage- and failure model accumulates a damage parameter *D* according to Eq. (4), where *n* is the rate of damage accumulation, ε<sub>f</sub>(η, θ̄) is the effective plastic failure strain, and ε̇<sub>p</sub> is the effective plastic strain increment.

$$ \dot{D} = \frac{n}{\varepsilon_f(\eta, \bar{\theta})} D^{(1-\frac{1}{n})} \dot{\varepsilon}_p \quad (4) $$

Similarly, an instability parameter *F* accumulates according to Eq. (5), where *e*<sub>i</sub>(η) is the effective plastic instability strain and *m* is the material degradation rate.

$$ \dot{F} = \frac{m}{\varepsilon_i(\eta)} F^{(1-\frac{1}{m})} \dot{\varepsilon}_p \quad (5) $$

When *F* = 1, damage coupling to the stress tensor is activated to account for the loss of load bearing capacity due to void growth. This reduction of material strength is common in ductile metals, such as CP1000HD or similar AHSS grades. The damage related coupling to the load bearing capacity is defined according to Eq. (6), where *D*<sub>c</sub> is the accumulated value of *D* when *F* = 1.

$$ \tilde{\sigma} = \sigma(1 - \tilde{D}) \text{ where } \tilde{D} = \left( \frac{D - D_c}{1 - D_c} \right)^m \quad (6) $$

When the damage parameter *D* reaches a critical threshold value of *D* = 0.99, the stiffness of the element is lost, and the element is removed from the post-processing for clearer visualization of the material failure.

Experimental values of effective plastic failure strain were obtained using Digital Image Correlation (DIC) according to the work by [27]. This method extracted the strain field with a square 0.1 mm grids continuously during tensile testing of various tensile specimen and the effective plastic failure strain and the corresponding stress-state was calculated for each specimen. The specimens were designed to deform and failed at designated stress-states, thus cover a wide range of stress-states. This procedure enabled calibration of a failure locus, providing ε<sub>f</sub>(η, θ̄) for the complete stress-state space. In this work, the Modified Mohr-Coulomb (MMC) locus developed by [28,29] was calibrated due to its renowned accuracy in failure modelling of ductile AHSS grades. Eq. (7) states the MMC equation, reduced to von Mises plasticity, where parameters *C*<sub>1</sub> to *C*<sub>3</sub> were calibrated with a least-squares fitting to the experimentally obtained values of the stress-state dependent effective plastic failure strains.

$$ \varepsilon_f(\eta, \bar{\theta}) = \left( C_2 \left( \sqrt{\frac{1+C_1^2}{3}} \cos\left(\frac{\bar{\theta}\pi}{6}\right) + C_1 \left( \eta + \frac{1}{3}\sin\left(\frac{\bar{\theta}\pi}{6}\right) \right) \right) \right)^{-\frac{1}{C_3}} \quad (7) $$

Eq. (8) relates the Lode angle parameter θ̄ to the stress triaxiality for plane stress assumption, which is considered during the tensile testing of the thin tensile specimen. Table 3 states the values of the calibrated parameters *C*<sub>1</sub> to *C*<sub>3</sub> for the CP1000HD MMC failure locus.
$$ \bar{\theta} = 1 - \frac{2}{\pi} \cos^{-1} \left( -\frac{27}{2} \eta \left( \eta^2 - \frac{1}{3} \right) \right) \qquad (8) $$

<table><caption>Table 3: Calibrated MMC parameters for the CP1000HD material.</caption><thead><tr><th>C<sub>1</sub></th><th>C<sub>2</sub></th><th>C<sub>3</sub></th></tr></thead><tbody><tr><td>0.1103</td><td>1.7166</td><td>0.4003</td></tr></tbody></table>

A critical topic of using such local phenomenological damage- and failure models is the mesh size dependency effects. As the experimental values of the effective plastic failure strains were determined using DIC facets of 0.1 mm, the values of $\epsilon_f(\eta, \bar{\theta})$ were only valid for such element size. Smaller elements than the nominal 0.1 mm could reach the failure strain values in localized zones earlier in the deformation event than the nominal sized elements, thus failure would be prematurely predicted. To overcome this mesh size implications, mesh regularization according to [30] was applied. The mesh regularization technique scales the failure strain values according to the element size such that the failure behavior matches for all element sizes. The regularization factors were determined iteratively on a small-scale model subjected to simple shear.

## Axisymmetric PFEM punching model

The axisymmetric PFEM model is schematically shown in Fig. 3, where the tools (dark grey) and blank (grey) are shown, along with the symmetry axis and the cutting clearance.

<figure><img src="image_1789.png" /><figcaption>Fig. 3: Schematic overview of the axisymmetric PFEM model.</figcaption></figure>

Small strain elasticity was applied to the tool parts, while the blank was assigned the elasto-plastic material model combined with the ductile damage model. A mixed displacement-pressure formulation was applied to the blank for avoiding volume locking issues that otherwise can occur using triangular elements with a single Gauss point. The mixed displacement theory was based on the work by Rodriguez et al. [18].

The process parameters of the various load cases are stated in Table 4, where the cutting die diameter was changed to vary the cutting clearance. As seen in Table 4, the tool edge radii were assumed to be circular with a radius of 30 µm, which represents sharp cutting tools. Laboratory punching experiments using the same clearances as in Table 4 were conducted with punching speeds of 0.05-2 mm/s which can be estimated as quasi-static conditions. The punching experiments were conducted using a servo-hydraulic clinching machine equipped with a dedicated
$$ \bar{\theta} = 1 - \frac{2}{\pi} \cos^{-1} \left( -\frac{27}{2} \eta \left( \eta^2 - \frac{1}{3} \right) \right) \quad (8) $$

<table><caption>Table 3: Calibrated MMC parameters for the CP1000HD material.</caption><thead><tr><th>C<sub>1</sub></th><th>C<sub>2</sub></th><th>C<sub>3</sub></th></tr></thead><tbody><tr><td>0.1103</td><td>1.7166</td><td>0.4003</td></tr></tbody></table>

A critical topic of using such local phenomenological damage- and failure models is the mesh size dependency effects. As the experimental values of the effective plastic failure strains were determined using DIC facets of 0.1 mm, the values of $\epsilon_f(\eta, \bar{\theta})$ were only valid for such element size. Smaller elements than the nominal 0.1 mm could reach the failure strain values in localized zones earlier in the deformation event than the nominal sized elements, thus failure would be prematurely predicted. To overcome this mesh size implications, mesh regularization according to [30] was applied. The mesh regularization technique scales the failure strain values according to the element size such that the failure behavior matches for all element sizes. The regularization factors were determined iteratively on a small-scale model subjected to simple shear.

## Axisymmetric PFEM punching model

The axisymmetric PFEM model is schematically shown in Fig. 3, where the tools (dark grey) and blank (grey) are shown, along with the symmetry axis and the cutting clearance.

<figure><img src="image_1787.png" /><figcaption>Fig. 3: Schematic overview of the axisymmetric PFEM model.</figcaption></figure>

Small strain elasticity was applied to the tool parts, while the blank was assigned the elasto-plastic material model combined with the ductile damage model. A mixed displacement-pressure formulation was applied to the blank for avoiding volume locking issues that otherwise can occur using triangular elements with a single Gauss point. The mixed displacement theory was based on the work by Rodriguez et al. [18].

The process parameters of the various load cases are stated in Table 4, where the cutting die diameter was changed to vary the cutting clearance. As seen in Table 4, the tool edge radii were assumed to be circular with a radius of 30 µm, which represents sharp cutting tools. Laboratory punching experiments using the same clearances as in Table 4 were conducted with punching speeds of 0.05-2 mm/s which can be estimated as quasi-static conditions. The punching experiments were conducted using a servo-hydraulic clinching machine equipped with a dedicated
ISO 16630 HET tool according to [31]. The low cutting speeds justifies the lack of strain rate dependency in the PFEM shear cutting model.

<table><caption>Table 4: Process parameters for experimental and numerical punching configurations, showing the punch diameter ($D_{Punch}$), die diameter ($D_{Die}$), punch edge radius ($R_{Punch,edge}$), die edge radius ($R_{Die,edge}$) and blank thickness ($T_{Blank}$).</caption><thead><tr><th>Clearance [%]</th><th>D<sub>Punch</sub> [mm]</th><th>D<sub>Die</sub> [mm]</th><th>R<sub>Punch,edge</sub> [µm]</th><th>R<sub>Die,edge</sub> [µm]</th><th>T<sub>Blank</sub> [mm]</th></tr></thead><tbody><tr><td>5.3</td><td>9.996</td><td>10.155</td><td>30</td><td>30</td><td>1.5</td></tr><tr><td>12.1</td><td>9.996</td><td>10.360</td><td>30</td><td>30</td><td>1.5</td></tr><tr><td>20.5</td><td>9.996</td><td>10.612</td><td>30</td><td>30</td><td>1.5</td></tr><tr><td>27.0</td><td>9.996</td><td>10.806</td><td>30</td><td>30</td><td>1.5</td></tr></tbody></table>

## Results and discussion

The results from the different experimental and numerical hole punching configurations shown in Table 4 are presented in Fig. 4. It compares the distribution of each cut edge parameter (Roll-over, Burnish, Fracture and Burr) over the range of cutting clearances, 5.3%-27.0%, and the error bars in Fig. 4 presents the circumferential variation of the experimental cut edge parameters. The validation results shows that the PFEM numerical modelling can with good accuracy predict the experimental cut edge morphology. The numerical model can predict the appearance of burr at 27.0% cutting clearance, which according to Larour et al. [12] was proven as detrimental to edge formability. The results shows that the axisymmetric assumption was well justified for 12.1% and 20.5% cutting clearance, while a significant circumferential variation for 5.3% cutting clearance and a partial burr formation for 27.0% cutting clearance need 3D capabilities to be modelled exactly. However, this will increase the simulation time tremendously.

<figure><img src="image_1790.png" /><figcaption>Fig. 4: Experimental (light grey) and numerical (dark grey) hole punching results in terms of cut edge parameters for the range of cutting clearances.</figcaption></figure>

For 5.3% cutting clearance, the formation of secondary burnish was distinguished, as presented by Fig. 5 b). Here, the mismatching fracture angles $\alpha_{Punch}$ and $\beta_{Die}$ cause the secondary burnish formation, as the cracks appearing at punch and could not be connected. However, the complex loading conditions of the secondary burnish formation, with bending and sudden change of fracture angle caused convergence issues using the implicit PFEM scheme. Therefore, the numerical modelling of the entire punching process of 5.3% was not able to finalize, but the fracture pattern of Fig. 5 b) manifests the formation of a secondary burnish surface. The cut edge parameters of Fig. 4 for 5.3% cutting clearance were furthermore based on the geometric markers of Fig. 5 b). Concludingly, further development of the PFEM implementation should incorporate explicit- or implicit dynamic schemes that can handle secondary burnish formation in a more computationally stable matter.
ISO 16630 HET tool according to [31]. The low cutting speeds justifies the lack of strain rate dependency in the PFEM shear cutting model.

<table><caption>Table 4: Process parameters for experimental and numerical punching configurations, showing the punch diameter ($D_{Punch}$), die diameter ($D_{Die}$), punch edge radius ($R_{Punch,edge}$), die edge radius ($R_{Die,edge}$) and blank thickness ($T_{Blank}$).</caption><thead><tr><td>Clearance [%]</td><td>D<sub>Punch</sub> [mm]</td><td>D<sub>Die</sub> [mm]</td><td>R<sub>Punch,edge</sub> [µm]</td><td>R<sub>Die,edge</sub> [µm]</td><td>T<sub>Blank</sub> [mm]</td></tr></thead><tbody><tr><td>5.3</td><td>9.996</td><td>10.155</td><td>30</td><td>30</td><td>1.5</td></tr><tr><td>12.1</td><td>9.996</td><td>10.360</td><td>30</td><td>30</td><td>1.5</td></tr><tr><td>20.5</td><td>9.996</td><td>10.612</td><td>30</td><td>30</td><td>1.5</td></tr><tr><td>27.0</td><td>9.996</td><td>10.806</td><td>30</td><td>30</td><td>1.5</td></tr></tbody></table>

## Results and discussion

The results from the different experimental and numerical hole punching configurations shown in Table 4 are presented in Fig. 4. It compares the distribution of each cut edge parameter (Roll-over, Burnish, Fracture and Burr) over the range of cutting clearances, 5.3%-27.0%, and the error bars in Fig. 4 presents the circumferential variation of the experimental cut edge parameters. The validation results shows that the PFEM numerical modelling can with good accuracy predict the experimental cut edge morphology. The numerical model can predict the appearance of burr at 27.0% cutting clearance, which according to Larour et al. [12] was proven as detrimental to edge formability. The results shows that the axisymmetric assumption was well justified for 12.1% and 20.5% cutting clearance, while a significant circumferential variation for 5.3% cutting clearance and a partial burr formation for 27.0% cutting clearance need 3D capabilities to be modelled exactly. However, this will increase the simulation time tremendously.

<figure><img src="image_1788.png" /><figcaption>Fig. 4: Experimental (light grey) and numerical (dark grey) hole punching results in terms of cut edge parameters for the range of cutting clearances.</figcaption></figure>

For 5.3% cutting clearance, the formation of secondary burnish was distinguished, as presented by Fig. 5 b). Here, the mismatching fracture angles $\alpha_{Punch}$ and $\beta_{Die}$ cause the secondary burnish formation, as the cracks appearing at punch and could not be connected. However, the complex loading conditions of the secondary burnish formation, with bending and sudden change of fracture angle caused convergence issues using the implicit PFEM scheme. Therefore, the numerical modelling of the entire punching process of 5.3% was not able to finalize, but the fracture pattern of Fig. 5 b) manifests the formation of a secondary burnish surface. The cut edge parameters of Fig. 4 for 5.3% cutting clearance were furthermore based on the geometric markers of Fig. 5 b). Concludingly, further development of the PFEM implementation should incorporate explicit- or implicit dynamic schemes that can handle secondary burnish formation in a more computationally stable matter.
<figure><img src="image_1791.png" /><figcaption>Fig. 5: Cut edges a) 12.1% cutting clearance and for b) 5.3% cutting clearance. a) shows the final cut edge where the ordinary cut edge shapes of roll-over, burnish and fracture were distinguished. Here the matching fracture angles $(\alpha_{\text{Punch}}, \beta_{\text{Die}})$ creates a uniform fracture surface. Meanwhile b) shows the mismatching fracture angles $(\alpha_{\text{Punch}}, \beta_{\text{Die}})$ and the corresponding secondary burnish formation. The length of the secondary burnish surface is estimated from the length of Burnish 2.</figcaption></figure>

## Conclusions

Based on the comparison between experimental and numerical shear cutting results, following conclusions are drawn:

* The presented PFEM shear cutting model is an accurate numerical tool for predicting the cut edge morphology over a large range of cutting clearances. The PFEM scheme ensures that element aspect ratios are kept adequate, and the ductile damage modelling enables modelling of the fracture process.

* By predicting the appearance of both secondary burnish (small clearance) and burr (large clearance), the PFEM model is useful for determining the feasible cutting clearance range for the AHSS grade investigated.

* The good correlation between experimental and numerical cut edge morphologies indicates that the residual cut edge results are useful for subsequent analysis of edge forming of fatigue.

* Given the circumferential variations of the experimental cut edge results it is suggested to investigate 3D PFEM shear cutting analysis. Such approach could further enhance modelling of subsequent forming- or fatigue analyses.

## References

[1] A. Konieczny, T. Henderson, On formability limitations in stamping involving sheared edge stretching, SAE Technical Papers (2007). https://doi.org/10.4271/2007-01-0340

[2] H.C. Shih, C. Chiriac, M.F. Shi, The effects of AHSS shear edge conditions on edge fracture, ASME 2010 International Manufacturing Science and Engineering Conference, MSEC 2010 1 (2010) 599-608. https://doi.org/10.1115/MSEC2010-34062

[3] J. Dykeman, S. Malcolm, B. Yan, J. Chintamani, G. Huang, N. Ramisetti, H. Zhu, Characterization of edge fracture in various types of advanced high strength steel, SAE Technical Papers (2011). https://doi.org/10.4271/2011-01-1058
<figure><img src="image_1789.png" /><figcaption>Fig. 5: Cut edges a) 12.1% cutting clearance and for b) 5.3% cutting clearance. a) shows the final cut edge where the ordinary cut edge shapes of roll-over, burnish and fracture were distinguished. Here the matching fracture angles $(\alpha_{\text{Punch}}, \beta_{\text{Die}})$ creates a uniform fracture surface. Meanwhile b) shows the mismatching fracture angles $(\alpha_{\text{Punch}}, \beta_{\text{Die}})$ and the corresponding secondary burnish formation. The length of the secondary burnish surface is estimated from the length of Burnish 2.</figcaption></figure>

## Conclusions

Based on the comparison between experimental and numerical shear cutting results, following conclusions are drawn:

* The presented PFEM shear cutting model is an accurate numerical tool for predicting the cut edge morphology over a large range of cutting clearances. The PFEM scheme ensures that element aspect ratios are kept adequate, and the ductile damage modelling enables modelling of the fracture process.

* By predicting the appearance of both secondary burnish (small clearance) and burr (large clearance), the PFEM model is useful for determining the feasible cutting clearance range for the AHSS grade investigated.

* The good correlation between experimental and numerical cut edge morphologies indicates that the residual cut edge results are useful for subsequent analysis of edge forming of fatigue.

* Given the circumferential variations of the experimental cut edge results it is suggested to investigate 3D PFEM shear cutting analysis. Such approach could further enhance modelling of subsequent forming- or fatigue analyses.

## References

[1] A. Konieczny, T. Henderson, On formability limitations in stamping involving sheared edge stretching, SAE Technical Papers (2007). https://doi.org/10.4271/2007-01-0340

[2] H.C. Shih, C. Chiriac, M.F. Shi, The effects of AHSS shear edge conditions on edge fracture, ASME 2010 International Manufacturing Science and Engineering Conference, MSEC 2010 1 (2010) 599-608. https://doi.org/10.1115/MSEC2010-34062

[3] J. Dykeman, S. Malcolm, B. Yan, J. Chintamani, G. Huang, N. Ramisetti, H. Zhu, Characterization of edge fracture in various types of advanced high strength steel, SAE Technical Papers (2011). https://doi.org/10.4271/2011-01-1058
[4] D.J. Thomas, Understanding the effects of mechanical and laser cut-edges to prevent formability ruptures during automotive manufacturing, Journal of Failure Analysis and Prevention 13 (2013) 451-462. https://doi.org/10.1007/s11668-013-9696-z

[5] D. Frómeta, M. Tedesco, J. Calvo, A. Lara, S. Molas, D. Casellas, Assessing edge cracking resistance in AHSS automotive parts by the Essential Work of Fracture methodology, J Phys Conf Ser 896 (2017). https://doi.org/10.1088/1742-6596/896/1/012102

[6] A. Lara, I. Picas, D. Casellas, Effect of the cutting process on the fatigue behaviour of press hardened and high strength dual phase steels, J Mater Process Technol 213 (2013) 1908-1919. https://doi.org/10.1016/j.jmatprotec.2013.05.003

[7] I. Paetzold, F. Dittmann, M. Feistle, R. Golle, P. Haefele, H. Hoffmann, W. Volk, Influence of shear cutting parameters on the fatigue behavior of a dual-phase steel, J Phys Conf Ser 896 (2017). https://doi.org/10.1088/1742-6596/896/1/012107

[8] J. Stahl, I. Pätzold, R. Golle, C. Sunderkötter, H. Sieurin, W. Volk, Effect of one- And two-stage shear cutting on the fatigue strength of truck frame parts, Journal of Manufacturing and Materials Processing 4 (2020). https://doi.org/10.3390/JMMP4020052

[9] T. Shiozaki, Y. Tamai, T. Urabe, Effect of residual stresses on fatigue strength of high strength steel sheets with punched holes, Int J Fatigue 80 (2015) 324-331. https://doi.org/10.1016/j.ijfatigue.2015.06.018

[10] S. Parareda, D. Fr, D. Casellas, H. Sieurin, A. Mateo, Understanding the Fatigue Notch Sensitivity of High-Strength Steels through Fracture Toughness, Metals (Basel) 13 (2023) 1117. https://doi.org/10.3390/met13061117

[11] D. Gustafsson, S. Parareda, L. Ortiz-Membrado, A. Mateo, E. Jiménez-Piqué, E. Olsson, Simulation of metal punching and trimming using minimal experimental characterization, J Mater Process Technol 321 (2023) 118148. https://doi.org/10.1016/j.jmatprotec.2023.118148

[12] P. Larour, J. Hinterdorfer, L. Wagner, J. Freudenthaler, A. Grünsteidl, M. Kerschbaum, Stretch flangeability of AHSS automotive grades versus cutting tool clearance, wear, angle and radial strain gradients, IOP Conf Ser Mater Sci Eng 1238 (2022) 012041. https://doi.org/10.1088/1757-899X/1238/1/012041

[13] O. Sandin, J.M.R. Prieto, S. Hammarberg, D. Casellas, Numerical modelling of shear cutting using particle methods, IOP Conf Ser Mater Sci Eng 1284 (2023) 012048. https://doi.org/10.1088/1757-899x/1284/1/012048

[14] X. Ye, J. Manuel, R. Prieto, R. Müller, An Improved Particle Finite Element Method for the Simulation of Machining Processes, 89 (2020) 13:1-13:0. https://doi.org/10.4230/OASIcs.iPMVM.2020.13

[15] J.M. Rodríguez, J.M. Carbonell, J.C. Cante, J. Oliver, Continuous chip formation in metal cutting processes using the Particle Finite Element Method (PFEM), Int J Solids Struct 120 (2017) 81-102. https://doi.org/10.1016/j.ijsolstr.2017.04.030

[16] E. Oñate, A. Franci, J.M. Carbonell, A particle finite element method for analysis of industrial forming processes, Comput Mech 54 (2014) 85-107. https://doi.org/10.1007/S00466-014-1016-2

[17] S.R. Idelsohn, E. Onate, F. Del Pin, The particle finite element method: A powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Numer Methods Eng 61 (2004) 964-989. https://doi.org/10.1002/nme.1096

[18] J.M. Rodriguez, J.M. Carbonell, J.C. Cante, J. Oliver, The particle finite element method (PFEM) in thermo-mechanical problems, Int J Numer Methods Eng 107 (2016) 733-785. https://doi.org/10.1002/NME.5186
[4] D.J. Thomas, Understanding the effects of mechanical and laser cut-edges to prevent formability ruptures during automotive manufacturing, Journal of Failure Analysis and Prevention 13 (2013) 451-462. https://doi.org/10.1007/s11668-013-9696-z

[5] D. Frómeta, M. Tedesco, J. Calvo, A. Lara, S. Molas, D. Casellas, Assessing edge cracking resistance in AHSS automotive parts by the Essential Work of Fracture methodology, J Phys Conf Ser 896 (2017). https://doi.org/10.1088/1742-6596/896/1/012102

[6] A. Lara, I. Picas, D. Casellas, Effect of the cutting process on the fatigue behaviour of press hardened and high strength dual phase steels, J Mater Process Technol 213 (2013) 1908-1919. https://doi.org/10.1016/j.jmatprotec.2013.05.003

[7] I. Paetzold, F. Dittmann, M. Feistle, R. Golle, P. Haefele, H. Hoffmann, W. Volk, Influence of shear cutting parameters on the fatigue behavior of a dual-phase steel, J Phys Conf Ser 896 (2017). https://doi.org/10.1088/1742-6596/896/1/012107

[8] J. Stahl, I. Pätzold, R. Golle, C. Sunderkötter, H. Sieurin, W. Volk, Effect of one- And two-stage shear cutting on the fatigue strength of truck frame parts, Journal of Manufacturing and Materials Processing 4 (2020). https://doi.org/10.3390/JMMP4020052

[9] T. Shiozaki, Y. Tamai, T. Urabe, Effect of residual stresses on fatigue strength of high strength steel sheets with punched holes, Int J Fatigue 80 (2015) 324-331. https://doi.org/10.1016/j.ijfatigue.2015.06.018

[10] S. Parareda, D. Fr, D. Casellas, H. Sieurin, A. Mateo, Understanding the Fatigue Notch Sensitivity of High-Strength Steels through Fracture Toughness, Metals (Basel) 13 (2023) 1117. https://doi.org/10.3390/met13061117

[11] D. Gustafsson, S. Parareda, L. Ortiz-Membrado, A. Mateo, E. Jiménez-Piqué, E. Olsson, Simulation of metal punching and trimming using minimal experimental characterization, J Mater Process Technol 321 (2023) 118148. https://doi.org/10.1016/j.jmatprotec.2023.118148

[12] P. Larour, J. Hinterdorfer, L. Wagner, J. Freudenthaler, A. Grünsteidl, M. Kerschbaum, Stretch flangeability of AHSS automotive grades versus cutting tool clearance, wear, angle and radial strain gradients, IOP Conf Ser Mater Sci Eng 1238 (2022) 012041. https://doi.org/10.1088/1757-899X/1238/1/012041

[13] O. Sandin, J.M.R. Prieto, S. Hammarberg, D. Casellas, Numerical modelling of shear cutting using particle methods, IOP Conf Ser Mater Sci Eng 1284 (2023) 012048. https://doi.org/10.1088/1757-899X/1284/1/012048

[14] X. Ye, J. Manuel, R. Prieto, R. Müller, An Improved Particle Finite Element Method for the Simulation of Machining Processes, 89 (2020) 13:1-13:0. https://doi.org/10.4230/OASIcs.iPMVM.2020.13

[15] J.M. Rodríguez, J.M. Carbonell, J.C. Cante, J. Oliver, Continuous chip formation in metal cutting processes using the Particle Finite Element Method (PFEM), Int J Solids Struct 120 (2017) 81-102. https://doi.org/10.1016/j.ijsolstr.2017.04.030

[16] E. Oñate, A. Franci, J.M. Carbonell, A particle finite element method for analysis of industrial forming processes, Comput Mech 54 (2014) 85-107. https://doi.org/10.1007/S00466-014-1016-2

[17] S.R. Idelsohn, E. Onate, F. Del Pin, The particle finite element method: A powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Numer Methods Eng 61 (2004) 964-989. https://doi.org/10.1002/nme.1096

[18] J.M. Rodriguez, J.M. Carbonell, J.C. Cante, J. Oliver, The particle finite element method (PFEM) in thermo-mechanical problems, Int J Numer Methods Eng 107 (2016) 733-785. https://doi.org/10.1002/NME.5186
[19] Juan Manuel Rodriguez Prieto, Numerical modeling of metal cutting processes using the Particle Finite Element Method, (2013) 185.

[20] J.M. Rodriguez, S. Larsson, J.M. Carbonell, P. Jonsén, Implicit or explicit time integration schemes in the PFEM modeling of metal cutting processes, Comput Part Mech 9 (2022) 709–733.
https://doi.org/10.1007/s40571-021-00439-5

[21] J.M. Rodriguez Prieto, J.M. Carbonell, J.C. Cante, J. Oliver, P. Jonsén, Generation of segmental chips in metal cutting modeled with the PFEM, Comput Mech 61 (2018) 639–655.
https://doi.org/10.1007/s00466-017-1442-z

[22] E. Oñate, S.R. Idelsohn, F. Del Pin, R. Aubry, the Particle Finite Element Method — an Overview, Int J Comput Methods 01 (2004) 267–307.
https://doi.org/10.1142/s0219876204000204

[23] J.R. Shewchuk, Condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations, in: Proceedings of the Annual Symposium on Computational Geometry, Minneapolis, MN, 1998: pp. 76–85. https://doi.org/10.1145/276884.276893

[24] K. Stiebler, H.D. Kunze, E. El-Magd, Description of the flow behaviour of a high strength austenitic steel under biaxial loading by a constitutive equation, Nuclear Engineering and Design 127 (1991) 85–93. https://doi.org/10.1016/0029-5493(91)90041-F

[25] ISO 16808:2014, Metallic materials — Sheet and strip — Determination of biaxial stress-strain curve by means of bulge test with optical measuring systems, (2014).

[26] F. Neukamm, M. Feucht, A. Haufe, K. Roll, On Closing the Constitutive Gap Between Forming and Crash Simulation, in: 10th International LS-DYNA Users Conference, 2008: pp. 12–21.

[27] T. Sjöberg, S. Marth, J. Kajberg, H.-A. Häggblad, Experimental characterisation of the evolution of triaxiality stress state for sheet metal materials, European Journal of Mechanics, A/Solids 66 (2017) 279–286. https://doi.org/10.1016/j.euromechsol.2017.07.013

[28] Y. Bai, X. Teng, T. Wierzbicki, On the application of stress triaxiality formula for plane strain fracture testing, Journal of Engineering Materials and Technology, Transactions of the ASME 131 (2009) 0210021–02100210. https://doi.org/10.1115/1.3078390

[29] Y. Bai, T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture, Int J Fract 161 (2010) 1–20. https://doi.org/10.1007/s10704-009-9422-8

[30] F. Andrade, M. Feucht, A. Haufe, F. Neukamm, An incremental stress state dependent damage model for ductile failure prediction, Int J Fract 200 (2016) 127–150.
https://doi.org/10.1007/s10704-016-0081-2

[31] ISO 16630:2017, Metallic materials — Sheet and strip — Hole expanding test, International Standard Second Edi (2017).
[19] Juan Manuel Rodriguez Prieto, Numerical modeling of metal cutting processes using the Particle Finite Element Method, (2013) 185.

[20] J.M. Rodriguez, S. Larsson, J.M. Carbonell, P. Jonsén, Implicit or explicit time integration schemes in the PFEM modeling of metal cutting processes, Comput Part Mech 9 (2022) 709–733.
https://doi.org/10.1007/s40571-021-00439-5

[21] J.M. Rodriguez Prieto, J.M. Carbonell, J.C. Cante, J. Oliver, P. Jonsén, Generation of segmental chips in metal cutting modeled with the PFEM, Comput Mech 61 (2018) 639–655.
https://doi.org/10.1007/s00466-017-1442-z

[22] E. Oñate, S.R. Idelsohn, F. Del Pin, R. Aubry, the Particle Finite Element Method — an Overview, Int J Comput Methods 01 (2004) 267–307.
https://doi.org/10.1142/s0219876204000204

[23] J.R. Shewchuk, Condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations, in: Proceedings of the Annual Symposium on Computational Geometry, Minneapolis, MN, 1998: pp. 76–85. https://doi.org/10.1145/276884.276893

[24] K. Stiebler, H.D. Kunze, E. El-Magd, Description of the flow behaviour of a high strength austenitic steel under biaxial loading by a constitutive equation, Nuclear Engineering and Design 127 (1991) 85–93. https://doi.org/10.1016/0029-5493(91)90041-F

[25] ISO 16808:2014, Metallic materials — Sheet and strip — Determination of biaxial stress-strain curve by means of bulge test with optical measuring systems, (2014).

[26] F. Neukamm, M. Feucht, A. Haufe, K. Roll, On Closing the Constitutive Gap Between Forming and Crash Simulation, in: 10th International LS-DYNA Users Conference, 2008: pp. 12–21.

[27] T. Sjöberg, S. Marth, J. Kajberg, H.-A. Häggblad, Experimental characterisation of the evolution of triaxiality stress state for sheet metal materials, European Journal of Mechanics, A/Solids 66 (2017) 279–286. https://doi.org/10.1016/j.euromechsol.2017.07.013

[28] Y. Bai, X. Teng, T. Wierzbicki, On the application of stress triaxiality formula for plane strain fracture testing, Journal of Engineering Materials and Technology, Transactions of the ASME 131 (2009) 0210021–02100210. https://doi.org/10.1115/1.3078390

[29] Y. Bai, T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture, Int J Fract 161 (2010) 1–20. https://doi.org/10.1007/s10704-009-9422-8

[30] F. Andrade, M. Feucht, A. Haufe, F. Neukamm, An incremental stress state dependent damage model for ductile failure prediction, Int J Fract 200 (2016) 127–150.
https://doi.org/10.1007/s10704-016-0081-2

[31] ISO 16630:2017, Metallic materials — Sheet and strip — Hole expanding test, International Standard Second Edi (2017).
# Green machining of Ti6Al4V/Polymers composite made by pellets additive manufacturing

BOSSU Julien<fnref n="1" />,ᵃ*, RIVIÈRE-LORPHÈVRE Edouard<fnref n="1" />, SPITAELS Laurent<fnref n="1" />, DUCOBU François<fnref n="1" />, DELAUNOIS Fabienne<fnref n="1" />, MARTIC Grégory<fnref n="2" />, DELMOTTE Cathy<fnref n="2" />, JUSTE Enrique<fnref n="2" />, PETIT Fabrice<fnref n="2" />

**Keywords:** Green Machining, Ti6Al4V, Polymers, Milling, Pellets Additive Manufacturing

**Abstract.** The poor surface finish (arithmetic roughness $R_a$ around 40 µm) of additive manufactured parts leads to the development of hybrid machines to increase the quality of the final part in a lower production time. Hybrid machine already exists for DED (Directed Energy Deposition) and SLS (Selective Laser Sintering) but due to the hardness and the abrasiveness of the sintered material, important tool wear or surface defects on the workpiece can be observed. Therefore, reduced cutting parameters and dedicated cutting tool must then be used which increase the cost of machining operation and the time to produce a part. Green machining can limit these problems: the machining step is performed before sintering when the part does not have its final properties. This kind of material has a pseudo-plastic behavior so machining can be performed with high productivity thanks to lower cutting forces and reduced tool wear. An innovative use of the tool-material couple standard AFNOR Norm NF E66-520 (1999) dedicated to metals is proposed to determine the cutting parameters of a composite based on titanium alloys Ti6Al4V and polymers by measuring surface roughness and cutting forces. A tool dedicated to thermoplastic polymers was tested. Cutting forces and surface roughness (arithmetic surface roughness $R_a$ and total surface roughness $R_t$) were evaluated for each test. Twelve sets of parameters considering the cutting speed $v_c$, the axial depth of cut $a_p$, the radial depth of cut $a_e$ and the feed per tooth $f_z$ as variables were tested. For the range of parameters selected, it is possible to achieve a satisfactory surface finish with low cutting forces ($R_a$ remains close to 3.2 µm and cutting forces < 5 N) and stable results.

**Introduction**

Pellets Additive Manufacturing PAM is an additive technology similar to FDM (Fused Deposition Modeling) process which uses injection molding pellets as raw material. Pellets are composed of a mix between a metal or ceramic powder (app. 90 wt.%) with a binder (polymer's blend and additives) around 10 wt.% [1,2]. The binder added to the feedstock has many functions compared to the pure metal or ceramic [2]:

- Reducing the abrasiveness of the powder,

- Inducing the rheological properties,

- Influencing the shaping temperature,

- Allowing the creation of porosity during the debinding step.

The method to manufacture a part by PAM technology is composed of 4 steps:

1. Powder blending (metal or ceramic solid loading + binder (blend of polymers and additives)

<figure><img src="image_1792.png" /></figure>

<footnote n="1">¹University of Mons, Faculty of Engineering, Materials Research Institute, Place du Parc 20, 7000 Mons, Belgium</footnote>

<footnote n="2">²BCRC: Belgian Ceramic Research Centre, Avenue du Gouverneur Émile Cornez 4, 7000 Mons, Belgium</footnote>

<footnote>ᵃjulien.bossu@umons.ac.be</footnote>
# Green machining of Ti6Al4V/Polymers composite made by pellets additive manufacturing

BOSSU Julien<fnref n="1" />,ᵃ*, RIVIÈRE-LORPHÈVRE Edouard<fnref n="1" />, SPITAELS Laurent<fnref n="1" />, DUCOBU François<fnref n="1" />, DELAUNOIS Fabienne<fnref n="1" />, MARTIC Grégory<fnref n="2" />, DELMOTTE Cathy<fnref n="2" />, JUSTE Enrique<fnref n="2" />, PETIT Fabrice<fnref n="2" />

**Keywords:** Green Machining, Ti6Al4V, Polymers, Milling, Pellets Additive Manufacturing

**Abstract.** The poor surface finish (arithmetic roughness *R*<sub>a</sub> around 40 µm) of additive manufactured parts leads to the development of hybrid machines to increase the quality of the final part in a lower production time. Hybrid machine already exists for DED (Directed Energy Deposition) and SLS (Selective Laser Sintering) but due to the hardness and the abrasiveness of the sintered material, important tool wear or surface defects on the workpiece can be observed. Therefore, reduced cutting parameters and dedicated cutting tool must then be used which increase the cost of machining operation and the time to produce a part. Green machining can limit these problems: the machining step is performed before sintering when the part does not have its final properties. This kind of material has a pseudo-plastic behavior so machining can be performed with high productivity thanks to lower cutting forces and reduced tool wear. An innovative use of the tool-material couple standard AFNOR Norm NF E66-520 (1999) dedicated to metals is proposed to determine the cutting parameters of a composite based on titanium alloys Ti6Al4V and polymers by measuring surface roughness and cutting forces. A tool dedicated to thermoplastic polymers was tested. Cutting forces and surface roughness (arithmetic surface roughness *R*<sub>a</sub> and total surface roughness *R*<sub>t</sub>) were evaluated for each test. Twelve sets of parameters considering the cutting speed *v*<sub>c</sub>, the axial depth of cut *a*<sub>p</sub>, the radial depth of cut *a*<sub>e</sub> and the feed per tooth *f*<sub>z</sub> as variables were tested. For the range of parameters selected, it is possible to achieve a satisfactory surface finish with low cutting forces (*R*<sub>a</sub> remains close to 3.2 µm and cutting forces < 5 N) and stable results.

**Introduction**

Pellets Additive Manufacturing PAM is an additive technology similar to FDM (Fused Deposition Modeling) process which uses injection molding pellets as raw material. Pellets are composed of a mix between a metal or ceramic powder (app. 90 wt.%) with a binder (polymer's blend and additives) around 10 wt.% [1,2]. The binder added to the feedstock has many functions compared to the pure metal or ceramic [2]:

- Reducing the abrasiveness of the powder,

- Inducing the rheological properties,

- Influencing the shaping temperature,

- Allowing the creation of porosity during the debinding step.

The method to manufacture a part by PAM technology is composed of 4 steps:

1. Powder blending (metal or ceramic solid loading + binder (blend of polymers and additives)

<figure><img src="image_1790.png" /></figure>

<footnote n="1">¹University of Mons, Faculty of Engineering, Materials Research Institute, Place du Parc 20, 7000 Mons, Belgium</footnote>

<footnote n="2">²BCRC : Belgian Ceramic Research Centre, Avenue du Gouverneur Émile Cornez 4, 7000 Mons, Belgium</footnote>

<footnote>ᵃjulien.bossu@umons.ac.be</footnote>
2. Printing (PAM)

3. Debinding (to remove the binder)

4. Sintering (to give the final mechanical properties to the part) [3]

Nevertheless, additive manufacturing as PAM or FDM process has an inherent disadvantage of additive manufacturing called the staircase effect that often creates a surface finish out of tolerance for industry expectations. Moreover, titanium and its alloys are very difficult to machine at the dense state because of its abrasiveness that causes a huge tool abrasive wear and due to its mechanical properties as a relatively high tensile strength, low ductile yield, 50% lower modulus of elasticity (104 GPa) and approximately 80% lower thermal conductivity than that of steel which create diffusion wear that improve the machining operation cost for dense part [4].

The poor surface finish ($R_d$ corresponding to the average roughness in the area between the roughness profile and its mean line is around 40 µm) of parts produced by FDM-like processes requiring finishing machining leads to the development of hybrid machines to increase the quality of the final part in a lower production time [5,6,7].

Hybrid machines already exist for DED (Directed Energy Deposition) and SLS (Selective Laser Sintering) but, due to the hardness and the abrasiveness of the sintered material, important tool wear or surface defects on the workpiece can be observed so reduced cutting parameters have to be selected. A dedicated cutting tool must then be used which increases the cost of machining operation and the time to produce a given part [6].

To address this issue, machining in the raw state, also known as the green state, enables the finishing of parts produced through the additive process before sintering, while the binder is still present. This makes the machining process easier compared to machining sintered materials with all their mechanical properties. Machining in the green state results in parts with mechanical properties similar to those of the polymer used, such as polyamide (e.g. PA66) [8-9].

The aim of this study is to find a wide range of stable cutting parameters to obtain a correct surface quality ($R_d \le 3.2$ µm) based on a previous study [8] carried out on a raw zirconia/polymer composite and the tool-material couple standard AFNOR NF E66-520 (1999) [10] also proving that this method can be used for all filler/polymer composite materials. In the approach to hybrid use, the cutting forces are also recorded in order to determine whether there is a risk of the workpiece detaching from the build plate during the machining step.

## Material

The experiments were performed using green titanium parts produced on a PAM printer Pollen AM Series MC. The feedstock used is made of 90 wt.% of Ti6Al4V powder and 10 wt% of thermoplastic binder (water-soluble but unknown composition). It is commercialized with the reference polyMIM® Ti6Al4V F 130E (80354) by the PolyMIM GmbH company (Bad Sobernheim, Germany). The geometry of the parts and their main dimensions are given in Fig. 1. It is composed of a cube (20×20 mm) on top of a cylinder (d=15 mm). The cube is first printed (on the building plate) followed by the cylinder. This allows us to obtain the parts without the need for a support structure. The main printing parameters are given in Table 1.
2. Printing (PAM)

3. Debinding (to remove the binder)

4. Sintering (to give the final mechanical properties to the part) [3]

Nevertheless, additive manufacturing as PAM or FDM process has an inherent disadvantage of additive manufacturing called the staircase effect that often creates a surface finish out of tolerance for industry expectations. Moreover, titanium and its alloys are very difficult to machine at the dense state because of its abrasiveness that causes a huge tool abrasive wear and due to its mechanical properties as a relatively high tensile strength, low ductile yield, 50% lower modulus of elasticity (104 GPa) and approximately 80% lower thermal conductivity than that of steel which create diffusion wear that improve the machining operation cost for dense part [4].

The poor surface finish ($R_d$ corresponding to the average roughness in the area between the roughness profile and its mean line is around 40 µm) of parts produced by FDM-like processes requiring finishing machining leads to the development of hybrid machines to increase the quality of the final part in a lower production time [5,6,7].

Hybrid machines already exist for DED (Directed Energy Deposition) and SLS (Selective Laser Sintering) but, due to the hardness and the abrasiveness of the sintered material, important tool wear or surface defects on the workpiece can be observed so reduced cutting parameters have to be selected. A dedicated cutting tool must then be used which increases the cost of machining operation and the time to produce a given part [6].

To address this issue, machining in the raw state, also known as the green state, enables the finishing of parts produced through the additive process before sintering, while the binder is still present. This makes the machining process easier compared to machining sintered materials with all their mechanical properties. Machining in the green state results in parts with mechanical properties similar to those of the polymer used, such as polyamide (e.g. PA66) [8-9].

The aim of this study is to find a wide range of stable cutting parameters to obtain a correct surface quality ($R_d \le 3.2$ µm) based on a previous study [8] carried out on a raw zirconia/polymer composite and the tool-material couple standard AFNOR NF E66-520 (1999) [10] also proving that this method can be used for all filler/polymer composite materials. In the approach to hybrid use, the cutting forces are also recorded in order to determine whether there is a risk of the workpiece detaching from the build plate during the machining step.

## Material

The experiments were performed using green titanium parts produced on a PAM printer Pollen AM Series MC. The feedstock used is made of 90 wt.% of Ti6Al4V powder and 10 wt% of thermoplastic binder (water-soluble but unknown composition). It is commercialized with the reference polyMIM® Ti6Al4V F 130E (80354) by the PolyMIM GmbH company (Bad Sobernheim, Germany). The geometry of the parts and their main dimensions are given in Fig. 1. It is composed of a cube (20×20 mm) on top of a cylinder (d=15 mm). The cube is first printed (on the building plate) followed by the cylinder. This allows us to obtain the parts without the need for a support structure. The main printing parameters are given in Table 1.
<table><caption>Table 1 : Main printing parameter</caption><tr><td>Nozzle diameter</td><td>1 [mm]</td></tr><tr><td>Layer thickness</td><td>0.35 [mm]</td></tr><tr><td>First layer thickness</td><td>0.3 [mm]</td></tr><tr><td>Extrusion temperature</td><td>250 [°C]</td></tr><tr><td>Build platform temperature</td><td>70 [°C]</td></tr><tr><td>Infill strategy</td><td>Lines</td></tr><tr><td>Infill percentage</td><td>100 [%]</td></tr><tr><td>Printing time</td><td>28 [min]</td></tr></table>

<figure><img src="image_1793.png" /><figcaption>Figure 1 : Part geometry and main dimensions.</figcaption></figure>

## Method

A robotic machining cell composed of a Stäubli TX200 robot fitted with a Teknomotor ATC71 electrospindle was used for the milling operations. The spindle can deliver up to 7.8 kW with a maximal rotational speed of 24000 rpm. A three-jaw chuck was used to clamp the part from the cylinder (Fig. 3) which was attached to a Kistler 9256C2 dynamometer.

The used cutting tool showed in Fig. 2 is originally dedicated to the milling of thermoplastics as PA66. The supplier company is Hoffmann and it's sold with the reference 209425-6. It has a 6 mm diameter with three cutting edges having a double helix angle and a maximal cutting length of 19 mm. It is made in tungsten carbide without any coating.

As presented in a previous study [8], this tool showed great capability to generate smooth and shiny surfaces with $R_a < 1.6 \ \mu m$ in finishing operations [8-9] for composite ceramic/polymer. This study was based on the tool-material couple standard AFNOR NF E66-520-6 (1999) [10] as the present study. Four cutting parameters were used: the cutting speed ($v_c$) corresponding to the speed at which the cutting tool or the workpiece moves relative to each other during machining, the feed per tooth ($f_z$) corresponding to the distance a cutting tool advances per tooth for each revolution of the spindle, the axial depth of cut ($a_p$) representing the depth of the tool's penetration into the workpiece material during a cutting operation, and the radial depth of cut ($a_e$) representing the lateral width of the material removed by the cutting tool. The standard proposes to perform six different experiments [10]: the selection of a stable operating point, the determination of $v_{c,min}$, the