under the machined surface and improved surface finish induced by the application of liquid nitrogen. Nevertheless, the latter study makes use of a pull-pull fatigue test approach that may not be suitable to evaluate the effect of the machining-affected sub-surface layer on the material fatigue resistance. The fatigue life of Ti6Al4V samples fabricated through the AM technology known as laser powder bed fusion (LPBF) and then cryogenic machined was evaluated in [5] under a rotating bending loading. There was proved a substantial increase in fatigue strength of the cryogenic machined samples compared to the ones machined under conventional flooding conditions, which was ascribed to the much more significant residual compressive layer induced by the cryogenic cutting as well as the development of a hard and harmonic microstructure [6].

Nevertheless, the effect of cryogenic machining on the Ti6Al4V fatigue properties needs to be further investigated, especially in the case of the wrought alloy. In this framework, the paper aims to evaluate the fatigue strength of the wrought Ti6Al4V after flood and cryogenic machining, correlating it to the surface integrity induced by the specific cutting operation.

## Materials and methods

The fatigue specimens were machined from round bars of 12 mm diameter and 3200 mm length of wrought Ti6Al4V titanium alloy, purchased in an annealed state. The microstructure of the wrought Ti6Al4V in the as-received condition was evaluated using optical microscopy (OM) using a Leica™ DMRE microscope. The material was prepared using a metallographic procedure, including hot mounting in a thermosetting resin, grinding with silicon carbide abrasive papers, fine polishing using a mapped cloth in a slurry of 2/3, in volume, 0.2 µm alkaline fumed silica suspension and 1/3 of 30% H₂O₂, cleaning in an ultrasonic bath, and final etching making use of the Kroll's etchant (10 ml HF, 5 ml HNO₃, 85 ml H₂O). Fig. 1 shows the as-received microstructure of the wrought Ti6Al4V, which consists of an equiaxed α phase and intergranular β phase, with an average grain size of 2.6 ± 0.3 µm calculated through image analysis with the ImageJ™ software. It is worth noting that the as-received microstructure is very fine, which should correspond to high fatigue strength as a consequence of the increased resistance to crack initiation provided by fine microstructural features [7]. The wrought Ti6Al4V micro-hardness in the as-received condition was measured by making use of a Leitz™ Durimet Miniload hardness tester with a load of 100 gr for 30 s of indentation duration. The average hardness resulted in 291.6 HV ± 16.3. Finally, the ultimate tensile strength (UTS) certified by the supplier was 963 MPa.

Fatigue specimens with an hourglass shape (geometry in Fig. 2a) were machined from the wrought Ti6Al4V bars. The specimen dimensions were chosen to ensure its failure within the medium-to-high-cycle fatigue range, that is between 10⁴ and 2*10⁶ cycles. The specimen machining was carried out on a Mori Seiki™ NL 1500 CNC lathe adopting two lubricating-cooling conditions, namely conventional flood with a water-based cutting fluid containing 5% semi-synthetic oil, and cryogenic cooling with liquid nitrogen sprayed towards the tool rake and flank faces through 0.9 mm diameter copper nozzles. A total of 30 specimens (15 flood and 15 cryogenic) were machined. Fig. 2b shows the machining set-up when applying cryogenic cooling. A Sandvik Coromant™ VCET 1103 01-UM 1115 cutting tool was chosen as suitable for machining difficult-to-cut metal alloys, adopting a cutting speed of 45 m/min and feed of 0.03 mm/rev as suggested by the tool manufacturer. The final turning step to obtain the geometry of the specimen gauge length was carried out using a depth of cut of 0.25 mm.

The machined surface finish was analyzed using the Sensofar Metrology™ S-Neox 3D optical profiler equipped with Nikon™ TU Plan Fluor-EPI 20x confocal objective. The surface finish was assessed according to the ISO 25178 standard, applying a 2.5 µm S-filter and 0.25 µm L-filter.
under the machined surface and improved surface finish induced by the application of liquid nitrogen. Nevertheless, the latter study makes use of a pull-pull fatigue test approach that may not be suitable to evaluate the effect of the machining-affected sub-surface layer on the material fatigue resistance. The fatigue life of Ti6Al4V samples fabricated through the AM technology known as laser powder bed fusion (LPBF) and then cryogenic machined was evaluated in [5] under a rotating bending loading. There was proved a substantial increase in fatigue strength of the cryogenic machined samples compared to the ones machined under conventional flooding conditions, which was ascribed to the much more significant residual compressive layer induced by the cryogenic cutting as well as the development of a hard and harmonic microstructure [6].

Nevertheless, the effect of cryogenic machining on the Ti6Al4V fatigue properties needs to be further investigated, especially in the case of the wrought alloy. In this framework, the paper aims to evaluate the fatigue strength of the wrought Ti6Al4V after flood and cryogenic machining, correlating it to the surface integrity induced by the specific cutting operation.

## Materials and methods

The fatigue specimens were machined from round bars of 12 mm diameter and 3200 mm length of wrought Ti6Al4V titanium alloy, purchased in an annealed state. The microstructure of the wrought Ti6Al4V in the as-received condition was evaluated using optical microscopy (OM) using a Leica™ DMRE microscope. The material was prepared using a metallographic procedure, including hot mounting in a thermosetting resin, grinding with silicon carbide abrasive papers, fine polishing using a mapped cloth in a slurry of 2/3, in volume, 0.2 µm alkaline fumed silica suspension and 1/3 of 30% H₂O₂, cleaning in an ultrasonic bath, and final etching making use of the Kroll's etchant (10 ml HF, 5 ml HNO₃, 85 ml H₂O). Fig. 1 shows the as-received microstructure of the wrought Ti6Al4V, which consists of an equiaxed α phase and intergranular β phase, with an average grain size of 2.6 ± 0.3 µm calculated through image analysis with the ImageJ™ software. It is worth noting that the as-received microstructure is very fine, which should correspond to high fatigue strength as a consequence of the increased resistance to crack initiation provided by fine microstructural features [7]. The wrought Ti6Al4V micro-hardness in the as-received condition was measured by making use of a Leitz™ Durimet Miniload hardness tester with a load of 100 gr for 30 s of indentation duration. The average hardness resulted in 291.6 HV ± 16.3. Finally, the ultimate tensile strength (UTS) certified by the supplier was 963 MPa.

Fatigue specimens with an hourglass shape (geometry in Fig. 2a) were machined from the wrought Ti6Al4V bars. The specimen dimensions were chosen to ensure its failure within the medium-to-high-cycle fatigue range, that is between 10⁴ and 2*10⁶ cycles. The specimen machining was carried out on a Mori Seiki™ NL 1500 CNC lathe adopting two lubricating-cooling conditions, namely conventional flood with a water-based cutting fluid containing 5% semi-synthetic oil, and cryogenic cooling with liquid nitrogen sprayed towards the tool rake and flank faces through 0.9 mm diameter copper nozzles. A total of 30 specimens (15 flood and 15 cryogenic) were machined. Fig. 2b shows the machining set-up when applying cryogenic cooling. A Sandvik Coromant™ VCET 1103 01-UM 1115 cutting tool was chosen as suitable for machining difficult-to-cut metal alloys, adopting a cutting speed of 45 m/min and feed of 0.03 mm/rev as suggested by the tool manufacturer. The final turning step to obtain the geometry of the specimen gauge length was carried out using a depth of cut of 0.25 mm.

The machined surface finish was analyzed using the Sensofar Metrology™ S-Neox 3D optical profiler equipped with Nikon™ TU Plan Fluor-EPI 20x confocal objective. The surface finish was assessed according to the ISO 25178 standard, applying a 2.5 µm S-filter and 0.25 µm L-filter.
<figure><img src="image_1826.png" /><figcaption>Fig. 1. Microstructure of the wrought Ti6Al4V in the as-received condition: 500x (a), and 1000x magnification (b).</figcaption></figure>

Besides the arithmetic mean height $Sa$, the reduced valley height $Svk$, kurtosis $Sku$, and skewness $Ssk$ were evaluated as surface texture parameters correlated to the metals' fatigue strength [8].

The FEI Quanta™ 450 scanning electron microscope (SEM) was used to inspect the severe plastic deformation (SPD) layer beneath the machined surface at the minimum diameter of the specimen gauge length. To do that, samples were metallographically prepared using the procedure above described, and the SPD layer extent was evaluated every 5 µm from the surface.

Residual stresses at the minimum diameter of the specimen gauge length were evaluated making use of a SpiderX™ GNR portable instrument equipped with a hybrid photon counting detector till a distance of 150 µm from the machined surface. To do that, a layer of material was removed after each acquisition by electropolishing in a solution consisting of 90 ml water, 730 ml ethanol, 100 ml butoxyethanol, and 78 ml perchloric acid.

Fatigue tests were carried out on a Metro Com™ machine adopting a four-point rotating bending configuration. Such configuration was chosen as it permits the evaluation of the actual influence of the cutting parameters on the material fatigue strength, being the specimen's outer region the most stressed. The runout criterion was fixed at $10^7$ cycles according to literature studies dealing with Ti6Al4V fatigue strength [7]. The specimens were tested using a load ratio $R=-1$ until their complete separation, which was recorded as the number of cycles to failure $N_f$.

<figure><img src="image_1827.png" /><figcaption>Fig. 2. Geometry of the specimen for fatigue testing (a), machining set-up employing cryogenic cooling (b), geometry of the cutting tool (c).</figcaption></figure>
<figure><img src="image_1824.png" /><figcaption>Fig. 1. Microstructure of the wrought Ti6Al4V in the as-received condition: 500x (a), and 1000x magnification (b).</figcaption></figure>

Besides the arithmetic mean height $Sa$, the reduced valley height $Svk$, kurtosis $Sku$, and skewness $Ssk$ were evaluated as surface texture parameters correlated to the metals' fatigue strength [8].

The FEI Quanta™ 450 scanning electron microscope (SEM) was used to inspect the severe plastic deformation (SPD) layer beneath the machined surface at the minimum diameter of the specimen gauge length. To do that, samples were metallographically prepared using the procedure above described, and the SPD layer extent was evaluated every 5 µm from the surface.

Residual stresses at the minimum diameter of the specimen gauge length were evaluated making use of a SpiderX™ GNR portable instrument equipped with a hybrid photon counting detector till a distance of 150 µm from the machined surface. To do that, a layer of material was removed after each acquisition by electropolishing in a solution consisting of 90 ml water, 730 ml ethanol, 100 ml butoxyethanol, and 78 ml perchloric acid.

Fatigue tests were carried out on a Metro Com™ machine adopting a four-point rotating bending configuration. Such configuration was chosen as it permits the evaluation of the actual influence of the cutting parameters on the material fatigue strength, being the specimen's outer region the most stressed. The runout criterion was fixed at $10^7$ cycles according to literature studies dealing with Ti6Al4V fatigue strength [7]. The specimens were tested using a load ratio $R=-1$ until their complete separation, which was recorded as the number of cycles to failure $N_f$.

<figure><img src="image_1825.png" /><figcaption>Fig. 2. Geometry of the specimen for fatigue testing (a), machining set-up employing cryogenic cooling (b), geometry of the cutting tool (c).</figcaption></figure>
The fatigue limit was determined using the staircase method according to ISO 12107 standard. SEM observations were carried out on the fatigue-fractured surfaces to identify the crack initiation location.

## Results and discussion

Representative surface topographies of the Ti6Al4V specimens machined adopting flood and cryogenic lubricating-cooling conditions are shown in Fig. 3. It can be noted that the cryogenic machined specimen is characterized by a more irregular surface than the flood machined one. Although the same cutting parameters were used, the latter is characterized by more visible, marked, and regular grooves due to the passage of the tool during turning, in accordance with other literature records on cryogenic machining [9].

The differences between the two sets of specimens in terms of surface quality can be more appreciated from the roughness profiles extracted from the above-shown surface topographies and reported in Fig. 4a and Fig. 4b. The corresponding areal parameters are shown in Fig. 4c and reported in Table 1, where the percentage difference (Δ%) between the flood and cryogenic machined specimens is also highlighted.

<figure><img src="image_1828.png" /><figcaption>Fig. 3. Representative surface topography of specimens machined using flood lubrication (a), and cryogenic cooling (b).</figcaption></figure>

<figure><img src="image_1829.png" /><figcaption>Fig. 4. Representative roughness profiles of the flood (a) and cryogenic (b) machined specimens; surface roughness parameters at varying lubricating-cooling conditions (c).</figcaption></figure>
The fatigue limit was determined using the staircase method according to ISO 12107 standard. SEM observations were carried out on the fatigue-fractured surfaces to identify the crack initiation location.

## Results and discussion

Representative surface topographies of the Ti6Al4V specimens machined adopting flood and cryogenic lubricating-cooling conditions are shown in Fig. 3. It can be noted that the cryogenic machined specimen is characterized by a more irregular surface than the flood machined one. Although the same cutting parameters were used, the latter is characterized by more visible, marked, and regular grooves due to the passage of the tool during turning, in accordance with other literature records on cryogenic machining [9].

The differences between the two sets of specimens in terms of surface quality can be more appreciated from the roughness profiles extracted from the above-shown surface topographies and reported in Fig. 4a and Fig. 4b. The corresponding areal parameters are shown in Fig. 4c and reported in Table 1, where the percentage difference (Δ%) between the flood and cryogenic machined specimens is also highlighted.

<figure><img src="image_1826.png" /><figcaption>Fig. 3. Representative surface topography of specimens machined using flood lubrication (a), and cryogenic cooling (b).</figcaption></figure>

<figure><img src="image_1827.png" /><figcaption>Fig. 4. Representative roughness profiles of the flood (a) and cryogenic (b) machined specimens; surface roughness parameters at varying lubricating-cooling conditions (c).</figcaption></figure>
<table><caption>Table 1. Surface roughness parameters at varying lubricating-cooling conditions.</caption><thead><tr><th>Conditions</th><th>Sa [µm]</th><th>Svk [µm]</th><th>Sv [µm]</th><th>Sp [µm]</th><th>Sz [µm]</th><th>Ssk</th><th>Sku</th></tr></thead><tbody><tr><td>Flood</td><td>0.40±0.10</td><td>0.26±0.06</td><td>1.40±0.19</td><td>2.40±0.82</td><td>3.80±0.81</td><td>0.54±0.23</td><td>3.13±0.65</td></tr><tr><td>Cryo</td><td>0.36±0.12</td><td>0.34±0.03</td><td>1.36±0.13</td><td>1.68±0.31</td><td>3.10±0.42</td><td>0.36±0.18</td><td>3.09±0.55</td></tr><tr><td>Δ %</td><td>-9%</td><td>31%</td><td>-3%</td><td>-30%</td><td>-18%</td><td>-33%</td><td>-1%</td></tr></tbody></table>

The quality of a machined surface is generally assessed through the average roughness Sa: the cryogenic machined specimens are characterized by Sa 9% lower than the one of the flood machined specimens, however, the standard deviation of the measured values does not allow assessing a statistically significant difference. When addressing fatigue phenomena, the Sv parameter, which represents the maximum pit depth, is particularly relevant because the valleys of the roughness profile can be considered as possible crack initiation sites. Nevertheless, both the flood and cryogenic machined samples show nearly the same Sv values. The cryogenic machined specimens present a surface characterized by a maximum roughness height Sz 18% lower than the one of the flood machined specimens, which should indicate better fatigue life of the cryogenic machined samples than the flood ones. More precisely, the difference in terms of Sz, which is defined as the sum of the largest peak height value and the largest pit depth value, in this case, is due to a significant reduction in the peak heights for the cryogenic samples. The latter shows the maximum peak height parameter Sp 30% lower than the flood one while maintaining the same Sv.

The value of Ssk (skewness) gives information about the asymmetry of the distribution of the material, in terms of peaks and valleys, on the surface. In particular, if Ssk < 0 there is a predominance of valleys, whereas if Ssk > 0 there is a predominance of peaks. If Ssk > 0, this means that the material is close to the valleys on the surface. Both the flood and cryogenic machined samples have Ssk > 0, namely a predominance of peaks, which is positive for the fatigue life.

The kurtosis Sku is a measure of the sharpness of the surface roughness and indicates the presence of excessive peaks and valleys if Sku > 3 or their absence on the surface if Sku < 3. A normal height distribution, so that sharp portions and indented portions coexist, is characterized by Sku = 3. Negative skewness with a predominance of valleys has an adverse effect on fatigue [8], while high kurtosis determines the presence of sharp peaks or valleys. Both the flood and cryogenic machined samples show a positive kurtosis.

Even if both sets of specimens exhibit Sku close to 3, however, the cryogenic machined specimens are characterized by more irregular valleys, which is evident from a higher Svk reduced valley height and lower skewness. The Svk parameter measures the depth of the valleys below the core roughness and is generally considered important in functional surface characteristics, such as lubrication, as a lubricant can pool in these small valleys and provide greater wear resistance. High Svk may indicate a higher number of crack initiation sites and crack propagation, however, the most influential parameter regarding fatigue life is the total height of the valleys, Sv, along with Ssk and Sku, which define or not the dominance of valleys and how acute these are [10]. Overall, the analysis of the surface topographies cannot lead to the conclusion that one surface is better than the other in terms of texture parameters correlated to fatigue life.

As it is well known, machining operations tend to form a severe plastic deformation (SPD) layer just below the machined surface. This is due to the large localized deformation that occurs at the shearing plane during chip formation.

Fig. 5 shows two SEM images obtained with the backscattered electron detector, highlighting the SPD layers developed when machining using flood and cryogenic cooling conditions.
<table><caption>Table 1. Surface roughness parameters at varying lubricating-cooling conditions.</caption><thead><tr><th>Conditions</th><th>Sa [µm]</th><th>Svk [µm]</th><th>Sv [µm]</th><th>Sp [µm]</th><th>Sz [µm]</th><th>Ssk</th><th>Sku</th></tr></thead><tbody><tr><td>Flood</td><td>0.40±0.10</td><td>0.26±0.06</td><td>1.40±0.19</td><td>2.40±0.82</td><td>3.80±0.81</td><td>0.54±0.23</td><td>3.13±0.65</td></tr><tr><td>Cryo</td><td>0.36±0.12</td><td>0.34±0.03</td><td>1.36±0.13</td><td>1.68±0.31</td><td>3.10±0.42</td><td>0.36±0.18</td><td>3.09±0.55</td></tr><tr><td>Δ %</td><td>-9%</td><td>31%</td><td>-3%</td><td>-30%</td><td>-18%</td><td>-33%</td><td>-1%</td></tr></tbody></table>

The quality of a machined surface is generally assessed through the average roughness Sa: the cryogenic machined specimens are characterized by Sa 9% lower than the one of the flood machined specimens, however, the standard deviation of the measured values does not allow assessing a statistically significant difference. When addressing fatigue phenomena, the Sv parameter, which represents the maximum pit depth, is particularly relevant because the valleys of the roughness profile can be considered as possible crack initiation sites. Nevertheless, both the flood and cryogenic machined samples show nearly the same Sv values. The cryogenic machined specimens present a surface characterized by a maximum roughness height Sz 18% lower than the one of the flood machined specimens, which should indicate better fatigue life of the cryogenic machined samples than the flood ones. More precisely, the difference in terms of Sz, which is defined as the sum of the largest peak height value and the largest pit depth value, in this case, is due to a significant reduction in the peak heights for the cryogenic samples. The latter shows the maximum peak height parameter Sp 30% lower than the flood one while maintaining the same Sv.

The value of Ssk (skewness) gives information about the asymmetry of the distribution of the material, in terms of peaks and valleys, on the surface. In particular, if Ssk < 0 there is a predominance of valleys, whereas if Ssk > 0 there is a predominance of peaks. If Ssk > 0, this means that the material is close to the valleys on the surface. Both the flood and cryogenic machined samples have Ssk > 0, namely a predominance of peaks, which is positive for the fatigue life.

The kurtosis Sku is a measure of the sharpness of the surface roughness and indicates the presence of excessive peaks and valleys if Sku > 3 or their absence on the surface if Sku < 3. A normal height distribution, so that sharp portions and indented portions coexist, is characterized by Sku = 3. Negative skewness with a predominance of valleys has an adverse effect on fatigue [8], while high kurtosis determines the presence of sharp peaks or valleys. Both the flood and cryogenic machined samples show a positive kurtosis.

Even if both sets of specimens exhibit Sku close to 3, however, the cryogenic machined specimens are characterized by more irregular valleys, which is evident from a higher Svk reduced valley height and lower skewness. The Svk parameter measures the depth of the valleys below the core roughness and is generally considered important in functional surface characteristics, such as lubrication, as a lubricant can pool in these small valleys and provide greater wear resistance. High Svk may indicate a higher number of crack initiation sites and crack propagation, however, the most influential parameter regarding fatigue life is the total height of the valleys, Sv, along with Ssk and Sku, which define or not the dominance of valleys and how acute these are [10]. Overall, the analysis of the surface topographies cannot lead to the conclusion that one surface is better than the other in terms of texture parameters correlated to fatigue life.

As it is well known, machining operations tend to form a severe plastic deformation (SPD) layer just below the machined surface. This is due to the large localized deformation that occurs at the shearing plane during chip formation.

Fig. 5 shows two SEM images obtained with the backscattered electron detector, highlighting the SPD layers developed when machining using flood and cryogenic cooling conditions.
<figure><img src="image_1830.png" /><figcaption>Fig. 5. Microstructure below the machined surface and highlight of SPD layer below the surface of the flood (a) and cryogenic (b) machined specimens.</figcaption></figure>

The SPD layer thickness was determined using 9 measurements per specimen type, spaced about 5 µm, as can be seen in Fig. 5. The samples obtained by turning with liquid nitrogen show considerable deformation of the grains close to the machined surface: in particular very elongated β grains can be observed along the cutting speed direction, in contrast to the bulk material, which has equiaxed grains. The layer affected by this remarkable deformation has a thickness of 3.61 ± 0.28 µm. In contrast, the flood machined specimens show less evident grain deformation along with a smaller thickness of the SPD layer, namely 2.50 ± 0.40 µm. The SPD layer observed after cryogenic machining is 44% higher than the one after flood machining, following other literature studies [11, 12]. The plastic deformations induced by machining, in addition to being visible in the thickness of the SPD layer, introduce constraints within the material that create a field of self-compensating stresses known as residual stresses. During the life of a mechanical component, residual stresses combine with applied external loads and can have both positive and negative effects. Residual stresses also influence the component's mechanical properties as well as its corrosion resistance [13, 14]. Compressive residual stresses are desirable as they generally have beneficial effects [15] in terms of fatigue resistance, especially when the component is subjected to high surface stresses during its service life. The residual stresses of the post-machined specimens along the axial direction σ<sub>r,zz</sub> were analyzed using X-ray diffraction, and are reported in the diagram of Fig. 6 as a function of the distance *d* from the machined surface. The residual stresses along the axial direction are here considered as the ones influencing the fatigue life of components whose surface is subjected to tension or bending, as in the case of this study. For better sake of comparison, the residual stress values under flood and cryogenic cooling conditions are also given in Table 2.

<table><caption>Table 2. Axial residual stresses of the flood and cryogenic machined specimens.</caption><thead><tr><th colspan="4">Flood</th><th colspan="2">Cryo</th></tr><tr><th>d [µm]</th><th colspan="2">σ<sub>r,zz</sub> [MPa]</th><th>d [µm]</th><th colspan="2">σ<sub>r,zz</sub> [MPa]</th></tr></thead><tbody><tr><td>0 ± 0</td><td colspan="2">-492 ± 25</td><td>0 ± 0</td><td colspan="2">-964 ± 27</td></tr><tr><td>9 ± 3</td><td colspan="2">-214 ± 14</td><td>7 ± 2</td><td colspan="2">-519 ± 16</td></tr><tr><td>23 ± 3</td><td>43 ± 13</td><td></td><td>43 ± 1</td><td>24 ± 12</td><td></td></tr><tr><td>30 ± 2</td><td>39 ± 8</td><td></td><td>52 ± 2</td><td>72 ± 14</td><td></td></tr><tr><td>85 ± 2</td><td>146 ± 12</td><td></td><td>79 ± 2</td><td>120 ± 11</td><td></td></tr><tr><td>140 ± 2</td><td>17 ± 12</td><td></td><td>150 ± 3</td><td>67 ± 12</td><td></td></tr></tbody></table>
<figure><img src="image_1828.png" /><figcaption>Fig. 5. Microstructure below the machined surface and highlight of SPD layer below the surface of the flood (a) and cryogenic (b) machined specimens.</figcaption></figure>

The SPD layer thickness was determined using 9 measurements per specimen type, spaced about 5 µm, as can be seen in Fig. 5. The samples obtained by turning with liquid nitrogen show considerable deformation of the grains close to the machined surface: in particular very elongated β grains can be observed along the cutting speed direction, in contrast to the bulk material, which has equiaxed grains. The layer affected by this remarkable deformation has a thickness of 3.61 ± 0.28 µm. In contrast, the flood machined specimens show less evident grain deformation along with a smaller thickness of the SPD layer, namely 2.50 ± 0.40 µm. The SPD layer observed after cryogenic machining is 44% higher than the one after flood machining, following other literature studies [11, 12]. The plastic deformations induced by machining, in addition to being visible in the thickness of the SPD layer, introduce constraints within the material that create a field of self-compensating stresses known as residual stresses. During the life of a mechanical component, residual stresses combine with applied external loads and can have both positive and negative effects. Residual stresses also influence the component's mechanical properties as well as its corrosion resistance [13, 14]. Compressive residual stresses are desirable as they generally have beneficial effects [15] in terms of fatigue resistance, especially when the component is subjected to high surface stresses during its service life. The residual stresses of the post-machined specimens along the axial direction σ<sub>r,zz</sub> were analyzed using X-ray diffraction, and are reported in the diagram of Fig. 6 as a function of the distance *d* from the machined surface. The residual stresses along the axial direction are here considered as the ones influencing the fatigue life of components whose surface is subjected to tension or bending, as in the case of this study. For better sake of comparison, the residual stress values under flood and cryogenic cooling conditions are also given in Table 2.

<table><caption>Table 2. Axial residual stresses of the flood and cryogenic machined specimens.</caption><thead><tr><th colspan="4">Flood</th><th colspan="2">Cryo</th></tr><tr><th>d [µm]</th><th colspan="2">σ<sub>r,zz</sub> [MPa]</th><th>d [µm]</th><th colspan="2">σ<sub>r,zz</sub> [MPa]</th></tr></thead><tbody><tr><td>0 ± 0</td><td colspan="2">-492 ± 25</td><td>0 ± 0</td><td colspan="2">-964 ± 27</td></tr><tr><td>9 ± 3</td><td colspan="2">-214 ± 14</td><td>7 ± 2</td><td colspan="2">-519 ± 16</td></tr><tr><td>23 ± 3</td><td>43 ± 13</td><td></td><td>43 ± 1</td><td>24 ± 12</td><td></td></tr><tr><td>30 ± 2</td><td>39 ± 8</td><td></td><td>52 ± 2</td><td>72 ± 14</td><td></td></tr><tr><td>85 ± 2</td><td>146 ± 12</td><td></td><td>79 ± 2</td><td>120 ± 11</td><td></td></tr><tr><td>140 ± 2</td><td>17 ± 12</td><td></td><td>150 ± 3</td><td>67 ± 12</td><td></td></tr></tbody></table>
<figure><img src="image_1831.png" /><figcaption>Fig. 6. Axial residual stresses of flood and cryogenic machined specimens as a function of distance from the machined surface (see Table 2 for the standard deviations data).</figcaption></figure>

The cryogenic machined specimens are characterized by remarkable residual compressive surface stresses, namely $\sigma_{r,zz} = -964 \pm 27$ MPa, whereas the conventionally machined specimens have a compressive surface stress that is about 51% lower, namely $\sigma_{r,zz} = -492 \pm 25$ MPa. The residual stress state of the cryogenic machined samples tends to disappear less rapidly than that of the flood machined samples, reaching 0 MPa within 40 µm of the surface under cryogenic cooling and 30 µm under flood one. The stresses gradient observed from the external surface to the bulk material is very high compared to what is usually found in the literature on additive manufactured Ti6Al4V specimens with lamellar microstructure processed by turning, nevertheless in the latter case the distances interested by the residual stress state are greater [5]. This is due to the particularly fine equiaxial microstructure that characterizes the specimens under consideration. The results in terms of axial residual stress of cryogenic and flood machined specimens are in accordance with the previous SPD layer measurements, highlighting the increased plastic deformation in cryogenic machining.

The four-point rotating bending test configuration was selected to determine fatigue curves because it ensures the highest stress intensity on the annular outer layers of the specimens, highlighting the effects of machining, surface integrity, and residual stresses. The tests were conducted using a load ratio R = -1, which is defined as the ratio between the minimum and maximum stress. Fig. 7a displays the experimental data and fatigue curves processed using the nominal stress approach with a 50% survival probability (SP), i.e. the Wöhler curve. The data are presented in terms of nominal stress amplitude ($\sigma_a$) versus cycles to failure (Nf).

The fatigue limit ($\sigma_A$), which is the stress amplitude for which a cyclically stressed specimen exhibits infinite life, was calculated using the modified staircase method, by using Eq. 1 where i is the i-th specimen in the test sequence using a $\sigma_i$ stress level and n is the number of effectively tested specimens. It is worth underlining that the first stress level is not counted in Eq. 1 because it is a non-statistical datum affected by the operator's choice. The adopted test sequences and the number n of effectively tested specimens (7 for flood and 6 for cryogenic) are shown in Table 3, where a 25 MPa stress step was assumed according to ISO 12107, which requires the use of at least 6 specimens for the application of Eq. 1.

$$ \sigma_A = \frac{1}{n} \sum_{i=2}^{n+1} \sigma_i \qquad (1) $$
<figure><img src="image_1829.png" /><figcaption>Fig. 6. Axial residual stresses of flood and cryogenic machined specimens as a function of distance from the machined surface (see Table 2 for the standard deviations data).</figcaption></figure>

The cryogenic machined specimens are characterized by remarkable residual compressive surface stresses, namely $\sigma_{r,zz} = -964 \pm 27$ MPa, whereas the conventionally machined specimens have a compressive surface stress that is about 51% lower, namely $\sigma_{r,zz} = -492 \pm 25$ MPa. The residual stress state of the cryogenic machined samples tends to disappear less rapidly than that of the flood machined samples, reaching 0 MPa within 40 µm of the surface under cryogenic cooling and 30 µm under flood one. The stresses gradient observed from the external surface to the bulk material is very high compared to what is usually found in the literature on additive manufactured Ti6Al4V specimens with lamellar microstructure processed by turning, nevertheless in the latter case the distances interested by the residual stress state are greater [5]. This is due to the particularly fine equiaxial microstructure that characterizes the specimens under consideration. The results in terms of axial residual stress of cryogenic and flood machined specimens are in accordance with the previous SPD layer measurements, highlighting the increased plastic deformation in cryogenic machining.

The four-point rotating bending test configuration was selected to determine fatigue curves because it ensures the highest stress intensity on the annular outer layers of the specimens, highlighting the effects of machining, surface integrity, and residual stresses. The tests were conducted using a load ratio R = -1, which is defined as the ratio between the minimum and maximum stress. Fig. 7a displays the experimental data and fatigue curves processed using the nominal stress approach with a 50% survival probability (SP), i.e. the Wöhler curve. The data are presented in terms of nominal stress amplitude ($\sigma_a$) versus cycles to failure ($N_f$).

The fatigue limit ($\sigma_A$), which is the stress amplitude for which a cyclically stressed specimen exhibits infinite life, was calculated using the modified staircase method, by using Eq. 1 where i is the i-th specimen in the test sequence using a $\sigma_i$ stress level and n is the number of effectively tested specimens. It is worth underlining that the first stress level is not counted in Eq. 1 because it is a non-statistical datum affected by the operator's choice. The adopted test sequences and the number n of effectively tested specimens (7 for flood and 6 for cryogenic) are shown in Table 3, where a 25 MPa stress step was assumed according to ISO 12107, which requires the use of at least 6 specimens for the application of Eq. 1.

$$ \sigma_A = \frac{1}{n} \sum_{i=2}^{n+1} \sigma_i \qquad (1) $$
<figure><img src="image_1832.png" /><figcaption>Fig. 7. Fatigue test data of Ti6Al4V wrought specimens in terms of nominal stress amplitude at varying machining cooling strategies (a), crack initiation zone at the fatigue fracture surface in the cryogenic (b) and flood conditions (c).</figcaption></figure>

<table><caption>Table 3. Modified staircase test data</caption><tbody><tr><td rowspan="2">Flood</td><td>Stress sequence (σ<sub>i</sub>) [MPa]</td><td>700</td><td>675</td><td>700</td><td>725</td><td>700</td><td>675</td><td>650</td><td>675</td></tr><tr><td>Event</td><td>X*</td><td>O</td><td>O</td><td>X</td><td>X</td><td>X</td><td>O</td><td>a</td></tr><tr><td rowspan="2">Cryo</td><td>Stress sequence (σ<sub>i</sub>) [MPa]</td><td>725</td><td>700</td><td>725</td><td>700</td><td>675</td><td>700</td><td>675</td><td></td></tr><tr><td>Event</td><td>X*</td><td>O</td><td>X</td><td>X</td><td>O</td><td>X</td><td>a</td><td></td></tr></tbody></table>

X: failure, O: no failure, a: not actually carried out (calculated from previous value), * not counted

The fatigue limit was found to be 686 MPa and 696 MPa for the flood and cryogenic cryo machined series, respectively (see Fig. 7a). The knee of the Wöhler curve was not imposed for a certain number of cycles, but it was determined as the intersection of the calculated fatigue limit and the fatigue curve at SP 50%, as reported in Table 4. The inverse slope (k) of the fatigue curve for the cryogenic machined specimens is only 2% higher than that of the flood machined ones, meaning that there are no appreciable differences in the high-cycle fatigue range below 10⁶ cycles (see Table 4). The scatter index T<sub>σ,10-90%</sub>, which is defined as the ratio between the fatigue strength at 10% SP and 90% SP at a given number of cycles, is 1.22 and 1.16 for the flood and cryogenic machined, respectively. The scatter index is perfectly comparable between the two series of specimens.

There is only a difference of 5%, which can be considered negligible. Furthermore, values lower than 1.6 are normally acceptable and indicate good repeatability between the results and low statistical deviation.

<table><caption>Table 4. Fatigue data of the flood and cryogenic machined specimens.</caption><thead><tr><td>Conditions</td><td>R</td><td># data</td><td># runout</td><td>σ<sub>A</sub> [MPa]</td><td>N<sub>A</sub></td><td>k</td><td>T<sub>σ,10-90%</sub></td></tr></thead><tbody><tr><td>Flood</td><td>-1</td><td>17</td><td>5</td><td>686</td><td>1.2·10<sup>6</sup></td><td>16.60</td><td>1.22</td></tr><tr><td>Cyo</td><td>-1</td><td>15</td><td>4</td><td>696</td><td>8.5·10<sup>5</sup></td><td>16.94</td><td>1.12</td></tr></tbody></table>

The fatigue ratio (R<sub>f</sub>) is the ratio between the fatigue limit and UTS. R<sub>f</sub> is typically around 0.5 for many metals, including steels and titanium alloys. However, in the case of titanium alloys as is Ti6Al4V, R<sub>f</sub> can vary significantly depending on the microstructure and grain size [7, 16]. In the conducted tests, the fatigue ratio was approximately 0.7 for both flood and cryogenic machined specimens. This indicates that the material has high fatigue strength, regardless of the
<figure><img src="image_1830.png" /><figcaption>Fig. 7. Fatigue test data of Ti6Al4V wrought specimens in terms of nominal stress amplitude at varying machining cooling strategies (a), crack initiation zone at the fatigue fracture surface in the cryogenic (b) and flood conditions (c).</figcaption></figure>

<table><caption>Table 3. Modified staircase test data</caption><tbody><tr><td rowspan="2">Flood</td><td>Stress sequence (σ<sub>i</sub>) [MPa]</td><td>700</td><td>675</td><td>700</td><td>725</td><td>700</td><td>675</td><td>650</td><td>675</td></tr><tr><td>Event</td><td>X*</td><td>O</td><td>O</td><td>X</td><td>X</td><td>X</td><td>O</td><td>a</td></tr><tr><td rowspan="2">Cryo</td><td>Stress sequence (σ<sub>i</sub>) [MPa]</td><td>725</td><td>700</td><td>725</td><td>700</td><td>675</td><td>700</td><td>675</td><td></td></tr><tr><td>Event</td><td>X*</td><td>O</td><td>X</td><td>X</td><td>O</td><td>X</td><td>a</td><td></td></tr></tbody></table>

X: failure, O: no failure, a: not actually carried out (calculated from previous value), * not counted

The fatigue limit was found to be 686 MPa and 696 MPa for the flood and cryogenic cryo machined series, respectively (see Fig. 7a). The knee of the Wöhler curve was not imposed for a certain number of cycles, but it was determined as the intersection of the calculated fatigue limit and the fatigue curve at SP 50%, as reported in Table 4. The inverse slope (k) of the fatigue curve for the cryogenic machined specimens is only 2% higher than that of the flood machined ones, meaning that there are no appreciable differences in the high-cycle fatigue range below 10⁶ cycles (see Table 4). The scatter index T<sub>σ,10-90%</sub>, which is defined as the ratio between the fatigue strength at 10% SP and 90% SP at a given number of cycles, is 1.22 and 1.16 for the flood and cryogenic machined, respectively. The scatter index is perfectly comparable between the two series of specimens.

There is only a difference of 5%, which can be considered negligible. Furthermore, values lower than 1.6 are normally acceptable and indicate good repeatability between the results and low statistical deviation.

<table><caption>Table 4. Fatigue data of the flood and cryogenic machined specimens.</caption><thead><tr><td>Conditions</td><td>R</td><td># data</td><td># runout</td><td>σ<sub>A</sub> [MPa]</td><td>N<sub>A</sub></td><td>k</td><td>T<sub>σ,10-90%</sub></td></tr></thead><tbody><tr><td>Flood</td><td>-1</td><td>17</td><td>5</td><td>686</td><td>1.2·10<sup>6</sup></td><td>16.60</td><td>1.22</td></tr><tr><td>Cyo</td><td>-1</td><td>15</td><td>4</td><td>696</td><td>8.5·10<sup>5</sup></td><td>16.94</td><td>1.12</td></tr></tbody></table>

The fatigue ratio (R<sub>f</sub>) is the ratio between the fatigue limit and UTS. R<sub>f</sub> is typically around 0.5 for many metals, including steels and titanium alloys. However, in the case of titanium alloys as is Ti6Al4V, R<sub>f</sub> can vary significantly depending on the microstructure and grain size [7, 16]. In the conducted tests, the fatigue ratio was approximately 0.7 for both flood and cryogenic machined specimens. This indicates that the material has high fatigue strength, regardless of the
strategy used to machine it, which can be ascribed to its fine equiaxial microstructure. This is in accordance with literature records, where Ti6Al4V, even if processed with other methods than the one of this study, with a fine equiaxial microstructure was characterized by higher fatigue strength compared to the same alloy but with coarse equiaxial or lamellar microstructures [1, 7].

Finally, the graph in Fig. 7a shows a difference of only 10 MPa between the two cutting conditions at the fatigue limit, around $10^6$ cycles. This difference can be attributed to the higher and deeper compressive residual stresses found in the cryogenic machined specimens. The effect of these stresses is not noticeable for a lower number of cycles where the phenomenon of residual stress relaxation occurs [14, 17].

After conducting the fatigue tests, the specimen fracture surfaces were analyzed and the crack initiation zones were identified (see Fig. 7b and 7c). No internal or sub-surface defects from which the crack could originate were found, meaning that the mechanism of initiation, propagation, and static fracture is the same for both the sets of specimens, namely the fatigue fracture starts from the valleys of the roughness profile, the latter being likely crack initiation sites.

## Conclusions

Ti6Al4V wrought specimens, characterized by an equiaxed α phase and intergranular β phase, with an average grain size of $2.6 \pm 0.3$ µm, were machined with two different lubricating-cooling strategies, i.e. cryogenic and flood. The surface integrity of the machined specimens was evaluated focusing on the fatigue-related roughness parameter, the SPD layer thickness, and axial residual stresses. Fatigue tests were conducted using a rotating bending load configuration and fatigue strength was derived. This study evaluates the fatigue strength of a wrought Ti6Al4V provided with a very fine microstructure and machined under flood and cryogenic cooling conditions. The following conclusions can be drawn:

* The average roughness of the flood and cryogenic machined specimens is very similar, whereas other surface texture parameters that are usually correlated to metal fatigue life do not provide a definitive answer about the likeliness of higher fatigue strength of any of the two sets of specimens.

* Cryogenic machined specimens show higher and deeper compressive residual stresses as well as higher SPD layers than flood-machined ones.

* The fatigue limit of the two sets of specimens is nearly the same, with fatigue fracture always starting from the valleys of the roughness profile. This very similar behavior in terms of fatigue strength can be ascribed to the very fine microstructure characterizing the wrought alloy in its as-received condition, which prevails over the other characteristics induced by any machining strategy.

## References

[1] C. Leyens, & M. Peters (Eds.), Titanium and titanium alloys: fundamentals and applications, Wiley-vch (2006).

[2] M. O. Bodunrin, L. H. Chown, J. W. van der Merwe, K. K. Alaneme, Hot working of Ti-6Al-4V with a complex initial microstructure, International Journal of Material Forming (2019), 12, pp. 857-874.

[3] Y. Yildiz, & M. Nalbant, A review of cryogenic cooling in machining processes, International Journal of Machine Tools and Manufacture (2008), 48(9), 947-964.

[4] D. Umbrello, & G. Rotella, Fatigue life of machined Ti6Al4V alloy under different cooling conditions, CIRP Annals (2018), 67(1), 99-102. https://doi.org/10.1016/j.cirp.2018.03.017
strategy used to machine it, which can be ascribed to its fine equiaxial microstructure. This is in accordance with literature records, where Ti6Al4V, even if processed with other methods than the one of this study, with a fine equiaxial microstructure was characterized by higher fatigue strength compared to the same alloy but with coarse equiaxial or lamellar microstructures [1, 7].

Finally, the graph in Fig. 7a shows a difference of only 10 MPa between the two cutting conditions at the fatigue limit, around $10^6$ cycles. This difference can be attributed to the higher and deeper compressive residual stresses found in the cryogenic machined specimens. The effect of these stresses is not noticeable for a lower number of cycles where the phenomenon of residual stress relaxation occurs [14, 17].

After conducting the fatigue tests, the specimen fracture surfaces were analyzed and the crack initiation zones were identified (see Fig. 7b and 7c). No internal or sub-surface defects from which the crack could originate were found, meaning that the mechanism of initiation, propagation, and static fracture is the same for both the sets of specimens, namely the fatigue fracture starts from the valleys of the roughness profile, the latter being likely crack initiation sites.

## Conclusions

Ti6Al4V wrought specimens, characterized by an equiaxed α phase and intergranular β phase, with an average grain size of $2.6 \pm 0.3$ µm, were machined with two different lubricating-cooling strategies, i.e. cryogenic and flood. The surface integrity of the machined specimens was evaluated focusing on the fatigue-related roughness parameter, the SPD layer thickness, and axial residual stresses. Fatigue tests were conducted using a rotating bending load configuration and fatigue strength was derived. This study evaluates the fatigue strength of a wrought Ti6Al4V provided with a very fine microstructure and machined under flood and cryogenic cooling conditions. The following conclusions can be drawn:

* The average roughness of the flood and cryogenic machined specimens is very similar, whereas other surface texture parameters that are usually correlated to metal fatigue life do not provide a definitive answer about the likeliness of higher fatigue strength of any of the two sets of specimens.

* Cryogenic machined specimens show higher and deeper compressive residual stresses as well as higher SPD layers than flood-machined ones.

* The fatigue limit of the two sets of specimens is nearly the same, with fatigue fracture always starting from the valleys of the roughness profile. This very similar behavior in terms of fatigue strength can be ascribed to the very fine microstructure characterizing the wrought alloy in its as-received condition, which prevails over the other characteristics induced by any machining strategy.

## References

[1] C. Leyens, & M. Peters (Eds.), Titanium and titanium alloys: fundamentals and applications, Wiley-vch (2006).

[2] M. O. Bodunrin, L. H. Chown, J. W. van der Merwe, K. K. Alaneme, Hot working of Ti-6Al-4V with a complex initial microstructure, International Journal of Material Forming (2019), 12, pp. 857-874.

[3] Y. Yildiz, & M. Nalbant, A review of cryogenic cooling in machining processes, International Journal of Machine Tools and Manufacture (2008), 48(9), 947-964.

[4] D. Umbrello, & G. Rotella, Fatigue life of machined Ti6Al4V alloy under different cooling conditions, CIRP Annals (2018), 67(1), 99-102. https://doi.org/10.1016/j.cirp.2018.03.017
[5] R. Bertolini, A. Campagnolo, M. Sorgato, A. Ghiotti, S. Bruschi, & G. Meneghetti, Fatigue strength of LPBF Ti6Al4V machined under flood and cryogenic lubri-cooling conditions, International Journal of Fatigue (2022), 162, 106973.
https://doi.org/10.1016/j.ijfatigue.2022.106973

[6] A. Ghiotti, R. Bertolini, M. Sorgato, A. Campagnolo, E. Savio, & S. Bruschi, Ti6Al4V titanium alloy fatigue strength after AM-and machining-based process chains, CIRP Annals (2022), 71(1), 461-464. https://doi.org/10.1016/j.cirp.2022.04.021

[7] G. Lütjering, J.C. Williams, Titanium, Springer (2007).

[8] M. Dumas, F. Cabanettes, R. Kaminski, F. Valiorgue, E. Picot, F. Lefebvre, & J. Rech Influence of the finish cutting operations on the fatigue performance of Ti-6Al-4V parts produced by Selective Laser Melting, Procedia CIRP (2018), 71, 429-434.
https://doi.org/10.1016/j.procir.2018.05.054

[9] S. Sartori, A. Bordin, A. Ghiotti, S. Bruschi, Analysis of the surface integrity in cryogenic turning of Ti6Al4V produced by Direct Melting Laser Sintering, procedia CIRP (2016), 45 123-126. https://doi.org/10.1016/j.procir.2016.02.328

[10] S. Lee, B. Rasoolian, D. F. Silva, J. W. Pegues, N. Shamsaei, Surface roughness parameter and modeling for fatigue behavior of additive manufactured parts: a non-destructive data-driven approach, Addit Manuf (2021), 46, 10209. https://doi.org/10.1016/j.addma.2021.102094

[11] Y. Sun, B. Huang, D. A. Puleo, J. Schoop, & I. S. Jawahir, Improved surface integrity from cryogenic machining of Ti-6Al-7Nb alloy for biomedical applications, Procedia Cirp (2016), 45, 63-66. https://doi.org/10.1016/j.procir.2016.02.362

[12] G. Rotella, O. W. Dillon, D. Umbrello, L. Settineri, & I. S. Jawahir, The effects of cooling conditions on surface integrity in machining of Ti6Al4V alloy, The International Journal of Advanced Manufacturing Technology (2014), 71, 47-55.
https://doi.org/10.1007/s00170-013-5477-9

[13] R. Bertolini, S. Bruschi, A. Bordin, A. Ghiotti, L. Pezzato, M. Dabalà, Fretting Corrosion Behavior of Additive Manufactured and Cryogenic-Machined Ti6Al4V for Biomedical Applications, Advanced Engineering Materials (2016), 19(6), 1500629.

[14] R. W. Landgraf, & R. A. Chernenkoff, Residual stress effects on fatigue of surface processed steels. Analytical and experimental methods for residual stress effects in fatigue, ASTM STP (1988), 1004, 1-12.

[15] G. S. Schajer, (Ed.), Practical residual stress measurement methods. John Wiley & Sons (2013).

[16] Y. Murakami, Metal fatigue: effects of small defects and nonmetallic inclusions, Elsevier (2019).

[17] R. C. McClung, A literature survey on the stability and significance of residual stresses during fatigue, Fatigue & Fracture of Engineering Materials & Structures (2007), 30(3), 173-205.
[5] R. Bertolini, A. Campagnolo, M. Sorgato, A. Ghiotti, S. Bruschi, & G. Meneghetti, Fatigue strength of LPBF Ti6Al4V machined under flood and cryogenic lubri-cooling conditions, International Journal of Fatigue (2022), 162, 106973.
https://doi.org/10.1016/j.ijfatigue.2022.106973

[6] A. Ghiotti, R. Bertolini, M. Sorgato, A. Campagnolo, E. Savio, & S. Bruschi, Ti6Al4V titanium alloy fatigue strength after AM-and machining-based process chains, CIRP Annals (2022), 71(1), 461-464. https://doi.org/10.1016/j.cirp.2022.04.021

[7] G. Lütjering, J.C. Williams, Titanium, Springer (2007).

[8] M. Dumas, F. Cabanettes, R. Kaminski, F. Valiorgue, E. Picot, F. Lefebvre, & J. Rech Influence of the finish cutting operations on the fatigue performance of Ti-6Al-4V parts produced by Selective Laser Melting, Procedia CIRP (2018), 71, 429-434.
https://doi.org/10.1016/j.procir.2018.05.054

[9] S. Sartori, A. Bordin, A. Ghiotti, S. Bruschi, Analysis of the surface integrity in cryogenic turning of Ti6Al4V produced by Direct Melting Laser Sintering, procedia CIRP (2016), 45 123-126. https://doi.org/10.1016/j.procir.2016.02.328

[10] S. Lee, B. Rasoolian, D. F. Silva, J. W. Pegues, N. Shamsaei, Surface roughness parameter and modeling for fatigue behavior of additive manufactured parts: a non-destructive data-driven approach, Addit Manuf (2021), 46, 10209. https://doi.org/10.1016/j.addma.2021.102094

[11] Y. Sun, B. Huang, D. A. Puleo, J. Schoop, & I. S. Jawahir, Improved surface integrity from cryogenic machining of Ti-6Al-7Nb alloy for biomedical applications, Procedia Cirp (2016), 45, 63-66. https://doi.org/10.1016/j.procir.2016.02.362

[12] G. Rotella, O. W. Dillon, D. Umbrello, L. Settineri, & I. S. Jawahir, The effects of cooling conditions on surface integrity in machining of Ti6Al4V alloy, The International Journal of Advanced Manufacturing Technology (2014), 71, 47-55.
https://doi.org/10.1007/s00170-013-5477-9

[13] R. Bertolini, S. Bruschi, A. Bordin, A. Ghiotti, L. Pezzato, M. Dabalà, Fretting Corrosion Behavior of Additive Manufactured and Cryogenic-Machined Ti6Al4V for Biomedical Applications, Advanced Engineering Materials (2016), 19(6), 1500629.

[14] R. W. Landgraf, & R. A. Chernenkoff, Residual stress effects on fatigue of surface processed steels. Analytical and experimental methods for residual stress effects in fatigue, ASTM STP (1988), 1004, 1-12.

[15] G. S. Schajer, (Ed.), Practical residual stress measurement methods. John Wiley & Sons (2013).

[16] Y. Murakami, Metal fatigue: effects of small defects and nonmetallic inclusions, Elsevier (2019).

[17] R. C. McClung, A literature survey on the stability and significance of residual stresses during fatigue, Fatigue & Fracture of Engineering Materials & Structures (2007), 30(3), 173-205.
# Impact of machining strategy on OFE copper for SRF applications

BELKHIR F.¹,²,ᵃ, KOLENIC M.¹,ᵇ*, RECH J.²,ᶜ, PÉREZ FONTENLA A.T.¹, ROSAZ G.¹, MOROS A.¹, GARLASCHÈ M.¹, LEITH S.¹, NAISSON P.¹, CARLOS C.P.A.¹

¹CERN, Geneva, Switzerland

²Centrale Lyon ENISE, Saint-Etienne, France

ᵃ faudel.belkhir@cern.ch, ᵇ michal.kolenic@cern.ch, ᶜjoel.rech@enise.fr

**Keywords:** Surface Integrity, Machining, SRF, Cavity, OFE Copper, Niobium, SEM, FIB, GIXRD, FCC

**Abstract.** The study evaluates the impact of various milling strategies - on the surface and subsurface quality of an Oxygen-Free Electronic (OFE) copper substrate, and subsequently on the niobium (Nb) coating performance- for Superconducting Radio Frequency (SRF) cavities. Several cutting tools, cutting conditions and machining paths are compared, given their paramount influence in the final 'SRF' quality of the machined surfaces. The near surface region is evaluated by different means: surface roughness and shape accuracy are measured using a profilometer and Coordinate Measuring Machine (CMM) respectively; the thickness of the layer affected by machining on the OFE copper substrate is estimated by Focused Ion Beam Scanning Electron Microscopy (FIB - SEM). The dislocation density in the near surface layer is assessed by Grazing Incidence X-Ray Diffraction (GI-XRD) in both the OFE copper substrate and afterwards in the niobium coating. Main investigation results are discussed, and conclusions drawn for new guidelines on machining strategy and for future research developments.

## Introduction

Radio Frequency Accelerating cavities are an essential part of particle colliders, as they provide energy to the charged particle beams for impact. As in many particle accelerators, SRF cavities are used in the Large Hadron Collider (LHC) at CERN; these are composed of an OFE copper (Cu) substrate, onto which a coating of superconducting niobium (Nb) is deposited via sputtering.

For optimizing the accelerating capability of SRF cavities, the surface integrity of the Niobium layer plays a key role [1]. It is known how machining OFE copper presents challenges due to its thermo-structural behaviour during cutting, its proneness to tool adhesion and to formation of build-up edges.

This study thus aims to explore the effects of various machining configurations on OFE copper substrates, to quantify and eventually to optimize their impact on substrate surface integrity, thus subsequently on the deposited Nb layer.

This study falls within a larger ongoing campaign at CERN: previous investigations focused on turning applications [2], revealing notable effects of cutting conditions on the subsurface layer of the copper substrate, particularly in terms of thickness and grain structure of the affected subsurface layers.

In the following, the campaign is extended to the examination of milling applications. The chosen case for this study is the Slotted Waveguide ELLiptical (SWELL) cavity Fig. 1, a promising fully milled concept [3], under study for high energy applications such as the Future Circular Collider (FCC) of CERN [4]. The samples used in the study have first been machined, then surface treated, then tested and measured, as described in the following chapter.

<figure><img src="image_1833.png" /></figure>
# Impact of machining strategy on OFE copper for SRF applications

BELKHIR F.¹,²,ᵃ, KOLENIC M.¹,ᵇ*, RECH J.²,ᶜ, PÉREZ FONTENLA A.T.¹, ROSAZ G.¹, MOROS A.¹, GARLASCHÈ M.¹, LEITH S.¹, NAISSON P.¹, CARLOS C.P.A.¹

¹CERN, Geneva, Switzerland

²Centrale Lyon ENISE, Saint-Etienne, France

ᵃ faudel.belkhir@cern.ch, ᵇ michal.kolenic@cern.ch, ᶜjoel.rech@enise.fr

**Keywords:** Surface Integrity, Machining, SRF, Cavity, OFE Copper, Niobium, SEM, FIB, GIXRD, FCC

**Abstract.** The study evaluates the impact of various milling strategies - on the surface and subsurface quality of an Oxygen-Free Electronic (OFE) copper substrate, and subsequently on the niobium (Nb) coating performance- for Superconducting Radio Frequency (SRF) cavities. Several cutting tools, cutting conditions and machining paths are compared, given their paramount influence in the final 'SRF' quality of the machined surfaces. The near surface region is evaluated by different means: surface roughness and shape accuracy are measured using a profilometer and Coordinate Measuring Machine (CMM) respectively; the thickness of the layer affected by machining on the OFE copper substrate is estimated by Focused Ion Beam Scanning Electron Microscopy (FIB - SEM). The dislocation density in the near surface layer is assessed by Grazing Incidence X-Ray Diffraction (GI-XRD) in both the OFE copper substrate and afterwards in the niobium coating. Main investigation results are discussed, and conclusions drawn for new guidelines on machining strategy and for future research developments.

**Introduction**

Radio Frequency Accelerating cavities are an essential part of particle colliders, as they provide energy to the charged particle beams for impact. As in many particle accelerators, SRF cavities are used in the Large Hadron Collider (LHC) at CERN; these are composed of an OFE copper (Cu) substrate, onto which a coating of superconducting niobium (Nb) is deposited via sputtering.

For optimizing the accelerating capability of SRF cavities, the surface integrity of the Niobium layer plays a key role [1]. It is known how machining OFE copper presents challenges due to its thermo-structural behaviour during cutting, its proneness to tool adhesion and to formation of build-up edges.

This study thus aims to explore the effects of various machining configurations on OFE copper substrates, to quantify and eventually to optimize their impact on substrate surface integrity, thus subsequently on the deposited Nb layer.

This study falls within a larger ongoing campaign at CERN: previous investigations focused on turning applications [2], revealing notable effects of cutting conditions on the subsurface layer of the copper substrate, particularly in terms of thickness and grain structure of the affected subsurface layers.

In the following, the campaign is extended to the examination of milling applications. The chosen case for this study is the Slotted Waveguide ELLiptical (SWELL) cavity Fig. 1, a promising fully milled concept [3], under study for high energy applications such as the Future Circular Collider (FCC) of CERN [4]. The samples used in the study have first been machined, then surface treated, then tested and measured, as described in the following chapter.

<figure><img src="image_1831.png" /></figure>
## Experimental Setup and Methodology

Fig. 1 shows two of the four Copper quadrants, of which the SWELL cavity is composed; the internal dark grey surface indicates the area undergoing subsequent Nb coating. The central bottom area of the cavity (Fig. 1) has been identified as area of interest, for obtaining the samples: when the cavity is powered, such area is subjected to the highest-intensity magnetic fields; while -in relation to fabrication via milling- the position and configuration of such area leads to low effective cutting speed - thus uncontrolled cutting [5] - during production of the given cavity. In order to reduce sample size and costs, discs (Ø84 x 10) containing only the area of interest have been produced, as shown in Fig. 2. Each milled profile (red) has been obtained with the same machine configuration and general parameters as if a full quadrant were being machined.

<figure><img src="image_1834.png" /><figcaption>Fig. 1 - SRF Cavity SWELL, two quadrants</figcaption></figure>

<figure><img src="image_1835.png" /><figcaption>Fig. 2 inner shape of cavity & disc sample geometry</figcaption></figure>

Specific machining parameters -such as cutting conditions, cutting edge radius and friction coefficient- influence the thermomechanical load during milling; they can thus impact surface integrity [6]. In order to benchmark such parameters, nine different scenarios (i.e. sample batches) were produced, permutating cutting tool material and geometry, cutting conditions and machining paths. The milling centre used for the machining of samples was a HERMLE C400. External cooling was used during milling (7% cutting emulsion, mineral miscible oil B-cool MC 610 + tap water). The clamping used was vise Lang Makro grip. All scenarios foresaw the same roughing process, while permutation of parameters was performed during the finishing stages. Since finishing and superfinishing operations have a particular impact on surface integrity as well as geometry of machined parts [7, 8], two sets of reference cutting conditions were used :

* For carbide cutters : $V_c$ = 245 m.min⁻¹, $A_p$ = 0,05 mm, $F_z$ = 0,03 mm.rev⁻¹.z⁻¹, $A_e$ = 0,091 mm, lateral inclination angle (Tilt) 20°

* For diamond cutters : $V_c$ = 650 m.min⁻¹, $A_p$ = 0,05 mm, $F_z$ = 0,03 mm.rev⁻¹.z⁻¹, $A_e$ = 0,091 mm, lateral inclination angle (Tilt) 20°

Most tests were carried out with the mentioned reference cutting conditions. On the other hand, cutting speed (Vc) and feed per tooth per revolution (Fz) have a preponderant influence on the surface, compared to the depth of cut (Ap) or radial engagement (Ae) [9], therefore, so-called *aggressive* and *soft* cutting conditions ($F_z$ and $V_c$ increased or decreased by 20% respectively) were also studied for carbide tools.

As mentioned, several different cutting tools were also compared:

* Carbide 1 – Ball end mill ø12 Z4 DLC sp² coated solid carbide (current CERN standard)- as a benchmark cutter to produce control sample,

* Carbide 2 - Ball end mill ø12 Z4 TiAlN-coated solid carbide,

* Carbide 3 - Ball end mill ø12 Z2 uncoated carbide tip - This cutter was chosen for its low edge radius, hence better sharpness due to the absence of coating,

* Diamond - Ball end mill ø12 Z1 monocrystalline diamond.

The impact of tool wear was also considered: the induced degradation of the cut, thus the augmented local plastic deformation are even more pronounced in copper. To simulate this
## Experimental Setup and Methodology

Fig. 1 shows two of the four Copper quadrants, of which the SWELL cavity is composed; the internal dark grey surface indicates the area undergoing subsequent Nb coating. The central bottom area of the cavity (Fig. 1) has been identified as area of interest, for obtaining the samples: when the cavity is powered, such area is subjected to the highest-intensity magnetic fields; while -in relation to fabrication via milling- the position and configuration of such area leads to low effective cutting speed - thus uncontrolled cutting [5] - during production of the given cavity. In order to reduce sample size and costs, discs (Ø84 x 10) containing only the area of interest have been produced, as shown in Fig. 2. Each milled profile (red) has been obtained with the same machine configuration and general parameters as if a full quadrant were being machined.

<figure><img src="image_1832.png" /><figcaption>Fig. 1 - SRF Cavity SWELL, two quadrants</figcaption></figure>

<figure><img src="image_1833.png" /><figcaption>Fig. 2 inner shape of cavity & disc sample geometry</figcaption></figure>

Specific machining parameters -such as cutting conditions, cutting edge radius and friction coefficient- influence the thermomechanical load during milling; they can thus impact surface integrity [6]. In order to benchmark such parameters, nine different scenarios (i.e. sample batches) were produced, permutating cutting tool material and geometry, cutting conditions and machining paths. The milling centre used for the machining of samples was a HERMLE C400. External cooling was used during milling (7% cutting emulsion, mineral miscible oil B-cool MC 610 + tap water). The clamping used was vise Lang Makro grip. All scenarios foresaw the same roughing process, while permutation of parameters was performed during the finishing stages. Since finishing and superfinishing operations have a particular impact on surface integrity as well as geometry of machined parts [7, 8], two sets of reference cutting conditions were used :

* For carbide cutters : $V_c$ = 245 m.min⁻¹, $A_p$ = 0,05 mm, $F_z$ = 0,03 mm.rev⁻¹.z⁻¹, $A_e$ = 0,091 mm, lateral inclination angle (Tilt) 20°

* For diamond cutters : $V_c$ = 650 m.min⁻¹, $A_p$ = 0,05 mm, $F_z$ = 0,03 mm.rev⁻¹.z⁻¹, $A_e$ = 0,091 mm, lateral inclination angle (Tilt) 20°

Most tests were carried out with the mentioned reference cutting conditions. On the other hand, cutting speed (Vc) and feed per tooth per revolution (Fz) have a preponderant influence on the surface, compared to the depth of cut (Ap) or radial engagement (Ae) [9], therefore, so-called *aggressive* and *soft* cutting conditions ($F_z$ and $V_c$ increased or decreased by 20% respectively) were also studied for carbide tools.

As mentioned, several different cutting tools were also compared:

* Carbide 1 – Ball end mill ø12 Z4 DLC sp² coated solid carbide (current CERN standard)- as a benchmark cutter to produce control sample,

* Carbide 2 - Ball end mill ø12 Z4 TiAlN-coated solid carbide,

* Carbide 3 - Ball end mill ø12 Z2 uncoated carbide tip - This cutter was chosen for its low edge radius, hence better sharpness due to the absence of coating,

* Diamond - Ball end mill ø12 Z1 monocrystalline diamond.

The impact of tool wear was also considered: the induced degradation of the cut, thus the augmented local plastic deformation are even more pronounced in copper. To simulate this
phenomenon, a tailor-made tool has been ground ("carbide 1" end mill) so as to replicate a typical
flank wear (VB) of approx. 0.15mm as one can be seen after a long period of machining.
Finally, two milling paths were also studied: unidirectional (so called "parallel planes" which is
the standard strategy used for this types of applications) and an outward spiral toolpath.

<table><caption>Table 1 - scenario permutations and corresponding sample nomenclature.</caption><thead><tr><th>Sample</th><th>Strategy</th><th>spring pass</th><th>Tool</th><th>cutting conditions</th></tr></thead><tbody><tr><td>CONTROL</td><td>Unidirectional</td><td>No</td><td>carbide 1</td><td>carbide reference</td></tr><tr><td>2</td><td>Unidirectional</td><td>No</td><td>carbide 1</td><td>carbide reference +20%</td></tr><tr><td>SLOW</td><td>Unidirectional</td><td>No</td><td>carbide 1</td><td>carbide reference -20%</td></tr><tr><td>4</td><td>Unidirectional</td><td>No</td><td>carbide 2</td><td>carbide reference</td></tr><tr><td>5</td><td>Unidirectional</td><td>No</td><td>carbide 3</td><td>carbide reference</td></tr><tr><td>DIA</td><td>Unidirectional</td><td>No</td><td>Diamond</td><td>diamond reference</td></tr><tr><td>WORN</td><td>Unidirectional</td><td>No</td><td>carbide 1 worn</td><td>carbide reference</td></tr><tr><td>SPRING PASS</td><td>Unidirectional</td><td>yes</td><td>carbide 1</td><td>carbide reference</td></tr><tr><td>SPIRAL</td><td>Spiral</td><td>No</td><td>carbide 1</td><td>carbide reference</td></tr></tbody></table>

As first qualification, right after milling operations, the **shape accuracy** of the samples has been measured, thanks to a ZEISS Prismo Ultra 12-24-10 CMM. The shape accuracy was considered in "Best-Fit" configuration.

**Surface roughness** has also been measured, using a MITUTOYO SV C3100 profilometer, equipped with a 12AAC736 probe (2µm radius of acuity). The Average Roughness (Ra), maximum profile height (Rz) and reduced peak height (Rpk) parameters were measured. Rpk provides an indication of the presence of peaks on the surface, particularly useful for studying the effect of a spring pass during milling. Each of them was measured parallel to the feed direction on 3 different lines (parallel to each other), then perpendicular to the feed direction on 3 lines (also parallel to each other). Then, the average was calculated for each direction.

In order for the study to be as consistent as possible with standard SRF manufacturing, following milling operations the samples underwent the surface treatment processes typical for this type of SRF cavities.

Prior to coating, SRF cavities undergo an **Electro-polishing (EP)** process, which firstly aims at reducing the surface roughness left from previous manufacturing operations. This surface roughness is detrimental to cavity performance and can cause electrical breakdown during service. The bath used for SWELL cavities is composed of 45% (vol.) Butanol ($C_4H_{10}O$) and 55% phosphoric acid ($H_3PO_4$). The Material removal rate is approximately 1 µm/min. The thickness removed is around 12 µm on the basis of the best results to the present day. The SWELL samples in this study are treated with the same EP procedure as described above for a full cavity. The samples are then immersed in sulfamic acid for 1 minute to remove surface oxides and then into ammonium citrate for 5 minutes to passivate the surface and prevent further oxide growth.

The samples have then been Nb-coated via **High-Power Impulse Magnetron Sputtering (HiPIMS)** system. HiPIMS generates high peak-currents, leading to increased ionization of the sputtered material compared to conventional methods like Direct Current Magnetron Sputtering (DCMS). This allows for precise control of the ion bombardment energy by applying a negative voltage at the substrate (DC substrate bias). This enables much higher impinging energies, which in turn result in denser films with improved RF performance [10]. The main parameters used for the coating of the SWELL cavity samples can be seen in Table 2:
phenomenon, a tailor-made tool has been ground ("carbide 1" end mill) so as to replicate a typical
flank wear (VB) of approx. 0.15mm as one can be seen after a long period of machining.
Finally, two milling paths were also studied: unidirectional (so called "parallel planes" which is
the standard strategy used for this types of applications) and an outward spiral toolpath.

<table><caption>Table 1 - scenario permutations and corresponding sample nomenclature.</caption><thead><tr><td>Sample</td><td>Strategy</td><td>spring pass</td><td>Tool</td><td>cutting conditions</td></tr></thead><tbody><tr><td>CONTROL</td><td>Unidirectional</td><td>No</td><td>carbide 1</td><td>carbide reference</td></tr><tr><td>2</td><td>Unidirectional</td><td>No</td><td>carbide 1</td><td>carbide reference +20%</td></tr><tr><td>SLOW</td><td>Unidirectional</td><td>No</td><td>carbide 1</td><td>carbide reference -20%</td></tr><tr><td>4</td><td>Unidirectional</td><td>No</td><td>carbide 2</td><td>carbide reference</td></tr><tr><td>5</td><td>Unidirectional</td><td>No</td><td>carbide 3</td><td>carbide reference</td></tr><tr><td>DIA</td><td>Unidirectional</td><td>No</td><td>Diamond</td><td>diamond reference</td></tr><tr><td>WORN</td><td>Unidirectional</td><td>No</td><td>carbide 1 worn</td><td>carbide reference</td></tr><tr><td>SPRING PASS</td><td>Unidirectional</td><td>yes</td><td>carbide 1</td><td>carbide reference</td></tr><tr><td>SPIRAL</td><td>Spiral</td><td>No</td><td>carbide 1</td><td>carbide reference</td></tr></tbody></table>

As first qualification, right after milling operations, the **shape accuracy** of the samples has been measured, thanks to a ZEISS Prismo Ultra 12-24-10 CMM. The shape accuracy was considered in "Best-Fit" configuration.

**Surface roughness** has also been measured, using a MITUTOYO SV C3100 profilometer, equipped with a 12AAC736 probe (2µm radius of acuity). The Average Roughness (Ra), maximum profile height (Rz) and reduced peak height (Rpk) parameters were measured. Rpk provides an indication of the presence of peaks on the surface, particularly useful for studying the effect of a spring pass during milling. Each of them was measured parallel to the feed direction on 3 different lines (parallel to each other), then perpendicular to the feed direction on 3 lines (also parallel to each other). Then, the average was calculated for each direction.

In order for the study to be as consistent as possible with standard SRF manufacturing, following milling operations the samples underwent the surface treatment processes typical for this type of SRF cavities.

Prior to coating, SRF cavities undergo an **Electro-polishing (EP)** process, which firstly aims at reducing the surface roughness left from previous manufacturing operations. This surface roughness is detrimental to cavity performance and can cause electrical breakdown during service. The bath used for SWELL cavities is composed of 45% (vol.) Butanol ($C_4H_{10}O$) and 55% phosphoric acid ($H_3PO_4$). The Material removal rate is approximately 1 µm/min. The thickness removed is around 12 µm on the basis of the best results to the present day. The SWELL samples in this study are treated with the same EP procedure as described above for a full cavity. The samples are then immersed in sulfamic acid for 1 minute to remove surface oxides and then into ammonium citrate for 5 minutes to passivate the surface and prevent further oxide growth.

The samples have then been Nb-coated via **High-Power Impulse Magnetron Sputtering (HiPIMS)** system. HiPIMS generates high peak-currents, leading to increased ionization of the sputtered material compared to conventional methods like Direct Current Magnetron Sputtering (DCMS). This allows for precise control of the ion bombardment energy by applying a negative voltage at the substrate (DC substrate bias). This enables much higher impinging energies, which in turn result in denser films with improved RF performance [10]. The main parameters used for the coating of the SWELL cavity samples can be seen in Table 2:
<table><caption>Table 2 – main parameters of HiPIMS coating process</caption><tr><td>average power</td><td>1.2 [kW]</td></tr><tr><td>substrate temperature during deposition</td><td>150 [°C]</td></tr><tr><td>Krypton pressure</td><td>2.3/2.4x10<sup>-3</sup> [mbar]</td></tr><tr><td>substrate-to-ground voltage</td><td>- 75 [V] (DC)</td></tr><tr><td>HiPIMS pulse length</td><td>200 [µS]</td></tr><tr><td>HiPIMS signal frequency</td><td>100 [Hz]</td></tr><tr><td>Deposition time</td><td>6 [h]</td></tr></table>

These parameters enable discharge voltages of 625 V and ion peak currents of around 159 A, resulting in a niobium layer of around 6 µm. Further details about the sputtering system and deposition procedure can be found in [11].

Presence of dislocations on the subsurface and coated layers has been evaluated, as **dislocation density** is believed to be one of the driving parameters affecting poor SRF performance of the Niobium coating. Dislocations in the top layer were evaluated by using the **GI-XRD** configuration in a BRUKER D8 DISCOVER X-ray diffractometer, equipped with Eiger 2R 500K detector. The incident Theta angle was fixed in two degrees. This shallow angle ensures that the X-rays interact exclusively with the material's surface enhancing the diffracted signal from the copper after machining or EP and subsequently from the Nb coating. In the present study, the collected signal came from a depth of approximately two microns for copper specimens, and approximately half micron for the Nb coated ones. Based on best practices, the surface scan in 2 thetas was chosen (with the receiver position fixed at 2°), a step size of 0.07° with an exposure time of 1.5 seconds per step and a 0.2 mm slit.

The obtained x-ray diffractograms were then processed using the MAUD software [12]. Full Rietveld refinement is performed to extract the crystallites' size, *D*, the microstrain $\epsilon$, and the lattice parameter, *a*. Instrumental widening is corrected using a corundum sample. The dislocation density was calculated as

$$ \rho_D = 2\sqrt{3} \frac{\langle \epsilon^2 \rangle^{1/2}}{D \times b}. \qquad (1) $$

where $\rho_D$ is the dislocation density (m⁻²), *D* is the crystallite size (m), and *b* is the burger vector expressed as $\frac{a\sqrt{3}}{2}$ (m) for BCC materials such as Nb and $a\sqrt{2}$ for FCC materials such as Cu.

The thickness of the Cu **substrate layers affected by milling** was estimated by **Focused Ion Beam Scanning Electron Microscopy** (FIB - SEM). The instrument used for FIB-SEM was a ZEISS XB 540, equipped with InLens Secondary Electron detector (InLens) and STEM (Scanning Transmission Electron Microscope) detector. The set-up used for FIB-SEM analysis mainly involves an FIB gun, a platinum sprayer used to protect the extreme surface of the FIB dispersion, and an electron detector for producing usable images. The FIB cut was initially made parallel to the milling marks, so as to observe any sub-surface grain elongation effects.
<table><caption>Table 2 – main parameters of HiPIMS coating process</caption><tr><td>average power</td><td>1.2 [kW]</td></tr><tr><td>substrate temperature during deposition</td><td>150 [°C]</td></tr><tr><td>Krypton pressure</td><td>2.3/2.4x10<sup>-3</sup> [mbar]</td></tr><tr><td>substrate-to-ground voltage</td><td>- 75 [V] (DC)</td></tr><tr><td>HiPIMS pulse length</td><td>200 [µS]</td></tr><tr><td>HiPIMS signal frequency</td><td>100 [Hz]</td></tr><tr><td>Deposition time</td><td>6 [h]</td></tr></table>

These parameters enable discharge voltages of 625 V and ion peak currents of around 159 A, resulting in a niobium layer of around 6 µm. Further details about the sputtering system and deposition procedure can be found in [11].

Presence of dislocations on the subsurface and coated layers has been evaluated, as **dislocation density** is believed to be one of the driving parameters affecting poor SRF performance of the Niobium coating. Dislocations in the top layer were evaluated by using the **GI-XRD** configuration in a BRUKER D8 DISCOVER X-ray diffractometer, equipped with Eiger 2R 500K detector. The incident Theta angle was fixed in two degrees. This shallow angle ensures that the X-rays interact exclusively with the material's surface enhancing the diffracted signal from the copper after machining or EP and subsequently from the Nb coating. In the present study, the collected signal came from a depth of approximately two microns for copper specimens, and approximately half micron for the Nb coated ones. Based on best practices, the surface scan in 2 thetas was chosen (with the receiver position fixed at 2°), a step size of 0.07° with an exposure time of 1.5 seconds per step and a 0.2 mm slit.

The obtained x-ray diffractograms were then processed using the MAUD software [12]. Full Rietveld refinement is performed to extract the crystallites' size, *D*, the microstrain $\epsilon$, and the lattice parameter, *a*. Instrumental widening is corrected using a corundum sample. The dislocation density was calculated as

$$ \rho_D = 2\sqrt{3} \frac{\langle\epsilon^2\rangle^{1/2}}{D \times b}. \qquad (1) $$

where $\rho_D$ is the dislocation density (m⁻²), *D* is the crystallite size (m), and *b* is the burger vector expressed as $\frac{a\sqrt{3}}{2}$ (m) for BCC materials such as Nb and $a\sqrt{2}$ for FCC materials such as Cu.

The thickness of the Cu **substrate layers affected by milling** was estimated by **Focused Ion Beam Scanning Electron Microscopy** (FIB - SEM). The instrument used for FIB-SEM was a ZEISS XB 540, equipped with InLens Secondary Electron detector (InLens) and STEM (Scanning Transmission Electron Microscope) detector. The set-up used for FIB-SEM analysis mainly involves an FIB gun, a platinum sprayer used to protect the extreme surface of the FIB dispersion, and an electron detector for producing usable images. The FIB cut was initially made parallel to the milling marks, so as to observe any sub-surface grain elongation effects.
# Results and Discussion

## Shape Accuracy

Fig. 3 shows the typical shape accuracy measurements for one of the samples, while - values of shape deviation for each scenario produced. Fig. 4 summarizes the highest absolute values of shape deviation, measured for each sample. It can be noted how the samples machined by lower cutting conditions (SLOW) and by using a spiral path (SPIRAL) are particularly unfavourable for obtaining an accurate geometry, showing 0,031 mm and 0,038 mm of shape deviation respectively. For the SLOW sample, the reason may be found in the less efficient cutting process and more pronounced ploughing effect. In the case of SPIRAL sample, these deviations can be linked to the high acceleration of the machine-tool axes movements. Moreover, since there are several axes moving simultaneously with a frequent change of direction of movement. Therefore, there is an accumulation of interpolation errors and pivot point error resulting in lowered accuracy [13]. Near-to-best shape accuracy can be found in DIA sample. This can be attributed to several factors, among which cutting edge sharpness and low copper/diamond chemical affinity.

<figure><img src="image_1836.png" /><figcaption>Fig. 3 - shape deviation visualised in space, according to the best-fit criterion. sample "SPIRAL"</figcaption></figure>

<figure><img src="image_1837.png" /><figcaption>Fig. 4 - values of shape deviation for each scenario produced.</figcaption></figure>

## Surface Roughness

Fig. 5 shows the results for each sample, in terms Ra, Rz, Rpk, which represent some of the most important roughness parameters for SRF. The Ra target is 1.6 µm. The other parameters are not currently defined in the technical specification for SWELL cavities.

It must be noted that the highest values are obtained when measuring roughness in the circumferential direction and are therefore the ones shown in figure.

<figure><img src="image_1838.png" /><figcaption>Fig. 5 - overview of surface roughness criteria</figcaption></figure>

The measured values show that all scenarios have Ra values below the maximum target value. The roughness values obtained with a diamond cutter (DIA) are the lowest in the study (Ra 0,16 µm, Rz 0,82 µm, Rpk 0,11 µm) followed by those of the sample milled with SLOW conditions. The low roughness obtained by the diamond cutter can be attributed to several factors. As shown
# Results and Discussion

## Shape Accuracy

Fig. 3 shows the typical shape accuracy measurements for one of the samples, while - *values of shape deviation for each scenario produced*. Fig. 4 summarizes the highest absolute values of shape deviation, measured for each sample. It can be noted how the samples machined by lower cutting conditions (SLOW) and by using a spiral path (SPIRAL) are particularly unfavourable for obtaining an accurate geometry, showing 0,031 mm and 0,038 mm of shape deviation respectively. For the SLOW sample, the reason may be found in the less efficient cutting process and more pronounced ploughing effect. In the case of SPIRAL sample, these deviations can be linked to the high acceleration of the machine-tool axes movements. Moreover, since there are several axes moving simultaneously with a frequent change of direction of movement. Therefore, there is an accumulation of interpolation errors and pivot point error resulting in lowered accuracy [13]. Near-to-best shape accuracy can be found in DIA sample. This can be attributed to several factors, among which cutting edge sharpness and low copper/diamond chemical affinity.

<figure><img src="image_1834.png" /><figcaption>Fig. 3 - shape deviation visualised in space, according to the best-fit criterion. sample "SPIRAL"</figcaption></figure>

<figure><img src="image_1835.png" /><figcaption>Fig. 4 - values of shape deviation for each scenario produced.</figcaption></figure>

## Surface Roughness

Fig. 5 shows the results for each sample, in terms Ra, Rz, Rpk, which represent some of the most important roughness parameters for SRF. The Ra target is 1.6 µm. The other parameters are not currently defined in the technical specification for SWELL cavities.

It must be noted that the highest values are obtained when measuring roughness in the circumferential direction and are therefore the ones shown in figure.

<figure><img src="image_1836.png" /><figcaption>Fig. 5 - overview of surface roughness criteria</figcaption></figure>

The measured values show that all scenarios have Ra values below the maximum target value. The roughness values obtained with a diamond cutter (DIA) are the lowest in the study (Ra 0,16 µm, Rz 0,82 µm, Rpk 0,11 µm) followed by those of the sample milled with SLOW conditions. The low roughness obtained by the diamond cutter can be attributed to several factors. As shown
in [14], diamond has a low chemical affinity ("lattice mismatch") with copper, which translates on a macroscopic scale into a lower friction coefficient than other material pairs (e.g. carbide/copper or TiAlN/copper). This coefficient reduces copper's grip on diamond, thereby reducing the ploughing effects mentioned above. The reduction of cutting conditions (SLOW) also results in a relatively smooth surface compared to the control sample (CONTROL).

On the contrary, the sample milled by spiral trajectory (sample SPIRAL) seems to give high values of surface roughness (Ra 0,83 µm, Rz 3.96µm, Rpk 1.84 µm). This can be partly explained by the fact that several of the machine's linear axes are in motion during this trajectory, reducing the system's rigidity on the one hand, and accumulating the backlash of several axes on the other. Another reason is the direction of measurement since in this scenario the roughness probe's path goes through multiple valleys and peaks which should theoretically be bigger than in the cutter's feed direction.

As expected, the sample milled with the worn cutter (WORN) also gives higher values. The sample milled with a spring pass (SPRING PASS) shows values of Ra and Rz that are almost identical with the control sample; the value of Rpk is though 50% smaller than with the control sample. This can be explained by the presence of micro-peaks which can be as a result of ploughing phenomenon occurring during machining and therefore imperfect shearing of the material. The following spring pass eliminates those pits without touching the core of the material. In any case, the amelioration seen with the additional spring pass is of high interest and will be implemented in the next productions requiring high quality of surface finish.

## Dislocation Density Comparison

The sample DIA is showing overall low degree of affectation in both machined and coated samples, proving to be the best amongst all samples in terms of low deformation of the subsurface. The small radius of its cutting edge seems to result in minimal material affectation. In addition to its sharp cutting edge and low chemical affinity with copper, such good results can be traced on the excellent thermal conductivity of single-crystal diamond : 5 times higher than copper [15], whereas the thermal conductivity of carbide is 4 times lower than that of copper, and therefore 20 times lower than that of diamond.

Oppositely, sample SLOW carries the highest estimated dislocation density in OFE copper substrate and one of the highest in niobium coating. This phenomenon is attributed to the ploughing effects which occurs more in these conditions. The dislocation density in the niobium layers of samples WORN and SPIRAL record highest among all samples. For what concerns WORN, this may be more easily attributed to more pressure being applied on the surface due to larger contact area tool/clearance face (worn). Hence mechanical compressive stress increases. For what concerns SPIRAL, reason may be due to the machine tool's lower rigidity and accumulated backlash, due to frequent axis inversion during machining. This may have disturbed the finishing pass having an impact on dislocation density.

As demonstrated on Fig. 7, there is an impact of the existing density of dislocation of the copper substrate to the dislocation density of the deposited niobium. One should remind that the EP process remove a significant amount of the copper surface. Even though a week direct correlation, a basic trend could be estimated. Dislocation density is quite sensitive to sample preparation and existing lattice structure. A way to increase the robustness of the correlation could be through an extensive campaign of measurement to average its inherent variability. On the other hand, the effects of substrate dislocation and similar 'defects' may not be so easy to notice, and the optimisation of substrate thus still plays a role. It can be seen how dislocation densities in electropolished Cu strongly do not to correlate with those of either Cu substrate after machining or Nb after coating; Their values are also greatly smaller than those in machined Cu and in the final Nb layer. Some sort of dislocation memory – or defects not observable or yet deemed of
in [14], diamond has a low chemical affinity ("lattice mismatch") with copper, which translates on a macroscopic scale into a lower friction coefficient than other material pairs (e.g. carbide/copper or TiAlN/copper). This coefficient reduces copper's grip on diamond, thereby reducing the ploughing effects mentioned above. The reduction of cutting conditions (SLOW) also results in a relatively smooth surface compared to the control sample (CONTROL).

On the contrary, the sample milled by spiral trajectory (sample SPIRAL) seems to give high values of surface roughness (Ra 0,83 µm, Rz 3.96µm, Rpk 1.84 µm). This can be partly explained by the fact that several of the machine's linear axes are in motion during this trajectory, reducing the system's rigidity on the one hand, and accumulating the backlash of several axes on the other. Another reason is the direction of measurement since in this scenario the roughness probe's path goes through multiple valleys and peaks which should theoretically be bigger than in the cutter's feed direction.

As expected, the sample milled with the worn cutter (WORN) also gives higher values. The sample milled with a spring pass (SPRING PASS) shows values of Ra and Rz that are almost identical with the control sample; the value of Rpk is though 50% smaller than with the control sample. This can be explained by the presence of micro-peaks which can be as a result of ploughing phenomenon occurring during machining and therefore imperfect shearing of the material. The following spring pass eliminates those pits without touching the core of the material. In any case, the amelioration seen with the additional spring pass is of high interest and will be implemented in the next productions requiring high quality of surface finish.

## Dislocation Density Comparison

The sample DIA is showing overall low degree of affectation in both machined and coated samples, proving to be the best amongst all samples in terms of low deformation of the subsurface. The small radius of its cutting edge seems to result in minimal material affectation. In addition to its sharp cutting edge and low chemical affinity with copper, such good results can be traced on the excellent thermal conductivity of single-crystal diamond : 5 times higher than copper [15], whereas the thermal conductivity of carbide is 4 times lower than that of copper, and therefore 20 times lower than that of diamond.

Oppositely, sample SLOW carries the highest estimated dislocation density in OFE copper substrate and one of the highest in niobium coating. This phenomenon is attributed to the ploughing effects which occurs more in these conditions. The dislocation density in the niobium layers of samples WORN and SPIRAL record highest among all samples. For what concerns WORN, this may be more easily attributed to more pressure being applied on the surface due to larger contact area tool/clearance face (worn). Hence mechanical compressive stress increases. For what concerns SPIRAL, reason may be due to the machine tool's lower rigidity and accumulated backlash, due to frequent axis inversion during machining. This may have disturbed the finishing pass having an impact on dislocation density.

As demonstrated on Fig. 7, there is an impact of the existing density of dislocation of the copper substrate to the dislocation density of the deposited niobium. One should remind that the EP process remove a significant amount of the copper surface. Even though a week direct correlation, a basic trend could be estimated. Dislocation density is quite sensitive to sample preparation and existing lattice structure. A way to increase the robustness of the correlation could be through an extensive campaign of measurement to average its inherent variability. On the other hand, the effects of substrate dislocation and similar 'defects' may not be so easy to notice, and the optimisation of substrate thus still plays a role. It can be seen how dislocation densities in electropolished Cu strongly do not to correlate with those of either Cu substrate after machining or Nb after coating; Their values are also greatly smaller than those in machined Cu and in the final Nb layer. Some sort of dislocation memory – or defects not observable or yet deemed of
interest- must thus be present and are still greatly influence the end result of coating. Due to this,
the control and minimisation of sublayer defects induced during milling is still paramount.

<figure><img src="image_1839.png" /><figcaption>Fig. 6 - estimated dislocation density</figcaption></figure>

<figure><img src="image_1840.png" /><figcaption>Fig. 7 - The dislocation density in the copper substrate vs. the dislocation density in Nb layer.</figcaption></figure>

Estimation of the Affected Layer

Based on previous GI-XRD results, the FIB-SEM cross sectional inspection of the samples DIA (lowest dislocation density) and SLOW (highest dislocation density) are further developed in this paper (Fig. 8 and Fig. 9 respectively), as these showed extreme dislocation density values in the Cu substrate after machining (sample DIA with the lowest dislocation density and SLOW with the highest).

An affected band is discernible on the near surface of the copper material in the DIA sample,
machined with a diamond tool (Fig. 10). The estimated thickness remains consistent for both the
cross-sectional view (aligned with the machining marks) and the view perpendicular to them.
However, in the latter case, there is a slight increase in variation along the cut. In contrast to the
diamond-milled sample, machining marks are clearly visible on SLOW sample (Fig. 11).

An affected band - more prominently evident on the SLOW sample than on the DIA sample, and
with an aspect similar to the one discussed in reference [16] - indicates a greater degree of plastic
deformation and, consequently, a more substantial density of dislocations. This hypothesis aligns
consistently with the results obtained from the GIXRD analyses.
interest- must thus be present and are still greatly influence the end result of coating. Due to this,
the control and minimisation of sublayer defects induced during milling is still paramount.

<figure><img src="image_1837.png" /><figcaption>Fig. 6 - estimated dislocation density</figcaption></figure>

<figure><img src="image_1838.png" /><figcaption>Fig. 7 - The dislocation density in the copper substrate vs. the dislocation density in Nb layer.</figcaption></figure>

Estimation of the Affected Layer

Based on previous GI-XRD results, the FIB-SEM cross sectional inspection of the samples DIA (lowest dislocation density) and SLOW (highest dislocation density) are further developed in this paper (Fig. 8 and Fig. 9 respectively), as these showed extreme dislocation density values in the Cu substrate after machining (sample DIA with the lowest dislocation density and SLOW with the highest).

An affected band is discernible on the near surface of the copper material in the DIA sample,
machined with a diamond tool (Fig. 10). The estimated thickness remains consistent for both the
cross-sectional view (aligned with the machining marks) and the view perpendicular to them.
However, in the latter case, there is a slight increase in variation along the cut. In contrast to the
diamond-milled sample, machining marks are clearly visible on SLOW sample (Fig. 11).
An affected band - more prominently evident on the SLOW sample than on the DIA sample, and
with an aspect similar to the one discussed in reference [16]- indicates a greater degree of plastic
deformation and, consequently, a more substantial density of dislocations. This hypothesis aligns
consistently with the results obtained from the GIXRD analyses.
<figure><img src="image_1841.png" /><figcaption>Fig. 8 – Sample DIA: general FIB-SEM overview (InLens, mag. x2’500)</figcaption></figure>

<figure><img src="image_1842.png" /><figcaption>Fig. 9 - Sample SLOW: general FIB-SEM overview (InLens, mag. x2'500)</figcaption></figure>

<figure><img src="image_1843.png" /><figcaption>Fig. 10 – Sample DIA: FIB-SEM cross-section (InLens, mag. x20’000)</figcaption></figure>

<figure><img src="image_1844.png" /><figcaption>Fig. 11- Sample SLOW: FIB-SEM cross-section (InLens, mag. x20'000)</figcaption></figure>

Fig. 12 provides the result of affected layer thickness for all samples in the study. In order to account for the embedded variability of the process and of the measurement, a minimum of three measurements were conducted per sample, to derive the representative mean value and standard deviation (the latter in parenthesis in the abscissa label).

Specifically for the DIA sample, measurements yield results ranging from 162 to 408 nm; while the SLOW sample displays affected thickness varying from 508 to 1597 nm. It can though be noted how the SLOW sample is not the one embedding worst values of affected layer thickness.

This result is in line with the results of GI-XRD: the presence of defects follows a trend where the best (DIA) and worst cutting conditions produce loosely consistent effects. Nevertheless, the worst performing cutting condition for the copper substrate (SLOW) are not the ultimately worst for the Nb layer (WORN).

<figure><img src="image_1845.png" /><figcaption>Fig. 12 - average thickness of affected layer. The standard deviations are visualized for each sample.</figcaption></figure>
<figure><img src="image_1839.png" /><figcaption>Fig. 8 – Sample DIA: general FIB-SEM overview (InLens, mag. x2’500)</figcaption></figure>

<figure><img src="image_1840.png" /><figcaption>Fig. 9 - Sample SLOW: general FIB-SEM overview (InLens, mag. x2'500)</figcaption></figure>

<figure><img src="image_1841.png" /><figcaption>Fig. 10 – Sample DIA: FIB-SEM cross-section (InLens, mag. x20’000)</figcaption></figure>

<figure><img src="image_1842.png" /><figcaption>Fig. 11- Sample SLOW: FIB-SEM cross-section (InLens, mag. x20'000)</figcaption></figure>

Fig. 12 provides the result of affected layer thickness for all samples in the study. In order to account for the embedded variability of the process and of the measurement, a minimum of three measurements were conducted per sample, to derive the representative mean value and standard deviation (the latter in parenthesis in the abscissa label).

Specifically for the DIA sample, measurements yield results ranging from 162 to 408 nm; while the SLOW sample displays affected thickness varying from 508 to 1597 nm. It can though be noted how the SLOW sample is not the one embedding worst values of affected layer thickness.

This result is in line with the results of GI-XRD: the presence of defects follows a trend where the best (DIA) and worst cutting conditions produce loosely consistent effects. Nevertheless, the worst performing cutting condition for the copper substrate (SLOW) are not the ultimately worst for the Nb layer (WORN).

<figure><img src="image_1843.png" /><figcaption>Fig. 12 - average thickness of affected layer. The standard deviations are visualized for each sample.</figcaption></figure>
## Conclusion and Next Steps

The study has allowed to further the insights on the impact of machining on the quality of the subsurface copper layer and thus on the superconducting niobium layer of SRF machined cavities. The influence of edge radius on changes in surface integrity emerges as a significant factor. Even low values of tool wear stand out as the parameter greatly affecting dislocation density of the copper substrate. Though its effects on measured final dislocation of the SRF layer seem to be reduced, optimal conditions for Nb coating are difficult to obtain, especially on complex geometries far from the samples studied; wear should be kept under close control, and it appears clearly that 0.15mm flank wear is already above acceptable limit.

The use of diamond tool stands out as the best configuration for minimising dislocation density of both copper substrate and Nb layer. Additional studies will be performed in the space of cutting parameters with this tool, in order to find an optimal setup.

In addition, results of dislocation density and affected layer open the door to novel considerations with respect to current state of the art: substrate defects such as dislocation density may be only one of the driving factors for optimal Nb layer performance. This is why RF performance checks, EBSD as well as complementary GIXRD analyses, are in progress at the time of writing. Such results will be needed to finalise the link between substrate and SRF layer quality with respect to final radiofrequency performance; though such link has been obtained for surfaces yielding from different processes (shaping, turning), milling tests results are in any case needed to validate the above considerations on dislocation density.

Further tests -with identical milling cutters differing only in edge radius- will be conducted to provide additional insight; additionally, a more comprehensive description of cutter geometry at the cutting zone level, encompassing factors like surface "reflection" and clearance angles, would enhance our understanding of the mechanisms at play during milling. It might be conclusive to investigate the type and rate of tool wear. Only flank wear has been taken into account but due to the harsh behaviour of OFE copper, built-up edge of crater wear could be seen and would greatly modify the tool/copper interface phenomenon.

## Acknowledgements

The authors would like to acknowledge the following CERN colleagues, for their instrumental support in preparation of the samples and of the tests: Romain Ninet, Alan Saillet, Philippe Richerot, Dominique Pugnat, Maciej Burkowski, Ahmed Cherif, Louise Viezzi, Marc Thiebert and Serge Forel.

## References

[1] C. P. A. Carlos et al., Nb/Cu thin film HiPIMS coatings optimization for SRF applications, FCC Week 2022, Paris, France, 30 May - 03 June 2022.

[2] A. Camelin et al. Experimental analysis of subsurface integrity during fine turning of OFE copper for radiofrequency cavity manufacturing. Journal of Materials Processing Technology. 302. (2021) 117483. https://doi.org/10.1016/j.jmatprotec.2021.117483

[3] A. Plaçais et al., Multipactor studies for the FCC-ee superconducting SWELL cavities, (2023).

[4] M. Benedikt et al., Future Circular Collider - European Strategy Update Documents, (2019).

[5] I. Perez et al., Effect of cutting speed on the surface integrity of face milled 7050-T7451 aluminium workpieces. Procedia CIRP. 71 (2018) 460-465. https://doi.org/10.1016/j.procir.2018.05.034

[6] K. Gutzeit et al., Influence of the cutting-edge radius on tool wear during cryogenic machining with cemented carbide end mills. (2022).
## Conclusion and Next Steps

The study has allowed to further the insights on the impact of machining on the quality of the subsurface copper layer and thus on the superconducting niobium layer of SRF machined cavities. The influence of edge radius on changes in surface integrity emerges as a significant factor. Even low values of tool wear stand out as the parameter greatly affecting dislocation density of the copper substrate. Though its effects on measured final dislocation of the SRF layer seem to be reduced, optimal conditions for Nb coating are difficult to obtain, especially on complex geometries far from the samples studied; wear should be kept under close control, and it appears clearly that 0.15mm flank wear is already above acceptable limit.

The use of diamond tool stands out as the best configuration for minimising dislocation density of both copper substrate and Nb layer. Additional studies will be performed in the space of cutting parameters with this tool, in order to find an optimal setup.

In addition, results of dislocation density and affected layer open the door to novel considerations with respect to current state of the art: substrate defects such as dislocation density may be only one of the driving factors for optimal Nb layer performance. This is why RF performance checks, EBSD as well as complementary GIXRD analyses, are in progress at the time of writing. Such results will be needed to finalise the link between substrate and SRF layer quality with respect to final radiofrequency performance; though such link has been obtained for surfaces yielding from different processes (shaping, turning), milling tests results are in any case needed to validate the above considerations on dislocation density.

Further tests -with identical milling cutters differing only in edge radius- will be conducted to provide additional insight; additionally, a more comprehensive description of cutter geometry at the cutting zone level, encompassing factors like surface "reflection" and clearance angles, would enhance our understanding of the mechanisms at play during milling. It might be conclusive to investigate the type and rate of tool wear. Only flank wear has been taken into account but due to the harsh behaviour of OFE copper, built-up edge of crater wear could be seen and would greatly modify the tool/copper interface phenomenon.

## Acknowledgements

The authors would like to acknowledge the following CERN colleagues, for their instrumental support in preparation of the samples and of the tests: Romain Ninet, Alan Saillet, Philippe Richerot, Dominique Pugnat, Maciej Burkowski, Ahmed Cherif, Louise Viezzi, Marc Thiebert and Serge Forel.

## References

[1] C. P. A. Carlos et al., Nb/Cu thin film HiPIMS coatings optimization for SRF applications, FCC Week 2022, Paris, France, 30 May - 03 June 2022.

[2] A. Camelin et al. Experimental analysis of subsurface integrity during fine turning of OFE copper for radiofrequency cavity manufacturing. Journal of Materials Processing Technology. 302. (2021) 117483. https://doi.org/10.1016/j.jmatprotec.2021.117483

[3] A. Plaçais et al., Multipactor studies for the FCC-ee superconducting SWELL cavities, (2023).

[4] M. Benedikt et al., Future Circular Collider - European Strategy Update Documents, (2019).

[5] I. Perez et al., Effect of cutting speed on the surface integrity of face milled 7050-T7451 aluminium workpieces. Procedia CIRP. 71 (2018) 460-465. https://doi.org/10.1016/j.procir.2018.05.034

[6] K. Gutzeit et al., Influence of the cutting-edge radius on tool wear during cryogenic machining with cemented carbide end mills. (2022).
[7] L. Denguir, José Outeiro, Guillaume Fromentin, Vincent Vignal, Rémy Besnard: Influence of cutting process mechanics on surface integrity and electrochemical behavior of OFHC copper. Procedia CIRP 13 (2014) 186–191. https://doi.org/10.1016/j.procir.2014.04.032

[8] J. P. Davim et al: Machining, edition Springer, Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal. (2008).

[9] Y. Zenchao, X. Yang, L. Yan, X. Jin, W. Quandai: The effect of milling parameters on surface integrity in high-speed milling of ultrahigh strength steel. Procedia CIRP 71 (2018) 83–88. https://doi.org/10.1016/j.procir.2018.05.076

[10] M. Arzeo et al., Enhanced radio-frequency performance of niobium films on copper substrates deposited by high power impulse magnetron sputtering. Supercond. Sci. Technol. 35 (2022) 054008. https://doi.org/10.1088/1361-6668/ac5646

[11] G.Rosaz et al., Niobium thin film thickness profile tailoring on complex shape substrates using unbalanced biased High Power Impulse Magnetron Sputtering, Surf. Coat. Technol. 436 (2022) 128306. https://doi.org/10.1016/j.surfcoat.2022.128306

[12] L. Lutterotti et al., A friendly java program for material analysis using diffraction. (1999).

[13] A. Saillet et al., Evaluation of computer-aided manufacturing software accuracy for high precision machining, euspen's 20th International Conference & Exhibition, Geneva, CH, June 2020.

[14] J. Ma, University of Waikato, New Zealand: Investigation on the interface structure and thermal conductivity of hot-forged Cu/ (Ti/W-coated)-diamond composites. (2020).

[15] J. E. Graebner: Thermal Conductivity of Diamond. In: Pan, L.S., Kania, D.R. (eds) Diamond Electronic Properties and Applications, (1995)285-318, editor: Springer. https://doi.org/10.1007/978-1-4615-2257-7_7

[16] S. Breumier et al., High strain rate micro-compression for crystal plasticity constitutive law parameters identification. (2021). https://doi.org/10.1016/j.matdes.2020.108789
[7] L. Denguir, José Outeiro, Guillaume Fromentin, Vincent Vignal, Rémy Besnard: Influence of cutting process mechanics on surface integrity and electrochemical behavior of OFHC copper. Procedia CIRP 13 (2014) 186–191. https://doi.org/10.1016/j.procir.2014.04.032

[8] J. P. Davim et al: Machining, edition Springer, Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal. (2008).

[9] Y. Zenchao, X. Yang, L. Yan, X. Jin, W. Quandai: The effect of milling parameters on surface integrity in high-speed milling of ultrahigh strength steel. Procedia CIRP 71 (2018) 83–88. https://doi.org/10.1016/j.procir.2018.05.076

[10] M. Arzeo et al., Enhanced radio-frequency performance of niobium films on copper substrates deposited by high power impulse magnetron sputtering. Supercond. Sci. Technol. 35 (2022) 054008. https://doi.org/10.1088/1361-6668/ac5646

[11] G.Rosaz et al., Niobium thin film thickness profile tailoring on complex shape substrates using unbalanced biased High Power Impulse Magnetron Sputtering, Surf. Coat. Technol. 436 (2022) 128306. https://doi.org/10.1016/j.surfcoat.2022.128306

[12] L. Lutterotti et al., A friendly java program for material analysis using diffraction. (1999).

[13] A. Saillet et al., Evaluation of computer-aided manufacturing software accuracy for high precision machining, euspen's 20th International Conference & Exhibition, Geneva, CH, June 2020.

[14] J. Ma, University of Waikato, New Zealand: Investigation on the interface structure and thermal conductivity of hot-forged Cu/ (Ti/W-coated)-diamond composites. (2020).

[15] J. E. Graebner: Thermal Conductivity of Diamond. In: Pan, L.S., Kania, D.R. (eds) Diamond Electronic Properties and Applications, (1995)285-318, editor: Springer. https://doi.org/10.1007/978-1-4615-2257-7_7

[16] S. Breumier et al., High strain rate micro-compression for crystal plasticity constitutive law parameters identification. (2021). https://doi.org/10.1016/j.matdes.2020.108789
# Study of cutting force in milling of aluminum-lithium alloy

TAMURA Shoichi¹,ᵃ*, MORII Daisuke¹,ᵇ and MATSUMURA Takashi¹,ᶜ

¹Tokyo Denki University, 5 Senjyu Asahi-cho, Adachi-ku, Tokyo, 120-8551, JAPAN

ᵃtamuras@mail.dendai.ac.jp, ᵇ22kmk28@ms.dendai.ac.jp, ᶜmatsumu@cck.dendai.ac.jp

**Keywords:** Milling, Aluminum-Lithium Alloy, Cutting Force

**Abstract.** Aluminum-lithium alloy has been applied to aircraft parts for reduction of the fuel consumption with its high specific strength. Cutting tests are performed to characterize the cutting force of aluminum-lithium alloy (Constellium, 2098-T8) and conventional extra-super duralumin (JIS A7075-T6) in slot milling at different spindle speeds. When the cutting speed increases, the tangential and radial components in cutting force of the aluminum-lithium alloy considerably decrease up to 300 m/min; while those of A7075 decrease monotonically. Then, the cutting process of aluminum-lithium alloy is discussed in an energy-minimum cutting force model. The shear angle and the friction angle increase with the cutting velocity, and the shear stress on the shear plane decreases with the increase of cutting velocity. According to the cutting model in milling of aluminum-lithium alloy, the cutting velocity should be taken higher than 300 m/min to not only reduce the cutting force but also control the surface finish.

**Introduction**

Aluminum-lithium alloy has been attracted in aerospace industry due to its lightweight and high strength, where adding 1 wt% lithium to aluminum reduces the density by 3% and enhances the elastic modulus by 6% [1]. Aluminum-lithium alloys recently have been applied to the parts used in not only military but also commercial aircrafts [1]. Therefore, high quality is required for cutting of aluminum-lithium alloy as well as high production rate.

J. Niu et al. [2] studied the corrosion resistance on the machined surface in milling of aluminum-lithium alloy 2A97 under dry cutting conditions. According to their discussion, a larger strain hardening occurs in subsurface formed by cutting than that of grinding or polishing. The machined surface in milling promotes the corrosion resistance with the strain hardening. H. Mu et al. [3] compared the surface integrity in face milling of aluminum-lithium alloy with air coolant and with liquid nitrogen. Liquid nitrogen efficiently induces compressive residual stress. Furthermore, residual stress was associated with the spindle speed, the depth of cut, the feed rate, and the feed direction with respect to the rolling direction, in regression analysis. J. Niu et al. [4] discussed characteristics of machined surface in milling of aluminum-lithium alloy for the cutting parameters. As the cutting velocity increases, they demonstrated that the effect of thermal softening suppresses the work hardening. Denkena et al. [5] discussed the effect of the sharpness of cutting edge on the stability in cutting process with the temperature rise in peripheral milling of Al-Li 2196. Although the cutting process of aluminum-lithium alloys has been studied so far, the cutting force has not been yet discussed in terms of the cutting model.

This paper discusses the cutting processes of aluminum-lithium alloy in milling. First, the cutting forces in milling of aluminum-lithium alloy are measured and compared to those of A7075 to discuss the effect of cutting velocity. Then, the cutting force is analyzed in an energy-minimum cutting force model, where the orthogonal cutting data used in the model are identified with referring to the actual cutting forces. The change in the cutting model is associated with the chip morphology and adhesion, which are related to the shear deformation for chip formation and the friction on the rake face, respectively.

<figure><img src="image_1846.png" /></figure>
# Study of cutting force in milling of aluminum-lithium alloy

TAMURA Shoichi¹,ᵃ*, MORII Daisuke¹,ᵇ and MATSUMURA Takashi¹,ᶜ

¹Tokyo Denki University, 5 Senjyu Asahi-cho, Adachi-ku, Tokyo, 120-8551, JAPAN

ᵃtamuras@mail.dendai.ac.jp, ᵇ22kmk28@ms.dendai.ac.jp, ᶜmatsumu@cck.dendai.ac.jp

**Keywords:** Milling, Aluminum-Lithium Alloy, Cutting Force

**Abstract.** Aluminum-lithium alloy has been applied to aircraft parts for reduction of the fuel consumption with its high specific strength. Cutting tests are performed to characterize the cutting force of aluminum-lithium alloy (Constellium, 2098-T8) and conventional extra-super duralumin (JIS A7075-T6) in slot milling at different spindle speeds. When the cutting speed increases, the tangential and radial components in cutting force of the aluminum-lithium alloy considerably decrease up to 300 m/min; while those of A7075 decrease monotonically. Then, the cutting process of aluminum-lithium alloy is discussed in an energy-minimum cutting force model. The shear angle and the friction angle increase with the cutting velocity, and the shear stress on the shear plane decreases with the increase of cutting velocity. According to the cutting model in milling of aluminum-lithium alloy, the cutting velocity should be taken higher than 300 m/min to not only reduce the cutting force but also control the surface finish.

**Introduction**

Aluminum-lithium alloy has been attracted in aerospace industry due to its lightweight and high strength, where adding 1 wt% lithium to aluminum reduces the density by 3% and enhances the elastic modulus by 6% [1]. Aluminum-lithium alloys recently have been applied to the parts used in not only military but also commercial aircrafts [1]. Therefore, high quality is required for cutting of aluminum-lithium alloy as well as high production rate.

J. Niu et al. [2] studied the corrosion resistance on the machined surface in milling of aluminum-lithium alloy 2A97 under dry cutting conditions. According to their discussion, a larger strain hardening occurs in subsurface formed by cutting than that of grinding or polishing. The machined surface in milling promotes the corrosion resistance with the strain hardening. H. Mu et al. [3] compared the surface integrity in face milling of aluminum-lithium alloy with air coolant and with liquid nitrogen. Liquid nitrogen efficiently induces compressive residual stress. Furthermore, residual stress was associated with the spindle speed, the depth of cut, the feed rate, and the feed direction with respect to the rolling direction, in regression analysis. J. Niu et al. [4] discussed characteristics of machined surface in milling of aluminum-lithium alloy for the cutting parameters. As the cutting velocity increases, they demonstrated that the effect of thermal softening suppresses the work hardening. Denkena et al. [5] discussed the effect of the sharpness of cutting edge on the stability in cutting process with the temperature rise in peripheral milling of Al-Li 2196. Although the cutting process of aluminum-lithium alloys has been studied so far, the cutting force has not been yet discussed in terms of the cutting model.

This paper discusses the cutting processes of aluminum-lithium alloy in milling. First, the cutting forces in milling of aluminum-lithium alloy are measured and compared to those of A7075 to discuss the effect of cutting velocity. Then, the cutting force is analyzed in an energy-minimum cutting force model, where the orthogonal cutting data used in the model are identified with referring to the actual cutting forces. The change in the cutting model is associated with the chip morphology and adhesion, which are related to the shear deformation for chip formation and the friction on the rake face, respectively.

<figure><img src="image_1844.png" /></figure>
## Cutting Test

The cutting tests in milling of grooves were conducted on a 3-axis vertical machining center (Makino, V33i), as shown in Fig. 1. 4 mm thick plates of aluminum-lithium alloy (Constellium, 2098-T8) and conventional extra-super duralumin (JIS A7075-T6) were employed in the cutting tests. The aluminum-lithium alloy and the conventional extra-super duralumin are hereinafter referred to as Al-Li2098 and A7075 in the paper. Measured hardness of Al-Li2098 was 170 HV, which was nearly the same as 168 HV of A7075 each other.

The workpiece was clamped on a piezoelectric dynamometer (Kisler, 9256C2) mounted on the machine table to measure the cutting force. The cutting force was acquired at 100 kHz. A carbide two-flute square end mill coated with a Cr-based thin layer was used in the cutting test. The tool diameter and the helix angle were 12 mm and 30°, respectively. The end mill was clamped to the spindle of machine tool with a collet chuck. The end mill was fed along X direction in slotting in an axial depth of cut of 2 mm, as shown in Table 1. In investigation of the effects of cutting velocity on the cutting force, the spindle speed was controlled in a range of cutting velocity from 60 to 600 m/min, where the feed rate was constant at 0.04 mm/tooth. The chip thickness and the surface finish were measured with an optical microscope (Keyence, VHX-2000) and a laser microscope (Keyence, VK-X100).

<figure><img src="image_1847.png" /><figcaption>Fig. 1 Cutting test in peripheral milling</figcaption></figure>

<table><caption>Table 1 Cutting conditions</caption><tr><td>Axial depth of cut [mm]</td><td>2</td></tr><tr><td>Gloove width [mm]</td><td>12</td></tr><tr><td>Cutting velocity [m/min]</td><td>60, 180, 300, 450, 600</td></tr><tr><td>Feed rate [mm/tooth]</td><td>0.04</td></tr><tr><td>Lubrication</td><td>Dry</td></tr></table>

## Cutting Force in Milling

Figure 2 shows the measured cutting forces in milling of Al-Li2098 at a cutting velocity of 60 m/min, where the cutting force are designated as the load applied to the tool. The cutting force changes periodically in half of the cutter rotation cycle of 0.019 s from a time of O to O' in Fig.2.
## Cutting Test

The cutting tests in milling of grooves were conducted on a 3-axis vertical machining center (Makino, V33i), as shown in Fig. 1. 4 mm thick plates of aluminum-lithium alloy (Constellium, 2098-T8) and conventional extra-super duralumin (JIS A7075-T6) were employed in the cutting tests. The aluminum-lithium alloy and the conventional extra-super duralumin are hereinafter referred to as Al-Li2098 and A7075 in the paper. Measured hardness of Al-Li2098 was 170 HV, which was nearly the same as 168 HV of A7075 each other.

The workpiece was clamped on a piezoelectric dynamometer (Kisler, 9256C2) mounted on the machine table to measure the cutting force. The cutting force was acquired at 100 kHz. A carbide two-flute square end mill coated with a Cr-based thin layer was used in the cutting test. The tool diameter and the helix angle were 12 mm and 30°, respectively. The end mill was clamped to the spindle of machine tool with a collet chuck. The end mill was fed along X direction in slotting in an axial depth of cut of 2 mm, as shown in Table 1. In investigation of the effects of cutting velocity on the cutting force, the spindle speed was controlled in a range of cutting velocity from 60 to 600 m/min, where the feed rate was constant at 0.04 mm/tooth. The chip thickness and the surface finish were measured with an optical microscope (Keyence, VHX-2000) and a laser microscope (Keyence, VK-X100).

<figure><img src="image_1845.png" /><figcaption>Fig. 1 Cutting test in peripheral milling</figcaption></figure>

<table><caption>Table 1 Cutting conditions</caption><tr><td>Axial depth of cut [mm]</td><td>2</td></tr><tr><td>Gloove width [mm]</td><td>12</td></tr><tr><td>Cutting velocity [m/min]</td><td>60, 180, 300, 450, 600</td></tr><tr><td>Feed rate [mm/tooth]</td><td>0.04</td></tr><tr><td>Lubrication</td><td>Dry</td></tr></table>

## Cutting Force in Milling

Figure 2 shows the measured cutting forces in milling of Al-Li2098 at a cutting velocity of 60 m/min, where the cutting force are designated as the load applied to the tool. The cutting force changes periodically in half of the cutter rotation cycle of 0.019 s from a time of O to O' in Fig.2.
<figure><img src="image_1848.png" /><figcaption>Fig. 2 Cutting force measurement Fig. 3 Cutting force at the maxmum uncut chip thickness</figcaption></figure>

<figure><img src="image_1849.png" /></figure>

<figure><img src="image_1850.png" /><figcaption>(a) Principal component</figcaption></figure>

<figure><img src="image_1851.png" /><figcaption>(b) Radial component</figcaption></figure>

<figure><img src="image_1852.png" /><figcaption>(c) Axial component</figcaption></figure>

<figure><img src="image_1853.png" /><figcaption>Fig. 5 Chip thickness</figcaption></figure>

Because the cutting force components of a rotating edge change periodically with not only the uncut chip thickness but also the cutting direction in the measurement coordinate system of dynamometer, as shown in Fig. 3 viewed from upside of tool. The cutting force changes as follows:

1) At a time of O, an edge engages in the workpiece, and another edge exits from the workpiece. Because the uncut chip thickness is small around 0 s, little cutting force components were measured. Because the cutting direction nearly coincides with +X direction just after engagement. The negative X and Z components in the cutting force increase with the uncut chip thickness.

2) From A to B, the cutting direction turns gradually to Y direction from X direction. Then, X component decreases; while Y component, in turn, increases with cutter rotation, respectively.

3) When the cutting direction is oriented to -Y direction at the maximum uncut chip thickness at B, Y component loaded on the tool becomes large.

4) From B to O', the cutting force components decreases with the uncut chip thickness.
<figure><img src="image_1846.png" /><figcaption>Fig. 2 Cutting force measurement Fig. 3 Cutting force at the maxmum uncut chip thickness</figcaption></figure>

<figure><img src="image_1847.png" /><figcaption>Fig. 4 Cutting force components with cutting velocity</figcaption></figure>

<figure><img src="image_1848.png" /><figcaption>Fig. 5 Chip thickness</figcaption></figure>

Because the cutting force components of a rotating edge change periodically with not only the uncut chip thickness but also the cutting direction in the measurement coordinate system of dynamometer, as shown in Fig. 3 viewed from upside of tool. The cutting force changes as follows:

1) At a time of O, an edge engages in the workpiece, and another edge exits from the workpiece. Because the uncut chip thickness is small around 0 s, little cutting force components were measured. Because the cutting direction nearly coincides with +X direction just after engagement. The negative X and Z components in the cutting force increase with the uncut chip thickness.

2) From A to B, the cutting direction turns gradually to Y direction from X direction. Then, X component decreases; while Y component, in turn, increases with cutter rotation, respectively.

3) When the cutting direction is oriented to -Y direction at the maximum uncut chip thickness at B, Y component loaded on the tool becomes large.

4) From B to O', the cutting force components decreases with the uncut chip thickness.
In Fig. 3, X, Y, and Z components ($F_X$, $F_Y$, and $F_Z$) in the measurement coordinate system are directly regarded as radial, tangential, and axial components ($F_R$, $F_P$ and $F_A$) loaded on the rotating edge at B. Fig. 4 shows force components at B in the coordinate system of rotating edge for the cutting velocities, where the measured components are averaged in 5 or more rotations. The cutting force components becomes small at high cutting velocities. The principal and the radial components in milling of Al-Li2098 decrease significantly up to 300 m/min; and then, the changing rates become small up to 600 m/min. Those of A7075 decrease monotonically up to 600 m/min. The axial components of Al-Li2098 are smaller in all cutting velocities than those of A7075. These results will be discussed in the next section with an analytical force model.

Fig. 5 shows the maximum chip thicknesses at cutting velocities of 60, 300, and 600 m/min. Because the chip thickness becomes small at higher cutting velocities, the shear angle increases with the cutting speed in the shear plane cutting model.

## Analytical Force Model

An energy force model was applied to characterize the cutting process in slot milling of Al-Li2098. The force model in milling was presented in Reference [6]. The force model is briefly described here. A three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities $V$ and the chip flow velocities $V_c$, as shown in Fig. 6. Although plastic deformation occurs in the chip formation, the interaction between each orthogonal cutting plane is ignored on the assumption that a rigid chip flows at an angular velocity. The orthogonal cutting models are given by the following equations:

$$ \left. \begin{aligned} \phi &= \exp(A_{00}V + A_{01}t_1 + A_{02}\alpha + A_{03}) \\ \tau_s &= \exp(A_{10}V + A_{11}t_1 + A_{12}\alpha + A_{13}) \\ \beta &= \exp(A_{20}V + A_{21}t_1 + A_{22}\alpha + A_{23}) \end{aligned} \right\} \quad (1) $$

where $\phi$, $\tau_s$ and $\beta$ are the shear angle, the shear stress on the shear plane, and the friction angle, respectively. $V$, $t_1$, and $\alpha$ are the rake angle, the cutting velocity, and the uncut chip thickness in the orthogonal cutting. $A_{ij}$ ($i=0,1,2$; $j=0,1,2,3$) are parameters acquired in the orthogonal cutting tests. $A_{ij}$ can also be identified or refined with referring to the actual cutting force in milling by inverse analysis [7]. The chip formation is controlled by the first equation of Eq. (1). Machinability of workpiece may be evaluated by the second equation. Friction of the tool-chip interface was characterized by the friction angle in the third equation. Because the cutting temperature is associated with the cutting speed, the thermal effect on material behavior is predominantly

<figure><img src="image_1854.png" /><figcaption>Fig. 6 Chip flow model in milling</figcaption></figure>
In Fig. 3, X, Y, and Z components ($F_X$, $F_Y$, and $F_Z$) in the measurement coordinate system are directly regarded as radial, tangential, and axial components ($F_R$, $F_P$ and $F_A$) loaded on the rotating edge at B. Fig. 4 shows force components at B in the coordinate system of rotating edge for the cutting velocities, where the measured components are averaged in 5 or more rotations. The cutting force components becomes small at high cutting velocities. The principal and the radial components in milling of Al-Li2098 decrease significantly up to 300 m/min; and then, the changing rates become small up to 600 m/min. Those of A7075 decrease monotonically up to 600 m/min. The axial components of Al-Li2098 are smaller in all cutting velocities than those of A7075. These results will be discussed in the next section with an analytical force model.

Fig. 5 shows the maximum chip thicknesses at cutting velocities of 60, 300, and 600 m/min. Because the chip thickness becomes small at higher cutting velocities, the shear angle increases with the cutting speed in the shear plane cutting model.

## Analytical Force Model

An energy force model was applied to characterize the cutting process in slot milling of Al-Li2098. The force model in milling was presented in Reference [6]. The force model is briefly described here. A three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities $V$ and the chip flow velocities $V_c$, as shown in Fig. 6. Although plastic deformation occurs in the chip formation, the interaction between each orthogonal cutting plane is ignored on the assumption that a rigid chip flows at an angular velocity. The orthogonal cutting models are given by the following equations:

$$ \left. \begin{aligned} \phi &= \exp(A_{00}V + A_{01}t_1 + A_{02}\alpha + A_{03}) \\ \tau_s &= \exp(A_{10}V + A_{11}t_1 + A_{12}\alpha + A_{13}) \\ \beta &= \exp(A_{20}V + A_{21}t_1 + A_{22}\alpha + A_{23}) \end{aligned} \right\} \quad (1) $$

where $\phi$, $\tau_s$ and $\beta$ are the shear angle, the shear stress on the shear plane, and the friction angle, respectively. $V$, $t_1$, and $\alpha$ are the rake angle, the cutting velocity, and the uncut chip thickness in the orthogonal cutting. $A_{ij}$ ($i=0,1,2$; $j=0,1,2,3$) are parameters acquired in the orthogonal cutting tests. $A_{ij}$ can also be identified or refined with referring to the actual cutting force in milling by inverse analysis [7]. The chip formation is controlled by the first equation of Eq. (1). Machinability of workpiece may be evaluated by the second equation. Friction of the tool-chip interface was characterized by the friction angle in the third equation. Because the cutting temperature is associated with the cutting speed, the thermal effect on material behavior is predominantly

<figure><img src="image_1849.png" /><figcaption>Fig. 6 Chip flow model in milling</figcaption></figure>
controlled by $A_{i0}$ ($i = 0,1,2$) in each equation. Based on the measured cutting forces in the range of cutting velocity from 60 to 300 m/min, the orthogonal cutting data were acquired as:

Al-Li2098:

$$ \left. \begin{aligned} \phi &= \exp(0.07092V + 7976t_1 + 0.005507\alpha - 1.215) \\ \tau_s &= \exp(-0.05393V - 1946t_1 + 0.25596\alpha + 19.95) \\ \beta &= \exp(0.00608V - 316.2t_1 + 0.09937\alpha - 0.4774) \end{aligned} \right\} \quad (2) $$

A7075:

$$ \left. \begin{aligned} \phi &= \exp(0.02509V + 7840t_1 + 0.005507\alpha - 1.010) \\ \tau_s &= \exp(-0.03950V - 1688t_1 + 0.1317\alpha + 20.03) \\ \beta &= \exp(0.04458V - 557.9t_1 + 0.02515\alpha - 0.6493) \end{aligned} \right\} \quad (3) $$

Figure 7 compares the simulated and the measured cutting forces in milling of Al-Li2098 and A7075 at cutting velocities of 60 and 300 m/min. The force model and the orthogonal cutting data are verified in the agreement of the simulated cutting forces with the measured ones.

## Change in Cutting Model

The cutting model at the center of cutting area is discussed in the range of cutting velocities from 60 to 300 m/min. Figure 8 shows the shear angles, the shear stress on the shear plane, and the friction angle in the cutting model. The shear angle increases with the cutting velocity in Fig. 8(a). In milling of Al-Li2098, the shear angle is more sensitive to the cutting velocity than that of A7075, where the sensitivity to cutting velocity is controlled by $A_{oo}$ in Eq. (1). Since the shear force reduces with the shear plane at a large shear angle, the cutting force components are considerably reduced with increasing the cutting velocity shown in Fig. 4.

<figure><img src="image_1855.png" /><figcaption>Fig. 7 Cutting force simulation</figcaption></figure>

Then, the shear stress on the shear plane becomes small at high cutting velocities, as shown in Fig. 8(b). As the cutting temperature increases with the cutting velocity, the workpiece undergoes thermal softening at high cutting velocities, which reduces the shear stress on the shear plane.
controlled by $A_{i0}$ ($i = 0,1,2$) in each equation. Based on the measured cutting forces in the range of cutting velocity from 60 to 300 m/min, the orthogonal cutting data were acquired as:

Al-Li2098:

$$ 
\left. 
\begin{aligned}
\phi &= \exp(0.07092V + 7976t_1 + 0.005507\alpha - 1.215) \\
\tau_s &= \exp(-0.05393V - 1946t_1 + 0.25596\alpha + 19.95) \\
\beta &= \exp(0.00608V - 316.2t_1 + 0.09937\alpha - 0.4774)
\end{aligned}
\right\} \quad (2)
$$

A7075:

$$ 
\left. 
\begin{aligned}
\phi &= \exp(0.02509V + 7840t_1 + 0.005507\alpha - 1.010) \\
\tau_s &= \exp(-0.03950V - 1688t_1 + 0.1317\alpha + 20.03) \\
\beta &= \exp(0.04458V - 557.9t_1 + 0.02515\alpha - 0.6493)
\end{aligned}
\right\} \quad (3)
$$

Figure 7 compares the simulated and the measured cutting forces in milling of Al-Li2098 and A7075 at cutting velocities of 60 and 300 m/min. The force model and the orthogonal cutting data are verified in the agreement of the simulated cutting forces with the measured ones.

## Change in Cutting Model

The cutting model at the center of cutting area is discussed in the range of cutting velocities from 60 to 300 m/min. Figure 8 shows the shear angles, the shear stress on the shear plane, and the friction angle in the cutting model. The shear angle increases with the cutting velocity in Fig. 8(a). In milling of Al-Li2098, the shear angle is more sensitive to the cutting velocity than that of A7075, where the sensitivity to cutting velocity is controlled by $A_{oo}$ in Eq. (1). Since the shear force reduces with the shear plane at a large shear angle, the cutting force components are considerably reduced with increasing the cutting velocity shown in Fig. 4.

<figure><img src="image_1850.png" /><figcaption>Fig. 7 Cutting force simulation</figcaption></figure>

Then, the shear stress on the shear plane becomes small at high cutting velocities, as shown in Fig. 8(b). As the cutting temperature increases with the cutting velocity, the workpiece undergoes thermal softening at high cutting velocities, which reduces the shear stress on the shear plane.
<figure><img src="image_1856.png" /><figcaption>(a) Shear angle</figcaption></figure>

<figure><img src="image_1857.png" /><figcaption>(b) Shear stress on shear plane
Fig. 8 Shear plane cutting model</figcaption></figure>

<figure><img src="image_1858.png" /><figcaption>(c) Friction angle</figcaption></figure>

Although both materials have similar hardness at room temperature, the shear stress on the shear plane of Al-Li2098 remains consistently lower compared to A7075. Generally, aluminum lithium alloys have lower thermal conductivity than conventional aluminum alloys. Therefore, the cutting temperature of Al-Li2098 is expected to be higher than that of A7075. Then, the mechanical strength of Al-Li2098 decreases significantly with the temperature rise. The effect of cutting speed on the thermal softening is evaluated by $A_{10}$ in Eq. (1). The relatively large negative $A_{10}$ in Eq.(2) gives more contribution to reduction of the shear stress when the cutting velocity increases in milling of Al-Li2098.

<figure><img src="image_1859.png" /><figcaption>Fig. 9 Height distribution on machined surface</figcaption></figure>

The friction angles of both materials increase with the cutting temperature due to activation of affinity in the interface between the thermal softened chip and the rake face, as shown in Fig. 8(c). Although the friction angles at 300 m/min are similar in both materials, the angles of Al-Li2098 indicate larger angles in comparison to that of A7075 at cutting velocities of 60 and 180 m/min. Fig. 9 compares the height distributions on the surface finishes of Al-Li2098 and A7075 at a cutting velocity of 60 m/min. Some residual adhesions are observed on the unstable cutter marks in Fig. 9(a) of Al-Li2098; while regular cutter marks are formed in Fig. 9(b) of A7075. Although further investigation is required for the scientific discussion between adhesion and the friction, the large friction force of Al-Li2098 may promote adhesion and repeat growing and dropping of built-up edges on the tool-chip interface at low cutting velocities. Adhesion of Al-Li2098 deteriorates the surface finish more than A7075.

According to the above discussions, the cutting velocity should be taken more than 300 m/min to finish fine surfaces with low cutting forces in milling of Al-Li2098.
<figure><img src="image_1851.png" /><figcaption>(a) Shear angle</figcaption></figure>

<figure><img src="image_1852.png" /><figcaption>(b) Shear stress on shear plane
Fig. 8 Shear plane cutting model</figcaption></figure>

<figure><img src="image_1853.png" /><figcaption>(c) Friction angle</figcaption></figure>

Although both materials have similar hardness at room temperature, the shear stress on the shear plane of Al-Li2098 remains consistently lower compared to A7075. Generally, aluminum lithium alloys have lower thermal conductivity than conventional aluminum alloys. Therefore, the cutting temperature of Al-Li2098 is expected to be higher than that of A7075. Then, the mechanical strength of Al-Li2098 decreases significantly with the temperature rise. The effect of cutting speed on the thermal softening is evaluated by $A_{10}$ in Eq. (1). The relatively large negative $A_{10}$ in Eq.(2) gives more contribution to reduction of the shear stress when the cutting velocity increases in milling of Al-Li2098.

<figure><img src="image_1854.png" /><figcaption>Fig. 9 Height distribution on machined surface</figcaption></figure>

The friction angles of both materials increase with the cutting temperature due to activation of affinity in the interface between the thermal softened chip and the rake face, as shown in Fig. 8(c). Although the friction angles at 300 m/min are similar in both materials, the angles of Al-Li2098 indicate larger angles in comparison to that of A7075 at cutting velocities of 60 and 180 m/min. Fig. 9 compares the height distributions on the surface finishes of Al-Li2098 and A7075 at a cutting velocity of 60 m/min. Some residual adhesions are observed on the unstable cutter marks in Fig. 9(a) of Al-Li2098; while regular cutter marks are formed in Fig. 9(b) of A7075. Although further investigation is required for the scientific discussion between adhesion and the friction, the large friction force of Al-Li2098 may promote adhesion and repeat growing and dropping of built-up edges on the tool-chip interface at low cutting velocities. Adhesion of Al-Li2098 deteriorates the surface finish more than A7075.

According to the above discussions, the cutting velocity should be taken more than 300 m/min to finish fine surfaces with low cutting forces in milling of Al-Li2098.
**Summary**

The paper has studied milling of Al-Li2089 in slotting to characterize the cutting force in terms of its sensitivity to cutting velocity. The cutting force is compared with A7075. The results are summarized as:

1) In milling of Al-Li2089, the cutting force components in tangential and radial directions at the maximum uncut chip thickness decrease significantly up to a cutting velocity of 300 m/min, while those of A7075 decrease monotonically up to a cutting force of 600 m/min.

2) Analytical cutting force model is applied to discuss the cutting process. Although the shear angle increases with the cutting velocity. The sensitivity of the shear angle of Al-Li2089 to the cutting velocity is larger than that of A7075. Therefore, the cutting force considerably reduce up to 300 m/min.

3) The shear stress on the shear plane of Al-Li2089 becomes small in all tested cutting velocity. Thermal softening of Al-Li 2089 may occur more at high cutting temperatures compared to that of A7075.

4) The friction angles become larger in milling of Al-Li2089 at low cutting velocities in comparison to those of A7075. The large friction force at low cutting velocity may induce growth of built-up edges on the rake face.

**References**

[1] N. Eswara, P. R. J. H. Wanhill, Aerospace Materials and Material Technologies, Indian Institute of Metals Series 1, (2017).

[2] J. Niu, Z. Liu, B. Wang, Y. Hua, G. Wang, Effect of Machining-induced Surface Integrity on the Corrosion Behavior of Al-Li alloy 2A97 in Sodium Chloride Solution, Materials and Corrosion, 70, (2019), 2, 259-267. https://doi.org/10.1002/maco.201810380

[3] H. Mou, X. Huang, X. Zhang, H. Ding, Experimental Study of Surface Integrity of Aluminum Lithium Alloy by Face Milling, Intelligent Robotics and Applications 6th international conference ICIRA 2013 (2013), 25-28. https://doi.org/10.1007/978-3-642-40849-6_50

[4] J. Niu, Z. Liu, X. Ai, W. Huang, G. Wang, R. Duan, Characteristics of Machined Surface Integrity in Face Milling Al-Li Alloy 2A97 with Carbide Inserts, International Journal of Advanced Manufacturing Technology, 101 (2019), 1-4, 839-848. https://doi.org/10.1007/s00170-018-2907-8

[5] B. Denkena, J. Brüning, D. Niederwestberg, R. Grabowski, Influence of Machining Parameters on Heat Generation during Milling of Aluminum Alloys, Procedia CIRP, 46 (2016), pp. 39-42. https://doi.org/10.1016/j.procir.2016.03.192

[6] T. Matsumura, E. Usui, Predictive Cutting Force Model in Complex-shaped End Milling based on Minimum Cutting Energy, Int. J. Mach. Tools Manuf., 50 (2010), 5, 458-466. https://doi.org/10.1016/j.ijmachtools.2010.01.008

[7] T. Matsumura, T. Shirakashi, and E. Usui, Adaptive cutting force prediction in milling processes, International Journal of Automation Technology, 4 (2010), 3, 221-228. https://doi.org/10.20965/ijat.2010.p0221
## Summary

The paper has studied milling of Al-Li2089 in slotting to characterize the cutting force in terms of its sensitivity to cutting velocity. The cutting force is compared with A7075. The results are summarized as:

1) In milling of Al-Li2089, the cutting force components in tangential and radial directions at the maximum uncut chip thickness decrease significantly up to a cutting velocity of 300 m/min, while those of A7075 decrease monotonically up to a cutting force of 600 m/min.

2) Analytical cutting force model is applied to discuss the cutting process. Although the shear angle increases with the cutting velocity. The sensitivity of the shear angle of Al-Li2089 to the cutting velocity is larger than that of A7075. Therefore, the cutting force considerably reduce up to 300 m/min.

3) The shear stress on the shear plane of Al-Li2089 becomes small in all tested cutting velocity. Thermal softening of Al-Li 2089 may occur more at high cutting temperatures compared to that of A7075.

4) The friction angles become larger in milling of Al-Li2089 at low cutting velocities in comparison to those of A7075. The large friction force at low cutting velocity may induce growth of built-up edges on the rake face.

## References

[1] N. Eswara, P. R. J. H. Wanhill, Aerospace Materials and Material Technologies, Indian Institute of Metals Series 1, (2017).

[2] J. Niu, Z. Liu, B. Wang, Y. Hua, G. Wang, Effect of Machining-induced Surface Integrity on the Corrosion Behavior of Al-Li alloy 2A97 in Sodium Chloride Solution, Materials and Corrosion, 70, (2019), 2, 259-267. https://doi.org/10.1002/maco.201810380

[3] H. Mou, X. Huang, X. Zhang, H. Ding, Experimental Study of Surface Integrity of Aluminum Lithium Alloy by Face Milling, Intelligent Robotics and Applications 6th international conference ICIRA 2013 (2013), 25-28. https://doi.org/10.1007/978-3-642-40849-6_50

[4] J. Niu, Z. Liu, X. Ai, W. Huang, G. Wang, R. Duan, Characteristics of Machined Surface Integrity in Face Milling Al-Li Alloy 2A97 with Carbide Inserts, International Journal of Advanced Manufacturing Technology, 101 (2019), 1-4, 839-848. https://doi.org/10.1007/s00170-018-2907-8

[5] B. Denkena, J. Brüning, D. Niederwestberg, R. Grabowski, Influence of Machining Parameters on Heat Generation during Milling of Aluminum Alloys, Procedia CIRP, 46 (2016), pp. 39-42. https://doi.org/10.1016/j.procir.2016.03.192

[6] T. Matsumura, E. Usui, Predictive Cutting Force Model in Complex-shaped End Milling based on Minimum Cutting Energy, Int. J. Mach. Tools Manuf., 50 (2010), 5, 458-466. https://doi.org/10.1016/j.ijmachtools.2010.01.008

[7] T. Matsumura, T. Shirakashi, and E. Usui, Adaptive cutting force prediction in milling processes, International Journal of Automation Technology, 4 (2010), 3, 221-228. https://doi.org/10.20965/ijat.2010.p0221
# Comparison of artificial intelligence techniques for cutting tool condition monitoring

COLANTONIO Lorenzo<sup>1,a*</sup>, EQUETER Lucas<sup>1,b</sup>, DEHOMBREUX Pierre<sup>1,c</sup> and DUCOBU François<sup>1,d</sup>

<sup>1</sup>Machine Design and Production Engineering Lab, University of Mons, 7000 Mons, Belgium

**Keywords:** Machining, Artificial Intelligence, Wear, Monitoring

**Abstract.** In manufacturing, tool wear monitoring is crucial as it directly influences production quality and operating costs. Inaccurate replacement strategies can result in increased costs and substandard parts. Various Artificial Intelligence (AI) methods have been proposed to monitor tool wear using cutting signals, but a comprehensive performance comparison is lacking. This paper evaluates three distinct AI approaches: Artificial Neural Networks (ANN), Support Vector Machines (SVM), and K-Nearest Neighbours (K-NN). The selection of these approach is based on their learning mechanisms. Each method is optimized using a GridSearch algorithm and their real-time wear monitoring capabilities are compared. The results shows that all AI techniques monitored tool wear with similar precision, making it challenging to draw a definitive conclusion in this regard. The choice of the most appropriate AI method is heavily dependent on the manufacturing environment. For large-scale manufacturing under similar cutting conditions, K-NN and SVM are a good choice. The ANN is better suited to all scenarios, but particularly where there are substantial fluctuations in cutting conditions or, in general, larger databases.

**Introduction**

The quality of a machined surface is related, among others, to the condition of the tool that was used to produce it. Despite often being overlooked in industrial context, the wear condition of the tool is of critical importance. Indeed, a worn cutting tool will lead to poor quality in terms of geometrical, residual constraints and tribological standpoints. In industrial context, tool replacement policies are often a compromise between the stopping of the operation and the quality of the production. Therefore, the choice of the replacement policies is of crucial importance as a wrong policy implies higher operating costs [1]. To optimize the replacement policies and by consequence limit the production of substandard parts, there is a need to monitor the degradation of the tool. The ISO 3685 standard defines the indicator to evaluate the state of the tool as the size of the flank wear (VB), thus most of monitoring methods focus on methods to estimate this type of wear.

The detection of the wear is often realised indirectly, by using signals from the cutting process to estimate the state of the tool. This approach has the advantage of not needing to stop the machining to inspect the state of the tool, but it needs to instrumentalize the machine. A complete analysis of the different signals used for indirect monitoring and their features is presented in [2]. Numerous strategies have been developed to assess the condition of the tool and therefore propose to follow its degradation path during machining. Earlier methods used statistical analysis or stochastic modelling of the process [3].

Recently and with industry 4.0, more Artificial Intelligence (AI) approaches tend to monitor the state of the tool. These approaches have the benefit of learning directly from the data and therefore automatically map the complex non-linearity between the condition monitoring signals and the state of the tool even in variable cutting conditions. Numerous applications, each

<figure><img src="image_1860.png" /></figure>

<footnote><sup>a</sup>Lorenzo.colantonio@umons.ac.be, <sup>b</sup>lucas.equeter@umons.ac.be,</footnote>

<footnote><sup>c</sup>Pierre.dehombreux@umons.ac.be, <sup>d</sup>francois.ducobu@umons.ac.be</footnote>
# Comparison of artificial intelligence techniques for cutting tool condition monitoring

COLANTONIO Lorenzo<sup>1,a*</sup>, EQUETER Lucas<sup>1,b</sup>, DEHOMBREUX Pierre<sup>1,c</sup> and DUCOBU François<sup>1,d</sup>

<sup>1</sup>Machine Design and Production Engineering Lab, University of Mons, 7000 Mons, Belgium

<sup>a</sup>Lorenzo.colantonio@umons.ac.be, <sup>b</sup>lucas.equeter@umons.ac.be,

<sup>c</sup>Pierre.dehombreux@umons.ac.be, <sup>d</sup>francois.ducobu@umons.ac.be

**Keywords:** Machining, Artificial Intelligence, Wear, Monitoring

**Abstract.** In manufacturing, tool wear monitoring is crucial as it directly influences production quality and operating costs. Inaccurate replacement strategies can result in increased costs and substandard parts. Various Artificial Intelligence (AI) methods have been proposed to monitor tool wear using cutting signals, but a comprehensive performance comparison is lacking. This paper evaluates three distinct AI approaches: Artificial Neural Networks (ANN), Support Vector Machines (SVM), and K-Nearest Neighbours (K-NN). The selection of these approach is based on their learning mechanisms. Each method is optimized using a GridSearch algorithm and their real-time wear monitoring capabilities are compared. The results shows that all AI techniques monitored tool wear with similar precision, making it challenging to draw a definitive conclusion in this regard. The choice of the most appropriate AI method is heavily dependent on the manufacturing environment. For large-scale manufacturing under similar cutting conditions, K-NN and SVM are a good choice. The ANN is better suited to all scenarios, but particularly where there are substantial fluctuations in cutting conditions or, in general, larger databases.

**Introduction**

The quality of a machined surface is related, among others, to the condition of the tool that was used to produce it. Despite often being overlooked in industrial context, the wear condition of the tool is of critical importance. Indeed, a worn cutting tool will lead to poor quality in terms of geometrical, residual constraints and tribological standpoints. In industrial context, tool replacement policies are often a compromise between the stopping of the operation and the quality of the production. Therefore, the choice of the replacement policies is of crucial importance as a wrong policy implies higher operating costs [1]. To optimize the replacement policies and by consequence limit the production of substandard parts, there is a need to monitor the degradation of the tool. The ISO 3685 standard defines the indicator to evaluate the state of the tool as the size of the flank wear (VB), thus most of monitoring methods focus on methods to estimate this type of wear.

The detection of the wear is often realised indirectly, by using signals from the cutting process to estimate the state of the tool. This approach has the advantage of not needing to stop the machining to inspect the state of the tool, but it needs to instrumentalize the machine. A complete analysis of the different signals used for indirect monitoring and their features is presented in [2]. Numerous strategies have been developed to assess the condition of the tool and therefore propose to follow its degradation path during machining. Earlier methods used statistical analysis or stochastic modelling of the process [3].

Recently and with industry 4.0, more Artificial Intelligence (AI) approaches tend to monitor the state of the tool. These approaches have the benefit of learning directly from the data and therefore automatically map the complex non-linearity between the condition monitoring signals and the state of the tool even in variable cutting conditions. Numerous applications, each

<figure><img src="image_1855.png" /></figure>
employing distinct AI techniques, have been suggested in various studies [4]. Each application has its unique set of input signals, pre-processing methods, ... which differ from one another, making it challenging to get a comprehensive comparison of performance between methods [5]. In general, the most common approach is to use an artificial neural network on cutting forces to monitor the degradation in real time [6].

Despite many approaches and generally good results obtained with AI [7], there is a lack of clear comparison of different AI methods. The only comparison is often limited to different pre-processing or data acquisition techniques or are limited to classification purpose [8]. In this paper, it is proposed to compare the performance of different AI regressors to monitor the state of the tool from cutting signals during machining. This article therefore compares 3 AI approaches, namely: Artificial Neural Networks (ANN), Support Vector Machine (SVM) and K-Nearest Neighbours (K-NN). The selection of these methods stems from their differences of concept to learn from the data. Each of them is explained in its respective section below.

The novelty of the approach consists of comparing the performance of different AI techniques using an identical optimisation and evaluation process. To optimise each approach, a GridSearch algorithm is used to identify the best combination of hyperparameters. The evaluation is realised on variable cutting conditions to ensure that the approaches can generalize their results on previously unseen cutting conditions. Differences in performance between the methods are assessed using a numerical indicator, and a visual representation of monitoring quality is also provided.

## Description of Database

The database presented in this article is from experimental turning tests. The lathe is a Weiler E35 that is used to machine C45 steel bars (Figure 1). The selected cutting tool is the CNMG120404-MF3 TP40 tool from SECO and it is one of the lowest grades to favorize the apparition of wear and limit the test duration and the quantity of wasted materials. A total of 30 tools are used under different cutting conditions. Those cutting conditions are presented in Table 1 and are selected to observe the impact of variation of the cutting speed on the wear.

<table><caption>Table 1 Testing Cutting Conditions</caption><thead><tr><th>Test n°</th><th>Cutting Speed [m/min]</th><th>Feed [mm/rev]</th><th>Depth of cut [mm]</th></tr></thead><tbody><tr><td>1 to 10</td><td>260</td><td>0.2</td><td>1</td></tr><tr><td>11 to 15</td><td>250</td><td>0.2</td><td>1</td></tr><tr><td>16</td><td>240</td><td>0.2</td><td>1</td></tr><tr><td>17 to 20</td><td>265</td><td>0.2</td><td>1</td></tr><tr><td>21 to 30</td><td>Variable during life: 240 to 260</td><td>0.2</td><td>1</td></tr></tbody></table>

<table><caption>Table 2 Measured Cutting Parameters</caption><thead><tr><th>Measured value</th><th>Equipment</th><th>Denomination</th></tr></thead><tbody><tr><td>Cutting force</td><td>Kistler 9257B</td><td>Fx, Fy, Fz</td></tr><tr><td>Cutting torque</td><td>Kistler 9257B</td><td>Mx, My, Mz</td></tr><tr><td>Wear of the tool</td><td>Byameeyee<br>EU-1000X 3</td><td>VB</td></tr></tbody></table>

During the turning tests, multiple quantities are measured at a recurrent inspection interval of 2.8 minutes and are listed in Table 2. The cutting forces and torques are measured during machining. To inspect the state of the tool, the machining is stopped, and the wear is measured with a Byameeyee EU-1000X 3 microscope according to the ISO 3685 standard. This standard defines $VB_{max}$ and VB as shown in Figure 2 and limits the maximum amount of wear before the tool is considered worn. For the test and according to the standard, it is considered that a tool is worn if the value of VB reaches 300 µm.
employing distinct AI techniques, have been suggested in various studies [4]. Each application has its unique set of input signals, pre-processing methods, ... which differ from one another, making it challenging to get a comprehensive comparison of performance between methods [5]. In general, the most common approach is to use an artificial neural network on cutting forces to monitor the degradation in real time [6].

Despite many approaches and generally good results obtained with AI [7], there is a lack of clear comparison of different AI methods. The only comparison is often limited to different pre-processing or data acquisition techniques or are limited to classification purpose [8]. In this paper, it is proposed to compare the performance of different AI regressors to monitor the state of the tool from cutting signals during machining. This article therefore compares 3 AI approaches, namely: Artificial Neural Networks (ANN), Support Vector Machine (SVM) and K-Nearest Neighbours (K-NN). The selection of these methods stems from their differences of concept to learn from the data. Each of them is explained in its respective section below.

The novelty of the approach consists of comparing the performance of different AI techniques using an identical optimisation and evaluation process. To optimise each approach, a GridSearch algorithm is used to identify the best combination of hyperparameters. The evaluation is realised on variable cutting conditions to ensure that the approaches can generalize their results on previously unseen cutting conditions. Differences in performance between the methods are assessed using a numerical indicator, and a visual representation of monitoring quality is also provided.

## Description of Database

The database presented in this article is from experimental turning tests. The lathe is a Weiler E35 that is used to machine C45 steel bars (Figure 1). The selected cutting tool is the CNMG120404-MF3 TP40 tool from SECO and it is one of the lowest grades to favorize the apparition of wear and limit the test duration and the quantity of wasted materials. A total of 30 tools are used under different cutting conditions. Those cutting conditions are presented in Table 1 and are selected to observe the impact of variation of the cutting speed on the wear.

<table><caption>Table 1 Testing Cutting Conditions</caption><thead><tr><th>Test n°</th><th>Cutting Speed [m/min]</th><th>Feed [mm/rev]</th><th>Depth of cut [mm]</th></tr></thead><tbody><tr><td>1 to 10</td><td>260</td><td>0.2</td><td>1</td></tr><tr><td>11 to 15</td><td>250</td><td>0.2</td><td>1</td></tr><tr><td>16</td><td>240</td><td>0.2</td><td>1</td></tr><tr><td>17 to 20</td><td>265</td><td>0.2</td><td>1</td></tr><tr><td>21 to 30</td><td>Variable during life: 240 to 260</td><td>0.2</td><td>1</td></tr></tbody></table>

<table><caption>Table 2 Measured Cutting Parameters</caption><thead><tr><th>Measured value</th><th>Equipment</th><th>Denomination</th></tr></thead><tbody><tr><td>Cutting force</td><td>Kistler 9257B</td><td>Fx, Fy, Fz</td></tr><tr><td>Cutting torque</td><td>Kistler 9257B</td><td>Mx, My, Mz</td></tr><tr><td>Wear of the tool</td><td>Byameeyee<br>EU-1000X 3</td><td>VB</td></tr></tbody></table>

During the turning tests, multiple quantities are measured at a recurrent inspection interval of 2.8 minutes and are listed in Table 2. The cutting forces and torques are measured during machining. To inspect the state of the tool, the machining is stopped, and the wear is measured with a Byameeyee EU-1000X 3 microscope according to the ISO 3685 standard. This standard defines $VB_{max}$ and VB as shown in Figure 2 and limits the maximum amount of wear before the tool is considered worn. For the test and according to the standard, it is considered that a tool is worn if the value of VB reaches 300 µm.
<figure><img src="image_1861.png" /><figcaption>Figure 1 Experimental Set-Up</figcaption></figure>

<figure><img src="image_1862.png" /><figcaption>Figure 2 Flank Face Wear Definition</figcaption></figure>

The cutting forces and torques are temporal signals that are pre-processed to extract meaningful information from it. There exists plenty of pre-processing approach but the most common have been selected based on their effectiveness in the literature [5]. The selected pre-processing techniques are: Mean, Root Mean Squared, Skewness, ... In addition to these values, other indicators are considered such as the cutting time and the machine length.

These values are not all correlated with the wear. To estimate their correlation with it, a Spearman's correlation analysis is performed according to [9]. This correlation analysis is the most adapted to the complete dataset. The most correlated signals and their associated correlation are: Mz RMS (correlation indicator: 0.89), Fx RMS (0.87), machining duration (0.84), total length machined (0.84) and Fz RMS (0.79). These signals are therefore used as inputs to all the AI approaches presented in this study.

## Methodology to Compare and Optimize the Results

In the following, multiple AI approaches are compared. Each approach can be tuned through different set of hyperparameters that can influence the quality of the results obtained with the approach. In this article, it is proposed that the determination of hyperparameters is systematically determined through a GridSearch optimization algorithm. This optimization approach consists of testing each combination of hyperparameters that are defined for each AI regressor.

To ensure that the approach does not overfit to the database, this GridSearch algorithm uses a 5-fold cross-validation to assess model performance. In this cross-validation, the dataset is split into five parts. Each part serves as a test set once, while the model is trained on the remaining data. The process is repeated five times, and the results are averaged to provide a robust performance estimate. The number of five folds is chosen to have 20% of the database for testing while training on the remaining 80%. This method allows to systematically identify the best combinations of hyperparameters for each approach and the 5-folds approach ensure that there is no overfitting to obtain the results presented in the following. The optimization is realised on Intel I7-9750H @ 2.6 GHz CPU.

Once the best hyperparameters are identified, a new optimized model is trained and tested. To compare the performance on an objective basis, the database is divided into a training database and a testing database. As it is common practice in AI, the training database accounts for 80 % of the whole database and the remaining 20 % are used for testing. The testing database consists of 6 trajectories that are: 23, 24, 26, 27, 28 and 29 (cf. Table 1). These trajectories are selected as they have variation in their cutting conditions between two inspections (Figure 3) and are therefore good indicator to assess the generalization capability of the AI approaches. Indeed, these variations are different from one another and from training database trajectories and therefore are not
<figure><img src="image_1856.png" /><figcaption>Figure 1 Experimental Set-Up</figcaption></figure>

<figure><img src="image_1857.png" /><figcaption>Figure 2 Flank Face Wear Definition</figcaption></figure>

The cutting forces and torques are temporal signals that are pre-processed to extract meaningful information from it. There exists plenty of pre-processing approach but the most common have been selected based on their effectiveness in the literature [5]. The selected pre-processing techniques are: Mean, Root Mean Squared, Skewness, ... In addition to these values, other indicators are considered such as the cutting time and the machine length.

These values are not all correlated with the wear. To estimate their correlation with it, a Spearman's correlation analysis is performed according to [9]. This correlation analysis is the most adapted to the complete dataset. The most correlated signals and their associated correlation are: Mz RMS (correlation indicator: 0.89), Fx RMS (0.87), machining duration (0.84), total length machined (0.84) and Fz RMS (0.79). These signals are therefore used as inputs to all the AI approaches presented in this study.

## Methodology to Compare and Optimize the Results

In the following, multiple AI approaches are compared. Each approach can be tuned through different set of hyperparameters that can influence the quality of the results obtained with the approach. In this article, it is proposed that the determination of hyperparameters is systematically determined through a GridSearch optimization algorithm. This optimization approach consists of testing each combination of hyperparameters that are defined for each AI regressor.

To ensure that the approach does not overfit to the database, this GridSearch algorithm uses a 5-fold cross-validation to assess model performance. In this cross-validation, the dataset is split into five parts. Each part serves as a test set once, while the model is trained on the remaining data. The process is repeated five times, and the results are averaged to provide a robust performance estimate. The number of five folds is chosen to have 20% of the database for testing while training on the remaining 80%. This method allows to systematically identify the best combinations of hyperparameters for each approach and the 5-folds approach ensure that there is no overfitting to obtain the results presented in the following. The optimization is realised on Intel I7-9750H @ 2.6 GHz CPU.

Once the best hyperparameters are identified, a new optimized model is trained and tested. To compare the performance on an objective basis, the database is divided into a training database and a testing database. As it is common practice in AI, the training database accounts for 80 % of the whole database and the remaining 20 % are used for testing. The testing database consists of 6 trajectories that are: 23, 24, 26, 27, 28 and 29 (cf. Table 1). These trajectories are selected as they have variation in their cutting conditions between two inspections (Figure 3) and are therefore good indicator to assess the generalization capability of the AI approaches. Indeed, these variations are different from one another and from training database trajectories and therefore are not
represented in the training database. This feature thus allows to compare the monitoring performance on previously unseen cutting conditions during the life of the tool.

The selected performance indicator for this study is the Mean Squared Error (MSE). It consists of computing the average of the squares of the n errors ($e_i$) between the n real value of VB and the n estimated one (Figure 4 and Eq.1). In the following, the MSE is computed for each testing trajectory and then the mean MSE is computed on the whole testing dataset. For the MSE, a lower value indicates lower error.

$$MSE = \frac{1}{n} \sum_{i=1}^{n} e_i^2 \qquad (1)$$

<figure><img src="image_1863.png" /><figcaption>Figure 3 Testing Trajectories</figcaption></figure>

<figure><img src="image_1864.png" /><figcaption>Figure 4 MSE Computation</figcaption></figure>

## Description of the AI Approaches

In this study, 3 AI approaches are compared: Artificial Neural Networks, Support Vector Machine and K-Nearest Neighbours.

Artificial Neural Networks (ANNs) are a leading approach in machine learning. Inspired by the structure and function of the human brain, they consist of interconnected layers of neurons that can model complex, non-linear relationships (Figure 5). The performance of an ANN is primarily dictated by its architecture. The neural network is constructed by layer, each one having a specific number of neurons with their respective activation function. The choice of structure is often induced by the complexity of the problem. Generally, more neurons and layers can model more complex function [10]. However, networks that are too deep may be less reliable if they are not warranted by the complexity of the problem.

The second approach is a Support Vector Machine (SVM). SVM in regression, known as Support Vector Regression (SVR), is a powerful regression tool. It operates by first applying a kernel function to the input space to transform the input data into a higher-dimensional space, enabling the conversion of a non-linear problem into a linear one (Figure 7). In addition to the kernel, there are 2 main hyperparameters: $\varepsilon$ and C. $\varepsilon$ defines the margin of tolerance where errors are not penalized, effectively controlling the width of the “tube” around the regression line. The C parameter, on the other hand, manages the trade-off between model complexity and its generalization ability [11].

The last approach is the K-Nearest Neighbour (K-NN) algorithm. It utilizes the structure of the input space of a given dataset to predict the value of a new entry. Specifically, it constructs a multidimensional feature space based on the input data and determines the value of a new entry based on the values of its ‘k’ nearest neighbours within this feature space. As shown Figure 6,
represented in the training database. This feature thus allows to compare the monitoring performance on previously unseen cutting conditions during the life of the tool.

The selected performance indicator for this study is the Mean Squared Error (MSE). It consists of computing the average of the squares of the n errors ($e_i$) between the n real value of VB and the n estimated one (Figure 4 and Eq.1). In the following, the MSE is computed for each testing trajectory and then the mean MSE is computed on the whole testing dataset. For the MSE, a lower value indicates lower error.

$$MSE = \frac{1}{n} \sum_{i=1}^{n} e_i^2 \qquad (1)$$

<figure><img src="image_1858.png" /><figcaption>Figure 3 Testing Trajectories</figcaption></figure>

<figure><img src="image_1859.png" /><figcaption>Figure 4 MSE Computation</figcaption></figure>

## Description of the AI Approaches

In this study, 3 AI approaches are compared: Artificial Neural Networks, Support Vector Machine and K-Nearest Neighbours.

Artificial Neural Networks (ANNs) are a leading approach in machine learning. Inspired by the structure and function of the human brain, they consist of interconnected layers of neurons that can model complex, non-linear relationships (Figure 5). The performance of an ANN is primarily dictated by its architecture. The neural network is constructed by layer, each one having a specific number of neurons with their respective activation function. The choice of structure is often induced by the complexity of the problem. Generally, more neurons and layers can model more complex function [10]. However, networks that are too deep may be less reliable if they are not warranted by the complexity of the problem.

The second approach is a Support Vector Machine (SVM). SVM in regression, known as Support Vector Regression (SVR), is a powerful regression tool. It operates by first applying a kernel function to the input space to transform the input data into a higher-dimensional space, enabling the conversion of a non-linear problem into a linear one (Figure 7). In addition to the kernel, there are 2 main hyperparameters: $\epsilon$ and C. $\epsilon$ defines the margin of tolerance where errors are not penalized, effectively controlling the width of the “tube” around the regression line. The C parameter, on the other hand, manages the trade-off between model complexity and its generalization ability [11].

The last approach is the K-Nearest Neighbour (K-NN) algorithm. It utilizes the structure of the input space of a given dataset to predict the value of a new entry. Specifically, it constructs a multidimensional feature space based on the input data and determines the value of a new entry based on the values of its ‘k’ nearest neighbours within this feature space. As shown Figure 6,
when 'k' is set to 4, the algorithm evaluates the new data point by considering the four closest existing points in the input space. The predicted value of the new entry is then typically determined by an average or weighted average of the values of its 'k' nearest neighbours [11].

<figure><img src="image_1865.png" /><figcaption>Figure 5 ANN Principle</figcaption></figure>

<figure><img src="image_1866.png" /><figcaption>Figure 6 K-NN Principle</figcaption></figure>

<figure><img src="image_1867.png" /><figcaption>Figure 7 SVM Principle</figcaption></figure>

## Results – Artificial Neural Networks

To determine the optimal network architecture, a series of architectures are systematically evaluated. The optimization parameters of the GridSearch algorithm are the activation function (hyperbolic tangent – Tanh, a Rectified Linear Unit – Relu and sigmoid), the number of neurons (1 to 40) and the number of layers (1 to 20). A total of 1600 architectures have been tested. On average, the training time is around 90 seconds. Figure 8 shows the results of the optimization. The Figure 9 shows that an increase in the number of layers has a negative impact on the quality of the monitoring. Also, above a certain number of layers, there is no benefit to add neurons in the layer. The data shown in the figures suggest that the ideal network consists of 2 to 6 layers, each with 6 to 10 neurons. Further optimization led to a network that is composed of two layers, each with six neurons. The first layer uses a hyperbolic tangent (Tanh) activation function, while the second layer utilizes a Rectified Linear Unit (Relu) activation function (Figure 5).
when 'k' is set to 4, the algorithm evaluates the new data point by considering the four closest existing points in the input space. The predicted value of the new entry is then typically determined by an average or weighted average of the values of its 'k' nearest neighbours [11].

<figure><img src="image_1860.png" /><figcaption>Figure 5 ANN Principle</figcaption></figure>

<figure><img src="image_1861.png" /><figcaption>Figure 6 K-NN Principle</figcaption></figure>

<figure><img src="image_1862.png" /><figcaption>Figure 7 SVM Principle</figcaption></figure>

## Results – Artificial Neural Networks

To determine the optimal network architecture, a series of architectures are systematically evaluated. The optimization parameters of the GridSearch algorithm are the activation function (hyperbolic tangent – Tanh, a Rectified Linear Unit – Relu and sigmoid), the number of neurons (1 to 40) and the number of layers (1 to 20). A total of 1600 architectures have been tested. On average, the training time is around 90 seconds. Figure 8 shows the results of the optimization. The Figure 9 shows that an increase in the number of layers has a negative impact on the quality of the monitoring. Also, above a certain number of layers, there is no benefit to add neurons in the layer. The data shown in the figures suggest that the ideal network consists of 2 to 6 layers, each with 6 to 10 neurons. Further optimization led to a network that is composed of two layers, each with six neurons. The first layer uses a hyperbolic tangent (Tanh) activation function, while the second layer utilizes a Rectified Linear Unit (Relu) activation function (Figure 5).
<figure><img src="image_1868.png" /><figcaption>Figure 8 ANN - Optimization
Results</figcaption></figure>

<figure><img src="image_1869.png" /><figcaption>Figure 9 ANN - Optimization
Detailed</figcaption></figure>

<figure><img src="image_1870.png" /><figcaption>Figure 10 ANN - Choice
Impact on Monitoring</figcaption></figure>

Figure 10 shows the difference between the optimized network and other network with 2 layers with 6 neurons each that exclusively employs a “ReLu”, “Tanh”, or “Sigmoid” activation function. As all networks tend to converge to the same range of MSE, the observation of the best performance is not visible in Figure 10. On average, over the whole testing dataset, the optimized network has better performance than the other networks as presented Table 3.

<table><caption>Table 3 ANN - Comparison of Performance for the Testing Trajectories</caption><thead><tr><th>Method</th><th>MSE 23</th><th>MSE 24</th><th>MSE 26</th><th>MSE 27</th><th>MSE 28</th><th>MSE 29</th><th>Average MSE</th><th>Average without 26</th></tr></thead><tbody><tr><td>Optimized</td><td>190.5</td><td>193.9</td><td>2412.4</td><td>379.8</td><td>102.4</td><td>1082.5</td><td>726.9</td><td>389.8</td></tr><tr><td>ReLu only</td><td>414.4</td><td>292.2</td><td>2237.6</td><td>362.6</td><td>343.0</td><td>548.5</td><td>699.7</td><td>392.1</td></tr><tr><td>Tanh only</td><td>1060.5</td><td>976.9</td><td>567.9</td><td>284.5</td><td>186.1</td><td>3159</td><td>1039.2</td><td>1133.4</td></tr><tr><td>Sigmoid only</td><td>308.5</td><td>399.0</td><td>1392.67</td><td>387.76</td><td>343.8</td><td>911.6</td><td>623.9</td><td>470.2</td></tr><tr><td>Overall best</td><td>Optimized</td><td>Optimized</td><td>Tanh</td><td>Tanh</td><td>Optimized</td><td>ReLu</td><td>Optimized</td><td>Optimized</td></tr></tbody></table>

## Results - Support Vector Machine

The combination of the kernel function, the parameter C and the parameter ε of the SVM approaches can be intricated. The tested GridSearch parameters and their values are the kernel function (Linear, Polynomial (1 to 10 degrees), Radial Basis Function (RBF), Sigmoid), the regulizer C (1 to 150) and ε (0.1 to 1 by 50 steps of 0.02). This choice of parameters space is made to ensure that a wide range of values are tested. A total of 97500 combinations of parameters are tested. On average, the training time is around 0.05 seconds.

The optimized parameters for each kernel and their respective global performances on the testing dataset are presented Table 4. Figure 11 shows the different performances of different kernels functions depending on the hyperparameters. This figure shows that the best performances are achieved with the RBF function and that there is a wide region where the results obtained are in the same range. It is also observable that the parameter ε has no effect on the results. On the other hand, the sigmoid kernel is not able to obtain good results and is not presented in the top of Figure 11.

To visually represent the impact of the choice of hyperparameters, Figure 12 shows the best combination of hyperparameter for each Kernel function. On this Figure, it is clearly observed that the sigmoid kernel function is to avoid as it tends to largely underestimate the wear at the end-of-life of the tool. The same phenomenon is observed for the linear approach. The polynomial approach tends to have a larger error in the middle of the life of the tool but at the end-of-life, there
<figure><img src="image_1863.png" /><figcaption>Figure 8 ANN - Optimization
Results</figcaption></figure>

<figure><img src="image_1864.png" /><figcaption>Figure 9 ANN - Optimization
Detailed</figcaption></figure>

<figure><img src="image_1865.png" /><figcaption>Figure 10 ANN - Choice
Impact on Monitoring</figcaption></figure>

Figure 10 shows the difference between the optimized network and other network with 2 layers with 6 neurons each that exclusively employs a “ReLu”, “Tanh”, or “Sigmoid” activation function. As all networks tend to converge to the same range of MSE, the observation of the best performance is not visible in Figure 10. On average, over the whole testing dataset, the optimized network has better performance than the other networks as presented Table 3.

<table><caption>Table 3 ANN - Comparison of Performance for the Testing Trajectories</caption><thead><tr><th>Method</th><th>MSE 23</th><th>MSE 24</th><th>MSE 26</th><th>MSE 27</th><th>MSE 28</th><th>MSE 29</th><th>Average MSE</th><th>Average without 26</th></tr></thead><tbody><tr><td>Optimized</td><td>190.5</td><td>193.9</td><td>2412.4</td><td>379.8</td><td>102.4</td><td>1082.5</td><td>726.9</td><td>389.8</td></tr><tr><td>ReLu only</td><td>414.4</td><td>292.2</td><td>2237.6</td><td>362.6</td><td>343.0</td><td>548.5</td><td>699.7</td><td>392.1</td></tr><tr><td>Tanh only</td><td>1060.5</td><td>976.9</td><td>567.9</td><td>284.5</td><td>186.1</td><td>3159</td><td>1039.2</td><td>1133.4</td></tr><tr><td>Sigmoid only</td><td>308.5</td><td>399.0</td><td>1392.67</td><td>387.76</td><td>343.8</td><td>911.6</td><td>623.9</td><td>470.2</td></tr><tr><td>Overall best</td><td>Optimized</td><td>Optimized</td><td>Tanh</td><td>Tanh</td><td>Optimized</td><td>ReLu</td><td>Optimized</td><td>Optimized</td></tr></tbody></table>

## Results - Support Vector Machine

The combination of the kernel function, the parameter *C* and the parameter *ε* of the SVM approaches can be intricated. The tested GridSearch parameters and their values are the kernel function (Linear, Polynomial (1 to 10 degrees), Radial Basis Function (RBF), Sigmoid), the regulizer *C* (1 to 150) and *ε* (0.1 to 1 by 50 steps of 0.02). This choice of parameters space is made to ensure that a wide range of values are tested. A total of 97500 combinations of parameters are tested. On average, the training time is around 0.05 seconds.

The optimized parameters for each kernel and their respective global performances on the testing dataset are presented Table 4. Figure 11 shows the different performances of different kernels functions depending on the hyperparameters. This figure shows that the best performances are achieved with the RBF function and that there is a wide region where the results obtained are in the same range. It is also observable that the parameter *ε* has no effect on the results. On the other hand, the sigmoid kernel is not able to obtain good results and is not presented in the top of Figure 11.

To visually represent the impact of the choice of hyperparameters, Figure 12 shows the best combination of hyperparameter for each Kernel function. On this Figure, it is clearly observed that the sigmoid kernel function is to avoid as it tends to largely underestimate the wear at the end-of-life of the tool. The same phenomenon is observed for the linear approach. The polynomial approach tends to have a larger error in the middle of the life of the tool but at the end-of-life, there
is less difference than other models. Finally, the RBF kernel gives the best results and follows almost perfectly the real degradation.

<table><caption>Table 4 SVM – Best Hyperparameters for Each Kernel and their Performance on Testing Set</caption><thead><tr><td>Kernel</td><td>C</td><td>ε</td><td>Global MSE (testing set)</td></tr></thead><tbody><tr><td>Radial Basis Function</td><td>51</td><td>0.85</td><td>670</td></tr><tr><td>Linear</td><td>9</td><td>0.79</td><td>1352</td></tr><tr><td>Polynomial (degree: 3)</td><td>1</td><td>0.22</td><td>6096</td></tr><tr><td>Sigmoid</td><td>1</td><td>0.78</td><td>5167</td></tr></tbody></table>

<figure><img src="image_1871.png" /><figcaption>Figure 11 SVM – Optimization Results</figcaption></figure>

<figure><img src="image_1872.png" /><figcaption>Figure 12 SVM – Kernel Impact on Performance</figcaption></figure>

## Results – K-Nearest Neighbour

Two primary hyperparameters significantly influence the results: the distance computation method and the number of neighbours. The distance computation can be either “uniform”, where each neighbour is given equal weight, or “distance”, where the weight of each neighbour is inversely proportional to its distance from the new point. The number of neighbours determines the size of the local neighbourhood used for the prediction. The optimization considers both distance computation and a neighbourhood from 1 to 150 neighbours. In total 300 combinations have been tested for an average fitting time of less than 0.002s for each.

The Figure 13 illustrates the training performance of K-NN, considering the weight function and the number of neighbours. The area labelled as the “Best performance zone” means that the MSE is around 10% of the optimal value. It is observed that the optimal zone is larger for the “distance” weight computation. Furthermore the “distance” weight computation has the best minimal MSE with a neighbourhood of 28. Given the broader optimal zone and the lower minimal MSE of the distance weight calculation, this method is recommended.

Figure 14 shows the difference of the best performance for “uniform” and “distance” approach. As their MSE are similar, the results are almost identical. There is simply a small difference at the end-of-life of the tool but this error as no impact in real life application.
is less difference than other models. Finally, the RBF kernel gives the best results and follows almost perfectly the real degradation.

<table><caption>Table 4 SVM – Best Hyperparameters for Each Kernel and their Performance on Testing Set</caption><thead><tr><td>Kernel</td><td>C</td><td>ε</td><td>Global MSE (testing set)</td></tr></thead><tbody><tr><td>Radial Basis Function</td><td>51</td><td>0.85</td><td>670</td></tr><tr><td>Linear</td><td>9</td><td>0.79</td><td>1352</td></tr><tr><td>Polynomial (degree: 3)</td><td>1</td><td>0.22</td><td>6096</td></tr><tr><td>Sigmoid</td><td>1</td><td>0.78</td><td>5167</td></tr></tbody></table>

<figure><img src="image_1866.png" /><figcaption>Figure 11 SVM – Optimization Results</figcaption></figure>

<figure><img src="image_1867.png" /><figcaption>Figure 12 SVM – Kernel Impact on Performance</figcaption></figure>

## Results – K-Nearest Neighbour

Two primary hyperparameters significantly influence the results: the distance computation method and the number of neighbours. The distance computation can be either “uniform”, where each neighbour is given equal weight, or “distance”, where the weight of each neighbour is inversely proportional to its distance from the new point. The number of neighbours determines the size of the local neighbourhood used for the prediction. The optimization considers both distance computation and a neighbourhood from 1 to 150 neighbours. In total 300 combinations have been tested for an average fitting time of less than 0.002s for each.

The Figure 13 illustrates the training performance of K-NN, considering the weight function and the number of neighbours. The area labelled as the “Best performance zone” means that the MSE is around 10% of the optimal value. It is observed that the optimal zone is larger for the “distance” weight computation. Furthermore the “distance” weight computation has the best minimal MSE with a neighbourhood of 28. Given the broader optimal zone and the lower minimal MSE of the distance weight calculation, this method is recommended.

Figure 14 shows the difference of the best performance for “uniform” and “distance” approach. As their MSE are similar, the results are almost identical. There is simply a small difference at the end-of-life of the tool but this error as no impact in real life application.
<figure><img src="image_1873.png" /><figcaption>Figure 13 K-NN – Optimization Results</figcaption></figure>

<figure><img src="image_1874.png" /><figcaption>Figure 14 K-NN Hyperparameters Impact</figcaption></figure>

## Results – Comparison

As each AI model is optimized, it is possible to compare their performance against each other. Table 5 shows the MSE of each optimized approach on the testing set. It is observed that all the approaches can achieve similar performance on average. Table 5 also shows that even though neural networks does not have the best mean MSE, it is the method that presents with the best results over the testing trajectories. The worst MSE for ANN is due to the error on trajectory 26 which leads to a significant increase in the mean MSE.

<table><caption>Table 5 Comparison of Performances for the 3 Presented Approaches</caption><thead><tr><th>Method</th><th>MSE 23</th><th>MSE 24</th><th>MSE 26</th><th>MSE 27</th><th>MSE 28</th><th>MSE 29</th><th>Average MSE</th></tr></thead><tbody><tr><td>ANN</td><td>190</td><td>193</td><td>2412</td><td>379</td><td>102</td><td>1082</td><td>694</td></tr><tr><td>SVM</td><td>124</td><td>1002</td><td>1002</td><td>41</td><td>165</td><td>1790</td><td>670</td></tr><tr><td>K-NN</td><td>513</td><td>982</td><td>523</td><td>44</td><td>213</td><td>1449</td><td>613</td></tr><tr><td>Best</td><td>SVM</td><td>ANN</td><td>K-NN</td><td>SVM</td><td>ANN</td><td>ANN</td><td>ANN</td></tr></tbody></table>

Figure 15 visually represent the performance of the different approaches on the testing trajectories. In Trajectory 23, both ANN and SVM provide similar wear estimations, while K-NN tends to overestimate the wear, predicting VB above 300 µm. Trajectory 24 reveals comparable monitoring for SVM and K-NN, with ANN proving more reliable during the tool's lifespan, but less so post end-of-life. Trajectory 26 displays similar errors across all estimators, but ANN overestimates the tool's wear, resulting in a high MSE score. For Trajectory 27, SVM and K-NN estimations align closely and accurately track the wear, whereas ANN deviates. In Trajectory 28, all approaches are similar, but ANN is slightly more accurate. Lastly, Trajectory 29 shows a steep degradation after 17 minutes, causing errors in the estimations. All estimators predicted higher wear, decreasing towards the end, with K-NN even reducing the VB value below the end-of-life. The analyse of performance, does not allow to clearly identify a best regressor over the other. Each model has its own strengths and limitations, and the choice of the best model depends on various factors beyond just performance metrics.

The K-NN model's effectiveness is heavily sensitive to the quality of the database, especially the noise and outliers within it. Furthermore, the amount of data can also be a limitation. In the database presented in this article, the number of points is limited. However, in industrial practice, databases can contain thousands of data points and cutting conditions. Given that this method requires the computation of the distance between each point for monitoring, it can be challenging to scale in industrial practice. The limitation of SVM is also in the database. Although it is less sensitive to outliers compared to K-NN, it struggles with scalability when dealing with large
<figure><img src="image_1868.png" /><figcaption>Figure 13 K-NN – Optimization Results</figcaption></figure>

<figure><img src="image_1869.png" /><figcaption>Figure 14 K-NN Hyperparameters Impact</figcaption></figure>

## Results – Comparison

As each AI model is optimized, it is possible to compare their performance against each other. Table 5 shows the MSE of each optimized approach on the testing set. It is observed that all the approaches can achieve similar performance on average. Table 5 also shows that even though neural networks does not have the best mean MSE, it is the method that presents with the best results over the testing trajectories. The worst MSE for ANN is due to the error on trajectory 26 which leads to a significant increase in the mean MSE.

<table><caption>Table 5 Comparison of Performances for the 3 Presented Approaches</caption><thead><tr><th>Method</th><th>MSE 23</th><th>MSE 24</th><th>MSE 26</th><th>MSE 27</th><th>MSE 28</th><th>MSE 29</th><th>Average MSE</th></tr></thead><tbody><tr><td>ANN</td><td>190</td><td>193</td><td>2412</td><td>379</td><td>102</td><td>1082</td><td>694</td></tr><tr><td>SVM</td><td>124</td><td>1002</td><td>1002</td><td>41</td><td>165</td><td>1790</td><td>670</td></tr><tr><td>K-NN</td><td>513</td><td>982</td><td>523</td><td>44</td><td>213</td><td>1449</td><td>613</td></tr><tr><td>Best</td><td>SVM</td><td>ANN</td><td>K-NN</td><td>SVM</td><td>ANN</td><td>ANN</td><td>ANN</td></tr></tbody></table>

Figure 15 visually represent the performance of the different approaches on the testing trajectories. In Trajectory 23, both ANN and SVM provide similar wear estimations, while K-NN tends to overestimate the wear, predicting VB above 300 µm. Trajectory 24 reveals comparable monitoring for SVM and K-NN, with ANN proving more reliable during the tool's lifespan, but less so post end-of-life. Trajectory 26 displays similar errors across all estimators, but ANN overestimates the tool's wear, resulting in a high MSE score. For Trajectory 27, SVM and K-NN estimations align closely and accurately track the wear, whereas ANN deviates. In Trajectory 28, all approaches are similar, but ANN is slightly more accurate. Lastly, Trajectory 29 shows a steep degradation after 17 minutes, causing errors in the estimations. All estimators predicted higher wear, decreasing towards the end, with K-NN even reducing the VB value below the end-of-life. The analyse of performance, does not allow to clearly identify a best regressor over the other. Each model has its own strengths and limitations, and the choice of the best model depends on various factors beyond just performance metrics.

The K-NN model's effectiveness is heavily sensitive to the quality of the database, especially the noise and outliers within it. Furthermore, the amount of data can also be a limitation. In the database presented in this article, the number of points is limited. However, in industrial practice, databases can contain thousands of data points and cutting conditions. Given that this method requires the computation of the distance between each point for monitoring, it can be challenging to scale in industrial practice. The limitation of SVM is also in the database. Although it is less sensitive to outliers compared to K-NN, it struggles with scalability when dealing with large