<table><caption>Table 1: Material characteristics for the investigated material batches</caption><thead><tr><th>Material Batch</th><th>t<br>(mm)</th><th>E<br>(GPa)</th><th>R<sub>p0.2</sub><br>(MPa)</th><th>R<sub>m</sub><br>(MPa)</th><th>r<sub>2-20/Ag</sub></th><th>A<sub>t</sub><br>(%)</th></tr></thead><tbody><tr><td>Batch 1</td><td>3.17</td><td>189</td><td>571</td><td>636</td><td>0.66</td><td>16.4</td></tr><tr><td>Batch 2</td><td>3.22</td><td>180</td><td>640</td><td>662</td><td>0.67</td><td>9.1</td></tr><tr><td>Batch 3</td><td>3.13</td><td>187</td><td>593</td><td>675</td><td>0.64</td><td>15.5</td></tr></tbody></table>

Shear cutting tests were conducted on the three material batches under consideration, and the resulting force-displacement curves were recorded. The tests were performed on a test press at the Fraunhofer IWU using a specialized measuring tool. The tool incorporates a load cell directly into the force flow of the cutting punch, while displacement is measured using a laser triangulation sensor. Figure 2 displays used the tool and the main process parameters. Figure 3 shows five force-displacement curves for each material batch. The graph shows the cutting force in relationship to the displacement of the punch relative to the specimen. It includes both the actual working stroke (positive forces) and the back stroke (negative forces). The curves recorded for the different batches exhibit significant differences. This indicates that the force-displacement curves are fundamentally suitable for detecting the different deformation behavior of the material batches.

<figure><img src="image_1290.png" /><figcaption>Fig. 2: Section view of used cutting tool and main experimental parameters</figcaption></figure>

<table><thead><tr><th colspan="2">tool components</th></tr></thead><tbody><tr><td>A</td><td>tool guidance</td></tr><tr><td>B</td><td>die</td></tr><tr><td>C</td><td>blank holder plate</td></tr><tr><td>D</td><td>cylindrical punch</td></tr><tr><td>E</td><td>load cell MEGATRON KMC100K 200kN</td></tr><tr><td>F</td><td>laser triangulation sensor MICRO-EPSILON optoNCDT 1420</td></tr></tbody><thead><tr><th colspan="2">experimental parameters</th></tr></thead><tbody><tr><td>punch diameter</td><td>5.8 mm (material: HSS)</td></tr><tr><td>clearance</td><td>0.125 mm</td></tr><tr><td>die velocity</td><td>3.5 mm/s</td></tr><tr><td>blank holder force</td><td>21 kN</td></tr></tbody></table>

<figure><img src="image_1291.png" /><figcaption>Fig. 3: Experimentally obtained cutting force signals for the 3 investigated material batches</figcaption></figure>
## FE-based Generation of Synthetic Training Data

To generate synthetic training data, a 2D FE model was created (see Fig. 3) in LS-Dyna® using axial symmetry in 2D. The process parameters, blank holder force ($F_{BH}$), and die velocity ($v_y$), were selected according to the experiments. The isotropic material model MAT024 was used to model the deformation behavior of the investigated material. We approximated the flow curve using the Hockett-Sherby approach (refer to Eq. 1), where C1 indicates the start of flow and C2 the maximum yield stress. The expression $exp(-C3 \cdot \varphi^{C4})$ describes the non-linear hardening behavior.

$$k_f = C2 - (C2 - C1) \cdot e^{-C3 \cdot \varphi^{C4}} \quad (1)$$

The yield curve parameters were determined based on the tensile test results for material batch 1 (see Table 3). The damage and failure behavior is modelled using the keyword ADD DAMAGE DIEM with the option DITYP = 1 where the damage is a function of the maximum shear stress.

<figure><img src="image_1289.png" /><figcaption>Fig. 4: FE model for the generation of synthetic training data</figcaption></figure>

The initial set of parameters was used to simulate the cutting process, resulting in the cutting force curve shown in Fig. 5. A significant deviation from the experimentally determined curve was observed, particularly in the area of elastic deformation ($P_1$ to $P_2$ (FEM 1)). This deviation was caused by the tool element being modeled as a rigid body. To address this, a spring element with the stiffness $k$ was introduced into the model to represent the tool stiffness. The spring constant $k$ was determined to $k = 60$ kN/mm through inverse identification. The resulting cutting force curve shows a much better match in the range from $P_1$ to $P_2$ (FEM 2). However, there is still a deviation between the experiment and simulation in the range from $P_2$ (FEM 2) to $P_3$ (FEM 2). When the yield point ($P_2$ (FEM 2)) is reached, the sheet material begins to flow. Due to the progressive deformation and the associated work hardening of the sheet metal material, the cutting force continues to increase. To achieve better fit in this range, the flow curve parameters C1 and C4 were adjusted inversely using the experimental cutting force curve. The FEM3 simulation model and the experiment show good agreement. Table 2 displays the adjusted flow curve parameters.
## FE-based Generation of Synthetic Training Data

To generate synthetic training data, a 2D FE model was created (see Fig. 3) in LS-Dyna® using axial symmetry in 2D. The process parameters, blank holder force ($F_{BH}$), and die velocity ($v_y$), were selected according to the experiments. The isotropic material model MAT024 was used to model the deformation behavior of the investigated material. We approximated the flow curve using the Hockett-Sherby approach (refer to Eq. 1), where C1 indicates the start of flow and C2 the maximum yield stress. The expression $exp(-C3 \cdot \varphi^{C4})$ describes the non-linear hardening behavior.

$$k_f = C2 - (C2 - C1) \cdot e^{-C3 \cdot \varphi^{C4}} \quad (1)$$

The yield curve parameters were determined based on the tensile test results for material batch 1 (see Table 3). The damage and failure behavior is modelled using the keyword ADD DAMAGE DIEM with the option DITYP = 1 where the damage is a function of the maximum shear stress.

<figure><img src="image_1292.png" /><figcaption>Fig. 4: FE model for the generation of synthetic training data</figcaption></figure>

The initial set of parameters was used to simulate the cutting process, resulting in the cutting force curve shown in Fig. 5. A significant deviation from the experimentally determined curve was observed, particularly in the area of elastic deformation ($P_1$ to $P_2$ (FEM 1)). This deviation was caused by the tool element being modeled as a rigid body. To address this, a spring element with the stiffness $k$ was introduced into the model to represent the tool stiffness. The spring constant $k$ was determined to $k = 60$ kN/mm through inverse identification. The resulting cutting force curve shows a much better match in the range from $P_1$ to $P_2$ (FEM 2). However, there is still a deviation between the experiment and simulation in the range from $P_2$ (FEM 2) to $P_3$ (FEM 2). When the yield point ($P_2$ (FEM 2)) is reached, the sheet material begins to flow. Due to the progressive deformation and the associated work hardening of the sheet metal material, the cutting force continues to increase. To achieve better fit in this range, the flow curve parameters C1 and C4 were adjusted inversely using the experimental cutting force curve. The FEM3 simulation model and the experiment show good agreement. Table 2 displays the adjusted flow curve parameters.
<figure><img src="image_1290.png" /><figcaption>Fig. 5: Comparison of experimental and simulated cutting force</figcaption></figure>

The simulation model FEM3 was used to generate the synthetic training data for the surrogate modelling. The varied parameters and the variation limits are summarized in Table 2.

<table><caption>Table 2: Identified model parameters and variation limits for generating the synthetic training data</caption><thead><tr><th rowspan="2">Parameter</th><th colspan="2">flow curve approximation based on</th><th colspan="2">Range for synthetic training data</th></tr><tr><th>tensile test</th><th>cutting force</th><th>lower bound</th><th>upper bound</th></tr></thead><tbody><tr><td>C1 in MPa</td><td>575.3</td><td>431</td><td>400</td><td>460</td></tr><tr><td>C2 in MPa</td><td>756.5</td><td>756.5</td><td>700</td><td>800</td></tr><tr><td>C3 [-]</td><td>3.5376</td><td>3.5376</td><td>2,5</td><td>4,5</td></tr><tr><td>C4 [-]</td><td>0.5369</td><td>1.0738</td><td>0,53</td><td>1,2</td></tr></tbody></table>

## Surrogate machine-learning models based on synthetic training data

The 163 synthetically generated force-displacement curves were then used to derive mechanical properties. We approached this in a two-fold approach. Firstly, characteristic quantities were extracted from each force displacement curve. We limit ourselves to the elastic gradient, maximum force, work and length of the punch phase [3]. Prior to extracting these quantities, we smoothed the force-displacement curves using the Savitzky-Golay-filter [7] to reduce the severe oscillations. The correlations between all input and extracted parameters can be seen in Fig. 6. Subsequently, we used these characteristic quantities as input for three different machine-learning algorithms: the decision tree based random forest (RF) [8] and XGBoost (XGB) [9] as well as a polynomial regression (PR) [8]. All models were trained using the scikit-learn package [10].
<figure><img src="image_1293.png" /><figcaption>Fig. 5: Comparison of experimental and simulated cutting force</figcaption></figure>

The simulation model FEM3 was used to generate the synthetic training data for the surrogate modelling. The varied parameters and the variation limits are summarized in Table 2.

<table><caption>Table 2: Identified model parameters and variation limits for generating the synthetic training data</caption><thead><tr><th rowspan="2">Parameter</th><th colspan="2">flow curve approximation based on</th><th colspan="2">Range for synthetic training data</th></tr><tr><th>tensile test</th><th>cutting force</th><th>lower bound</th><th>upper bound</th></tr></thead><tbody><tr><td>C1 in MPa</td><td>575.3</td><td>431</td><td>400</td><td>460</td></tr><tr><td>C2 in MPa</td><td>756.5</td><td>756.5</td><td>700</td><td>800</td></tr><tr><td>C3 [-]</td><td>3.5376</td><td>3.5376</td><td>2,5</td><td>4,5</td></tr><tr><td>C4 [-]</td><td>0.5369</td><td>1.0738</td><td>0,53</td><td>1,2</td></tr></tbody></table>

## Surrogate machine-learning models based on synthetic training data

The 163 synthetically generated force-displacement curves were then used to derive mechanical properties. We approached this in a two-fold approach. Firstly, characteristic quantities were extracted from each force displacement curve. We limit ourselves to the elastic gradient, maximum force, work and length of the punch phase [3]. Prior to extracting these quantities, we smoothed the force-displacement curves using the Savitzky-Golay-filter [7] to reduce the severe oscillations. The correlations between all input and extracted parameters can be seen in Fig. 6. Subsequently, we used these characteristic quantities as input for three different machine-learning algorithms: the decision tree based random forest (RF) [8] and XGBoost (XGB) [9] as well as a polynomial regression (PR) [8]. All models were trained using the scikit-learn package [10].
<figure><img src="image_1291.png" /><figcaption>Fig. 6: Correlation between input- (y-axis) and output-parameters (x-axis) for the ML-algorithms.</figcaption></figure>

To obtain a statistically well-behaved data set and improve convergence we normalized our data set using the min-max normalization they are scaled to values of [0,1]. Then, we split our dataset into a training and a test set with a ratio of 0.9 to 0.1. Hyperparameters (HP) for the tree base algorithms were determined using a Bayesian optimization (BO) and generalization was improved with a 10-fold cross-validation. The 10 models with the lowest mean-squared-error on the training set were used to predict the test set. The resulting root-mean-squared-error (RMSE) was compared to results of a model with default HPs and finally, the lowest RMSE model was chosen. For the RF the default set of HPs yielded the best results while best HPs for XGB are: 'colsample_bytree' = 1.0, 'learning_rate' = 0.07404622431244764, 'max_depth' = 10, 'n_estimators' = 48, 'subsample' = 0.6675843330634745. We trained the RF with degrees of 1 to 8 and again used the test set as metric to choose an appropriate model. As a result, a first-order-degree polynomial fit was chosen.

Overall, the XGB gives the best fitting result while yielding similar RMSE values as the RF for the test set separately. The polynomial fit clearly underperforms compared to the other regression methods. The relevant values are shown in Table 3 and Table 4.

<table><caption>Table 3: RMSE values for the total data set for all three ML-algorithms</caption><thead><tr><th>RMSE Full Dataset</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB</td><td>4.68</td><td><strong>8.34</strong></td><td>0.17</td><td>0.05</td></tr><tr><td>RF</td><td><strong>5.57</strong></td><td><strong>9.21</strong></td><td>0.22</td><td>0.06</td></tr><tr><td>PR</td><td>12.51</td><td><strong>16.97</strong></td><td>0.44</td><td>0.10</td></tr></tbody></table>
<figure><img src="image_1294.png" /><figcaption>Fig. 6: Correlation between input- (y-axis) and output-parameters (x-axis) for the ML-algorithms.</figcaption></figure>

To obtain a statistically well-behaved data set and improve convergence we normalized our data set using the min-max normalization they are scaled to values of [0,1]. Then, we split our dataset into a training and a test set with a ratio of 0.9 to 0.1. Hyperparameters (HP) for the tree base algorithms were determined using a Bayesian optimization (BO) and generalization was improved with a 10-fold cross-validation. The 10 models with the lowest mean-squared-error on the training set were used to predict the test set. The resulting root-mean-squared-error (RMSE) was compared to results of a model with default HPs and finally, the lowest RMSE model was chosen. For the RF the default set of HPs yielded the best results while best HPs for XGB are: 'colsample_bytree' = 1.0, 'learning_rate' = 0.07404622431244764, 'max_depth' = 10, 'n_estimators' = 48, 'subsample' = 0.6675843330634745. We trained the RF with degrees of 1 to 8 and again used the test set as metric to choose an appropriate model. As a result, a first-order-degree polynomial fit was chosen.

Overall, the XGB gives the best fitting result while yielding similar RMSE values as the RF for the test set separately. The polynomial fit clearly underperforms compared to the other regression methods. The relevant values are shown in Table 3 and Table 4.

<table><caption>Table 3: RMSE values for the total data set for all three ML-algorithms</caption><thead><tr><th>RMSE Full Dataset</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB</td><td>4.68</td><td><strong>8.34</strong></td><td>0.17</td><td>0.05</td></tr><tr><td>RF</td><td><strong>5.57</strong></td><td><strong>9.21</strong></td><td>0.22</td><td>0.06</td></tr><tr><td>PR</td><td>12.51</td><td><strong>16.97</strong></td><td>0.44</td><td>0.10</td></tr></tbody></table>
<table><caption>Table 4: RMSE values the test set for all three ML-algorithms</caption><thead><tr><th>RMSE Test Dataset</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB</td><td>10.83</td><td>23.12</td><td>0.45</td><td>0.12</td></tr><tr><td>RF</td><td>9.6</td><td>23.23</td><td>0.5</td><td>0.16</td></tr><tr><td>PR</td><td><b>10.78</b></td><td>27.64</td><td>0.48</td><td>0.15</td></tr></tbody></table>

As the XGB algorithm gave the best results for the training and test set Figure 7 shows the one-to-one correspondence of all output quantities. Both the training and test set are depicted. Clearly the general trend is predicted well for all four material parameters. C1 shows reduced regression accuracy for measured values around 400 and 460, i.e. the lowest and highest simulated values. A similar effect can be seen for the remaining parameters. This is readily explained by the low data density in these intervals. The test set shows some larger outliers in all four cases.

<figure><img src="image_1292.png" /><figcaption>Fig. 7: One-to-one correspondence between predictions by the XGB algorithm and measured values for the parameters C1 to C4. The training set is indicated by red and the test set by yellow circles</figcaption></figure>

For a more intuitive evaluation, Table 5 shows the relative absolute deviation (RAD) for the XGB algorithm defined as

$$ RAD = \frac{1}{N} \sum_{i}^{N} |(x_{i} - y_{i})/y_{i}| \quad (2) $$
<table><caption>Table 4: RMSE values the test set for all three ML-algorithms</caption><thead><tr><th>RMSE Test Dataset</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB</td><td>10.83</td><td>23.12</td><td>0.45</td><td>0.12</td></tr><tr><td>RF</td><td>9.6</td><td>23.23</td><td>0.5</td><td>0.16</td></tr><tr><td>PR</td><td><b>10.78</b></td><td>27.64</td><td>0.48</td><td>0.15</td></tr></tbody></table>

As the XGB algorithm gave the best results for the training and test set Figure 7 shows the one-to-one correspondence of all output quantities. Both the training and test set are depicted. Clearly the general trend is predicted well for all four material parameters. C1 shows reduced regression accuracy for measured values around 400 and 460, i.e. the lowest and highest simulated values. A similar effect can be seen for the remaining parameters. This is readily explained by the low data density in these intervals. The test set shows some larger outliers in all four cases.

<figure><img src="image_1295.png" /><figcaption>Fig. 7: One-to-one correspondence between predictions by the XGB algorithm and measured values for the parameters C1 to C4. The training set is indicated by red and the test set by yellow circles</figcaption></figure>

For a more intuitive evaluation, Table 5 shows the relative absolute deviation (RAD) for the XGB algorithm defined as

$$ RAD = \frac{1}{N} \sum_{i}^{N} |(x_{i} - y_{i})/y_{i}| \qquad (2) $$
where $x_i$ are the predicted and $y_i$ the expected values and N is the total number of data points. The larger error within the test set is not surprising, as these values are predicted, not fit and the test set is small, whereby outliers statistically have a larger impact on the metric. Additionally, we provide the R²-score in Table 6. This metric quantifies how much of the variance of a dependent variable can be explained by an independent variable of a trained regression model. For the full dataset we find high values of 0.88 to 0.96, indicating a good fit. As expected, the test set performs worse, C1 even yielding a negative value of -0.06. The variable C4 yields a relatively high value of 0.75.

<table><caption>Table 5: RAD for the XGB on full and test dataset</caption><thead><tr><th>RAD</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB (full dataset)</td><td>0.08</td><td>0.07</td><td>0.16</td><td>0.17</td></tr><tr><td>XGB (test dataset)</td><td>0.12</td><td>0.11</td><td>0.31</td><td>0.28</td></tr></tbody></table>

<table><caption>Table 6: R²-score for the XGB on full and test dataset</caption><thead><tr><th>R²</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB (full dataset)</td><td>0.88</td><td>0.89</td><td>0.90</td><td>0.96</td></tr><tr><td>XGB (test dataset)</td><td>-0.06</td><td>0.42</td><td>0.21</td><td>0.75</td></tr></tbody></table>

Overall, we have shown using relatively easily accessible synthetic data from Fe-simulations in combination with ML-algorithms that force-displacement curves from shear-cutting processes are a valid approach to predict various material parameters. The XGB algorithm fits and predicts the data well, but few significant outliers remain, which significantly impacts the prediction of variance. This issue may be resolved using a larger data set with a more homogeneously distributed input parameter space and by finding further input parameters, which have a significant influence on the material parameters. One such example could be the sheet thickness or other parameters extracted using feature-extraction or -engineering. Finally, a comparison with experimental data is necessary to validate this approach. These issues will be covered in future research.

## Summary

The experimental results demonstrate that the deformation behavior of the investigated material varies significantly between different batches. The cutting force curves obtained from the punching tests also vary depending on the material batch. Therefore, analyzing the cutting force curves can provide valuable information about the mechanical properties of the semi-finished products used. Furthermore, a FE model was developed for the shear cutting process being studied. A material model was parameterized based on the results of the tensile test and validated using the experimentally determined cutting force curves. This demonstrated the importance of considering tool stiffness. The optimized FE model was then used to perform variant calculations and generate synthetic training data to build predictive models to predict the flow curve and its parameters. Several machine learning algorithms were trained and evaluated using this data. The XGB algorithm demonstrated the best performance, accurately predicting the flow curve parameters. Future work will focus on optimizing and validating the prediction models using real experimental data.

## Acknowledgments

The results presented in this paper were generated in the AdaProQ project (FKZ: 13IK006F), which is funded by the BMWK as well as in the Priority Program 2422 founded by the German Research Foundation (DFG).
where $x_i$ are the predicted and $y_i$ the expected values and N is the total number of data points. The larger error within the test set is not surprising, as these values are predicted, not fit and the test set is small, whereby outliers statistically have a larger impact on the metric. Additionally, we provide the R²-score in Table 6. This metric quantifies how much of the variance of a dependent variable can be explained by an independent variable of a trained regression model. For the full dataset we find high values of 0.88 to 0.96, indicating a good fit. As expected, the test set performs worse, C1 even yielding a negative value of -0.06. The variable C4 yields a relatively high value of 0.75.

<table><caption>Table 5: RAD for the XGB on full and test dataset</caption><thead><tr><th>RAD</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB (full dataset)</td><td>0.08</td><td>0.07</td><td>0.16</td><td>0.17</td></tr><tr><td>XGB (test dataset)</td><td>0.12</td><td>0.11</td><td>0.31</td><td>0.28</td></tr></tbody></table>

<table><caption>Table 6: R²-score for the XGB on full and test dataset</caption><thead><tr><th>R²</th><th>C1</th><th>C2</th><th>C3</th><th>C4</th></tr></thead><tbody><tr><td>XGB (full dataset)</td><td>0.88</td><td>0.89</td><td>0.90</td><td>0.96</td></tr><tr><td>XGB (test dataset)</td><td>-0.06</td><td>0.42</td><td>0.21</td><td>0.75</td></tr></tbody></table>

Overall, we have shown using relatively easily accessible synthetic data from Fe-simulations in combination with ML-algorithms that force-displacement curves from shear-cutting processes are a valid approach to predict various material parameters. The XGB algorithm fits and predicts the data well, but few significant outliers remain, which significantly impacts the prediction of variance. This issue may be resolved using a larger data set with a more homogeneously distributed input parameter space and by finding further input parameters, which have a significant influence on the material parameters. One such example could be the sheet thickness or other parameters extracted using feature-extraction or -engineering. Finally, a comparison with experimental data is necessary to validate this approach. These issues will be covered in future research.

## Summary

The experimental results demonstrate that the deformation behavior of the investigated material varies significantly between different batches. The cutting force curves obtained from the punching tests also vary depending on the material batch. Therefore, analyzing the cutting force curves can provide valuable information about the mechanical properties of the semi-finished products used. Furthermore, a FE model was developed for the shear cutting process being studied. A material model was parameterized based on the results of the tensile test and validated using the experimentally determined cutting force curves. This demonstrated the importance of considering tool stiffness. The optimized FE model was then used to perform variant calculations and generate synthetic training data to build predictive models to predict the flow curve and its parameters. Several machine learning algorithms were trained and evaluated using this data. The XGB algorithm demonstrated the best performance, accurately predicting the flow curve parameters. Future work will focus on optimizing and validating the prediction models using real experimental data.

## Acknowledgments

The results presented in this paper were generated in the AdaProQ project (FKZ: 13IK006F), which is funded by the BMWK as well as in the Priority Program 2422 founded by the German Research Foundation (DFG).
## References

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[6] A. Schenek, M. Görz, M. Liewald, K. R. Riedmüller, Data-Driven Derivation of Sheet Metal Properties Gained from Punching Forces Using an Artificial Neural Network, Key Engineering Materials Volume 926 (2022) 2174-2182. https://doi.org/10.4028/p-41602a

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## References

[1] P. Fischer, J. Heingärtner, Y. Renkci, P. Hora, Experiences with inline feedback control and data acquisition in deep drawing, Procedia Manufacturing. 15 (2008) 949-954. https://doi.org/10.1016/j.promfg.2018.07.401

[2] T. de Souza, B. F. Rolfe, Characterising material and process variation effects on springback robustness for a semi-cylindrical sheet metal forming process, International Journal of Mechanical Sciences. 52 (2010) 1756-1766. https://doi.org/10.1016/j.ijmecsci.2010.09.009

[3] J. Maier, Inline-Qualitätsprüfung im Presswerk durch intelligente Nachfolgewerkzeuge, TUM.University Press (2018). doi:10.14459/2018md1429197

[4] M. Liewald, T. Bergs, P. Groche, B.-A. Behrens, D. Briesenick, M. Müller, P. Niemitz, C. Kubik, Perspectives on data-driven models and its potentials in metal forming and blanking technologies, Production Engineering 16 (2022) 607-625. https://doi.org/10.1007/s11740-022-01115-0

[5] M. Schwind, Zerstörungsfreie Ermittlung mechanischer Eigenschaften von Feinblechen mit dem Wirbelstromverfahren, Diss. Reihe Fertigungstechnik, Band 77 (1997). https://doi.org/10.25593/3-87525-102-4

[6] A. Schenek, M. Görz, M. Liewald, K. R. Riedmüller, Data-Driven Derivation of Sheet Metal Properties Gained from Punching Forces Using an Artificial Neural Network, Key Engineering Materials Volume 926 (2022) 2174-2182. https://doi.org/10.4028/p-41602a

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# Correlation between sheet formability and joint strength of A1050-O/SPCC butt laser welded tailored blanks

JIN Jianchen<sup>1,a*</sup>, SAKAMOTO Hiromu<sup>2,b</sup> and IIZUKA Takashi<sup>3,c</sup>

**Keywords:** Tailor Welded Blanks, Sheet Formability, Aluminum, Dissimilar Metals, Laser Welding

**Abstract.** Laser-welded tailored blanks are useful for lightweight automobiles. However, three major problems remain unresolved: low joint strength, low formability, and galvanic corrosion. Although considerable research has been conducted on the lap form, the studies on the use of lasers to weld dissimilar metals in the butt form are scarce. For practical applications of dissimilar metal tailored blanks, formability must also be investigated. In this study, Japan Industrial Standard A1050-O aluminum and SPCC steel were welded as dissimilar metal tailored blanks and used for Erichsen, flat punch stretch, and hole expansion tests. Welded materials with different joint strengths were produced to investigate the correlation between joint strength and formability. Two patterns of fracture owing to differences in joint strength were observed during the flat punch stretch test. The results of the formability test confirmed that the formability improved with an increase in the joint strength.

## Introduction

Extreme weather conditions are occurring more frequently owing to greenhouse gas emissions. To prevent this situation from worsening and create a better world for all human beings, emissions of CO₂ gas, which among the primary greenhouse gases, should be curbed. Worldwide, the Union Nations and governments have taken actions to decrease the CO₂ gas emissions and increase the absorption capacity of those gases. Moreover, efforts have been undertaken to reach the goal of realizing emissions equivalent to absorption, which is referred to as carbon neutrality. Many developed countries have set the goal of achieving carbon neutrality by the year 2050. CO₂ gas emissions from automobiles account for a portion total such emissions and are thought to have decreased off late. To further decrease this type of emission, exhaust gas regulations for automobiles are becoming stricter annually. The European Union has even decided to ban engine vehicles from the market. Therefore, the development of engine vehicles has become unprofitable according to the policy, and automobile manufacturers have shifted their direction of development to electric vehicles. However, even if engine vehicles are outdated, lightweight capability remains an important issue for electric vehicles for increasing the driving quality and maximum driving distance. The use of light metal and tailored blanks is an effective method for achieving lightweight requirements [1]. Through multi-materialization, the total weight of vehicles decreases by approximately 34% and has a lower production cost than light metal [2]. By preferring to light metals, tailored blanks appear to be better method for automobile manufacturing.

<figure><img src="image_1293.png" /></figure>

<footnote n="1"><sup>1</sup>Department of Engineering Design, Kyoto Institute of Technology, Matsugasaki Goshokaido-cho, Sakyo-ku, Kyoto 606-8585, Japan</footnote>

<footnote n="2"><sup>2</sup>Advanced Technology Center, Kyoto Institute of Technology, Matsugasaki goshokaido-cho, Sakyo-ku, Kyoto 606-8585, Japan</footnote>

<footnote n="3"><sup>3</sup>Faculty of Mechanical Engineering, Kyoto Institute of Technology, Matsugasaki Goshokaido-cho, Sakyo-ku, Kyoto 606-8585, Japan</footnote>

<footnote><sup>a</sup>d1821502@edu.kit.ac.jp, <sup>b</sup>sakamoto@kit.ac.jp, <sup>c</sup>tiizuka@kit.ac.jp</footnote>
# Correlation between sheet formability and joint strength of A1050-O/SPCC butt laser welded tailored blanks

JIN Jianchen<fnref n="1" />, a*, SAKAMOTO Hiromu<fnref n="2" />, b and IIZUKA Takashi<fnref n="3" />, c

**Keywords:** Tailor Welded Blanks, Sheet Formability, Aluminum, Dissimilar Metals, Laser Welding

**Abstract.** Laser-welded tailored blanks are useful for lightweight automobiles. However, three major problems remain unresolved: low joint strength, low formability, and galvanic corrosion. Although considerable research has been conducted on the lap form, the studies on the use of lasers to weld dissimilar metals in the butt form are scarce. For practical applications of dissimilar metal tailored blanks, formability must also be investigated. In this study, Japan Industrial Standard A1050-O aluminum and SPCC steel were welded as dissimilar metal tailored blanks and used for Erichsen, flat punch stretch, and hole expansion tests. Welded materials with different joint strengths were produced to investigate the correlation between joint strength and formability. Two patterns of fracture owing to differences in joint strength were observed during the flat punch stretch test. The results of the formability test confirmed that the formability improved with an increase in the joint strength.

## Introduction

Extreme weather conditions are occurring more frequently owing to greenhouse gas emissions. To prevent this situation from worsening and create a better world for all human beings, emissions of CO₂ gas, which among the primary greenhouse gases, should be curbed. Worldwide, the Union Nations and governments have taken actions to decrease the CO₂ gas emissions and increase the absorption capacity of those gases. Moreover, efforts have been undertaken to reach the goal of realizing emissions equivalent to absorption, which is referred to as carbon neutrality. Many developed countries have set the goal of achieving carbon neutrality by the year 2050. CO₂ gas emissions from automobiles account for a portion total such emissions and are thought to have decreased off late. To further decrease this type of emission, exhaust gas regulations for automobiles are becoming stricter annually. The European Union has even decided to ban engine vehicles from the market. Therefore, the development of engine vehicles has become unprofitable according to the policy, and automobile manufacturers have shifted their direction of development to electric vehicles. However, even if engine vehicles are outdated, lightweight capability remains an important issue for electric vehicles for increasing the driving quality and maximum driving distance. The use of light metal and tailored blanks is an effective method for achieving lightweight requirements [1]. Through multi-materialization, the total weight of vehicles decreases by approximately 34% and has a lower production cost than light metal [2]. By preferring to light metals, tailored blanks appear to be better method for automobile manufacturing.

<figure><img src="image_1296.png" /></figure>

<footnote n="1">¹Department of Engineering Design, Kyoto Institute of Technology, Matsugasaki Goshokaido-cho, Sakyo-ku, Kyoto 606-8585, Japan</footnote>

<footnote n="2">²Advanced Technology Center, Kyoto Institute of Technology, Matsugasaki goshokaido-cho, Sakyo-ku, Kyoto 606-8585, Japan</footnote>

<footnote n="3">³Faculty of Mechanical Engineering, Kyoto Institute of Technology, Matsugasaki Goshokaido-cho, Sakyo-ku, Kyoto 606-8585, Japan</footnote>

<footnote>a¹d1821502@edu.kit.ac.jp, b¹sakamoto@kit.ac.jp, c¹tiizuka@kit.ac.jp</footnote>
Tailored welded blanks (TWBs) are semi-finished blanks used for pressing processes and is welded from different metals or metals with different thicknesses using laser welding, friction stir welding, or other welding methods. Although similar metal TWBs produced from steel using laser welding have been widely used in automobile manufacturing, dissimilar metal TWBs, particular aluminum/steel TWBs, are considered more effective. However, three main issues remain regarding the development of aluminum/steel TWBs. Difficulty in welding owing to the formation of intermetallic compounds, low formability, and low corrosion resistance owing to galvanic corrosion.

The first issue of difficultly in welding was solved by using solid-phase welding such as friction stir welding. Aluminum/steel welded material achieved joint efficiency of over 100% was achieved by using friction stir welding [3,4]. Laser welding is widely used in automobile manufacturing because aluminum/steel laser welding is required to produce products. Cao et al. welded 5052 aluminum alloy and press-hardened steel (PHS) and obtained joint strength of 129.6MPa [5]. Itani and Iizuka welded Japan Industrial Standard (JIS) A5052P-H aluminum and JIS SPCC steel in butt form and obtained a joint strength of approximately 80% of that of the raw materials [6]; however, this should be further improved.

The formability of aluminum/steel-welded materials is also an important issue. However, considerable research has been conducted on the overlapping form, but the formability of these materials has not been investigated. On the other hand, only a few studies on the formability of laser-welded materials have been reported, such as the one by Iizuka et al., which JIS A1100 aluminum and JIS SPC steel butt laser welded materials were produced for formability tests. After Erichsen and punch stretching tests were conducted, welded materials showed low formability, with 20% of the raw steel materials and 50% of the raw steel materials in the Erichsen value (IE) and limit demo height (LDH). Consequently, the welded materials gained a joint strength that exceeded that of the raw aluminum materials [7].

And corrosion resistance is also an important issue, because galvanic corrosion occurs between aluminum and steel-welded materials. Galvanic corrosion leads to an unknown corrosion resistance, which should be investigated through corrosion tests. Research like Jin and Iizuka investigated the corrosion resistance of JIS A6000 series aluminum and JIS SPCC steel friction welding materials [8].

Due to lack of study in formability on aluminum/steel butt laser welded materials. It is considered that formability should be further studied. Thus, in this study, aluminum/steel dissimilar metal TWBs were welded using JIS A1050-O aluminum and SPCC steel via laser welding in the butt form. Four welded materials were produced at different joint strengths and formability tests were conducted separately. First, the distribution of joint strength for all types of welded materials were confirmed. Then three types of formability test were conducted: Erichsen, punch stretching, and hole expansion test. Finally, the punch load and stroke line were compared to investigate the correlation between the joint strength and formability.

## Experimental methods

Butt laser welding. Solid-phase welding such as friction welding, use friction heat to soften the metal and welds the material by apply compression. Here, it is considered that if laser beam could achieve similar effect to heat metal like solid-phase welding. Thus, a laser welding method with compression applied to one side was developed and used in this study. Fig. 1 illustrates the mechanism of this laser welding method. Like friction welding, compression was applied to the aluminum and the steel side was fixed, and then the laser beam irradiates the materials, as shown in Fig. 1(a). As aluminum has a high reflection from the laser beam, it was considered that almost no energy was input into the aluminum, and the laser would only heat the steel side in this situation. After the laser energy increased on the steel side, the steel melted, and a melt pool occurred. As the temperature increased, heat conduction occurred between aluminum and steel, as shown in Fig.
Tailored welded blanks (TWBs) are semi-finished blanks used for pressing processes and is welded from different metals or metals with different thicknesses using laser welding, friction stir welding, or other welding methods. Although similar metal TWBs produced from steel using laser welding have been widely used in automobile manufacturing, dissimilar metal TWBs, particular aluminum/steel TWBs, are considered more effective. However, three main issues remain regarding the development of aluminum/steel TWBs. Difficulty in welding owing to the formation of intermetallic compounds, low formability, and low corrosion resistance owing to galvanic corrosion.

The first issue of difficultly in welding was solved by using solid-phase welding such as friction stir welding. Aluminum/steel welded material achieved joint efficiency of over 100% was achieved by using friction stir welding [3,4]. Laser welding is widely used in automobile manufacturing because aluminum/steel laser welding is required to produce products. Cao et al. welded 5052 aluminum alloy and press-hardened steel (PHS) and obtained joint strength of 129.6MPa [5]. Itani and Iizuka welded Japan Industrial Standard (JIS) A5052P-H aluminum and JIS SPCC steel in butt form and obtained a joint strength of approximately 80% of that of the raw materials [6]; however, this should be further improved.

The formability of aluminum/steel-welded materials is also an important issue. However, considerable research has been conducted on the overlapping form, but the formability of these materials has not been investigated. On the other hand, only a few studies on the formability of laser-welded materials have been reported, such as the one by Iizuka et al., which JIS A1100 aluminum and JIS SPC steel butt laser welded materials were produced for formability tests. After Erichsen and punch stretching tests were conducted, welded materials showed low formability, with 20% of the raw steel materials and 50% of the raw steel materials in the Erichsen value (IE) and limit demo height (LDH). Consequently, the welded materials gained a joint strength that exceeded that of the raw aluminum materials [7].

And corrosion resistance is also an important issue, because galvanic corrosion occurs between aluminum and steel-welded materials. Galvanic corrosion leads to an unknown corrosion resistance, which should be investigated through corrosion tests. Research like Jin and Iizuka investigated the corrosion resistance of JIS A6000 series aluminum and JIS SPCC steel friction welding materials [8].

Due to lack of study in formability on aluminum/steel butt laser welded materials. It is considered that formability should be further studied. Thus, in this study, aluminum/steel dissimilar metal TWBs were welded using JIS A1050-O aluminum and SPCC steel via laser welding in the butt form. Four welded materials were produced at different joint strengths and formability tests were conducted separately. First, the distribution of joint strength for all types of welded materials were confirmed. Then three types of formability test were conducted: Erichsen, punch stretching, and hole expansion test. Finally, the punch load and stroke line were compared to investigate the correlation between the joint strength and formability.

## Experimental methods

Butt laser welding. Solid-phase welding such as friction welding, use friction heat to soften the metal and welds the material by apply compression. Here, it is considered that if laser beam could achieve similar effect to heat metal like solid-phase welding. Thus, a laser welding method with compression applied to one side was developed and used in this study. Fig. 1 illustrates the mechanism of this laser welding method. Like friction welding, compression was applied to the aluminum and the steel side was fixed, and then the laser beam irradiates the materials, as shown in Fig. 1(a). As aluminum has a high reflection from the laser beam, it was considered that almost no energy was input into the aluminum, and the laser would only heat the steel side in this situation. After the laser energy increased on the steel side, the steel melted, and a melt pool occurred. As the temperature increased, heat conduction occurred between aluminum and steel, as shown in Fig.
1 (b). As shown in Fig. 1 (c), the heat conducted from the steel softened or melted the aluminum. With compression on the aluminum side, the oxide layer was pushed out from the weld interface, and a new weld interface occurred between the aluminum and steel raw material. Using this method, a maximum joint strength of 140MPa was achieved by welding JIS 5052P-H34 aluminum and JIS SPCC [6]. A joint strength of approximately 95 MPa which is almost equivalent to that of basic aluminum materials was achieved [7].

<figure><img src="image_1294.png" /><figcaption>Fig. 1 Mechanism of butt laser welding.</figcaption></figure>

Fig. 2 (a) shows the top view of compression apparatus for butt laser welding. Two linear guides were set on the backing plate. Fixed, and moveable holders were installed on the linear guide for setting raw materials. On the left side of the backing plate, three air cylinders were set, and an air compressor was connected to air cylinders to apply compression. The moveable holder was pulled onto the fixed holder to provide compression to the welded materials during laser welding. Steel was set on the fixed holder and aluminum was set on the moveable holder owing to the low deformation resistance of the latter. Fig. 2 (b) shows the butt laser welding in the side view. Compression was applied on weld materials through cylinder and holder. The laser beam irradiated welded materials in vertical direction.

<figure><img src="image_1295.png" /><figcaption>Fig. 2 Compression apparatus for butt laser welding.</figcaption></figure>

Test materials and welding parameters. Herein, 1mm-thickness JIS A1050-O aluminum and JIS SPCC steel were used as test materials. Both the raw materials were milled to 44.5mm × 90mm, as shown in Fig. 3 (a). Further, 90mm side of each material was butted to each other during welding. The definitions of the butt-laser welding parameters are shown in Fig. 3 (b). A CO₂ laser was used to produce the welded materials in this study. An x-y-z coordinate system was set on the material surface during welding to determine the laser beam status. The x and y axis defined the position of laser irradiation on the surface of the material. The z axis was defined as vertical to the weld
1 (b). As shown in Fig. 1 (c), the heat conducted from the steel softened or melted the aluminum. With compression on the aluminum side, the oxide layer was pushed out from the weld interface, and a new weld interface occurred between the aluminum and steel raw material. Using this method, a maximum joint strength of 140MPa was achieved by welding JIS 5052P-H34 aluminum and JIS SPCC [6]. A joint strength of approximately 95 MPa which is almost equivalent to that of basic aluminum materials was achieved [7].

<figure><img src="image_1297.png" /><figcaption>Fig. 1 Mechanism of butt laser welding.</figcaption></figure>

Fig. 2 (a) shows the top view of compression apparatus for butt laser welding. Two linear guides were set on the backing plate. Fixed, and moveable holders were installed on the linear guide for setting raw materials. On the left side of the backing plate, three air cylinders were set, and an air compressor was connected to air cylinders to apply compression. The moveable holder was pulled onto the fixed holder to provide compression to the welded materials during laser welding. Steel was set on the fixed holder and aluminum was set on the moveable holder owing to the low deformation resistance of the latter. Fig. 2 (b) shows the butt laser welding in the side view. Compression was applied on weld materials through cylinder and holder. The laser beam irradiated welded materials in vertical direction.

<figure><img src="image_1298.png" /><figcaption>Fig. 2 Compression apparatus for butt laser welding.</figcaption></figure>

Test materials and welding parameters. Herein, 1mm-thickness JIS A1050-O aluminum and JIS SPCC steel were used as test materials. Both the raw materials were milled to 44.5mm × 90mm, as shown in Fig. 3 (a). Further, 90mm side of each material was butted to each other during welding. The definitions of the butt-laser welding parameters are shown in Fig. 3 (b). A CO₂ laser was used to produce the welded materials in this study. An x-y-z coordinate system was set on the material surface during welding to determine the laser beam status. The x and y axis defined the position of laser irradiation on the surface of the material. The z axis was defined as vertical to the weld
interface and y axis was parallel to the weld interface. The origin of x axis was set on the welding interface; the steel side was defined as the positive direction and aluminum side as the negative direction. The laser beam moved from the outer direction to the direction along y axis. The z axis defines the focal position of the laser beam. The focal position was positive when setting the above material surface and negative below the surface. The details of the welding parameters are listed in Table 1. The laser output and frequency were set as 400 W and 100 Hz, respectively. The focal position was 1.5mm above the surface of the material. Compression was set as 31MPa, and it should pay attention to this mean 2790 N force was apply on the materials through air cylinders. Laser welding was performed between offset distance of 0 and +0.40 mm. The welding speed was set to 600 mm/min. The laser output, frequency, and other parameter would all influence joint strength of the welded materials. In this study, only the offset distance was varied to produce welded materials with different joint strengths.

<figure><img src="image_1296.png" /><figcaption>Fig.3 Size of raw materials and geometrical parameters of laser welding.</figcaption></figure>

<table><caption>Table 1 Parameter of butt laser welding.</caption><tr><td>Laser output [W]</td><td>400</td><td>Compression [MPa]</td><td>31</td></tr><tr><td>Frequency [Hz]</td><td>100</td><td>Offset distance [mm]</td><td>0 ~ +0.40</td></tr><tr><td>Focal position [mm]</td><td>+1.5</td><td>Weld speed [mm/min]</td><td>600</td></tr></table>

To confirm the welding parameters and produce welded materials with different joint strengths, the correlation between the joint strengths and the offset distance was first investigated, and the results are shown in Fig.4. Dots shown the joint strength of joint material whose offset distance was between 0 to 0.4mm, 0.05mm interval. The welded materials had a joint strength of approximately 40 MPa on the welding interface and slowly increased to approximately 60MPa at 0.1 mm and reached a maximum joint strength of approximately 70MPa when the offset distance reached to 0.2 mm. After the offset distance exceeded 0.2 mm, joint strength slowly decreased to approximately 60 MPa at 0.3 mm and then rapidly decreased to 0 MPa on 0.4 mm. The welded materials with offset distances 0, 0.1, 0.2 and 0.3 mm were chosen as test materials and are highlighted in red in Fig.4.

Tensile and formability tests. The welded materials and fabrication method of tensile test pieces is shown in Fig. 5. The welded materials had a length of 90 mm and width of 89.5 mm and used as the formability test pieces. However, the distribution of the joint strength at the welding interface should be confirmed before the formability tests. Because defaults may occur near the laser start and end positions, 5 mm of welded materials from the two positions were cut, and the remaining welded materials were cut into 10mm pieces to investigate the joint strength of the welded materials.
interface and y axis was parallel to the weld interface. The origin of x axis was set on the welding interface; the steel side was defined as the positive direction and aluminum side as the negative direction. The laser beam moved from the outer direction to the direction along y axis. The z axis defines the focal position of the laser beam. The focal position was positive when setting the above material surface and negative below the surface. The details of the welding parameters are listed in Table 1. The laser output and frequency were set as 400 W and 100 Hz, respectively. The focal position was 1.5mm above the surface of the material. Compression was set as 31MPa, and it should pay attention to this mean 2790 N force was apply on the materials through air cylinders. Laser welding was performed between offset distance of 0 and +0.40 mm. The welding speed was set to 600 mm/min. The laser output, frequency, and other parameter would all influence joint strength of the welded materials. In this study, only the offset distance was varied to produce welded materials with different joint strengths.

<figure><img src="image_1299.png" /><figcaption>(a) Size of raw materials</figcaption></figure>

<figure><img src="image_1300.png" /><figcaption>(b) Geometrical parameters</figcaption></figure>

<caption>Fig. 3 Size of raw materials and geometrical parameters of laser welding.</caption>

<table><caption>Table 1 Parameter of butt laser welding.</caption><tr><td>Laser output [W]</td><td>400</td><td>Compression [MPa]</td><td>31</td></tr><tr><td>Frequency [Hz]</td><td>100</td><td>Offset distance [mm]</td><td>0 ~ +0.40</td></tr><tr><td>Focal position [mm]</td><td>+1.5</td><td>Weld speed [mm/min]</td><td>600</td></tr></table>

To confirm the welding parameters and produce welded materials with different joint strengths, the correlation between the joint strengths and the offset distance was first investigated, and the results are shown in Fig. 4. Dots shown the joint strength of joint material whose offset distance was between 0 to 0.4mm, 0.05mm interval. The welded materials had a joint strength of approximately 40 MPa on the welding interface and slowly increased to approximately 60MPa at 0.1 mm and reached a maximum joint strength of approximately 70MPa when the offset distance reached to 0.2 mm. After the offset distance exceeded 0.2 mm, joint strength slowly decreased to approximately 60 MPa at 0.3 mm and then rapidly decreased to 0 MPa on 0.4 mm. The welded materials with offset distances 0, 0.1, 0.2 and 0.3 mm were chosen as test materials and are highlighted in red in Fig. 4.

Tensile and formability tests. The welded materials and fabrication method of tensile test pieces is shown in Fig. 5. The welded materials had a length of 90 mm and width of 89.5 mm and used as the formability test pieces. However, the distribution of the joint strength at the welding interface should be confirmed before the formability tests. Because defaults may occur near the laser start and end positions, 5 mm of welded materials from the two positions were cut, and the remaining welded materials were cut into 10mm pieces to investigate the joint strength of the welded materials.
<figure><img src="image_1297.png" /><figcaption>Fig. 4 Correlation between joint strength and offset distance of welded materials.</figcaption></figure>

<figure><img src="image_1298.png" /><figcaption>Fig. 5 Production of tensile test pieces.</figcaption></figure>

Fig. 6 shows the molds used in this study. In Erichsen tests, a common ball head punch with ball head diameter of φ20mm was used. The inner diameter of dies and blank holder were φ27 and φ33 mm, respectively. The outer diameter was 55 mm for both the dies and blank holder. Blank holder force was set to 10 kN during the test. In the flat punch stretch test, a flat punch instead of round head punch was used. The diameter of this punch was φ29 mm and that of the dies was φ31 mm. Owing to the use of mold without a bead, blank holder force was set as 50 kN to provide the material-flood in the flange. Finally, a φ39 mm diameter punch with a 60° head angle was used for the hole expansion test.

<figure><img src="image_1299.png" /><figcaption>Fig. 6 Mold using for Erichsen and flat punch stretch tests.</figcaption></figure>

## Results

Tensile test results. Before this study, tensile strength of the raw aluminum materials was investigated and confirmed that was approximately 74 MPa. The distribution of joint strength for each welded material is shown in Fig. 7. The distance from the laser starting point indicated the position of tensile test pieces. The welded materials with an offset distance of 0 mm exhibited a joint strength of approximately 48 MPa near the laser starting point. As the laser beam moved away from the starting point, the joint strength decreased slowly to a minimum of approximately 38 MPa near the laser end position. For the welded materials with an offset distance of 0.1 mm, a maximum joint strength of approximately 61 MPa was observed near the laser start position. The
<figure><img src="image_1301.png" /><figcaption>Fig. 4 Correlation between joint strength and offset distance of welded materials.</figcaption></figure>

<figure><img src="image_1302.png" /><figcaption>Fig. 5 Production of tensile test pieces.</figcaption></figure>

Fig. 6 shows the molds used in this study. In Erichsen tests, a common ball head punch with ball head diameter of φ20mm was used. The inner diameter of dies and blank holder were φ27 and φ33 mm, respectively. The outer diameter was 55 mm for both the dies and blank holder. Blank holder force was set to 10 kN during the test. In the flat punch stretch test, a flat punch instead of round head punch was used. The diameter of this punch was φ29 mm and that of the dies was φ31 mm. Owing to the use of mold without a bead, blank holder force was set as 50 kN to provide the material-flood in the flange. Finally, a φ39 mm diameter punch with a 60° head angle was used for the hole expansion test.

<figure><img src="image_1303.png" /><figcaption>Fig. 6 Mold using for Erichsen and flat punch stretch tests.</figcaption></figure>

## Results

Tensile test results. Before this study, tensile strength of the raw aluminum materials was investigated and confirmed that was approximately 74 MPa. The distribution of joint strength for each welded material is shown in Fig. 7. The distance from the laser starting point indicated the position of tensile test pieces. The welded materials with an offset distance of 0 mm exhibited a joint strength of approximately 48 MPa near the laser starting point. As the laser beam moved away from the starting point, the joint strength decreased slowly to a minimum of approximately 38 MPa near the laser end position. For the welded materials with an offset distance of 0.1 mm, a maximum joint strength of approximately 61 MPa was observed near the laser start position. The
joint strength decreased slightly to approximately 59 MPa at the center of the welded materials and then returned to approximately 61 MPa at the laser end position. The welded materials with an offset distance of 0.2 mm exhibited the highest joint strength among all welded materials. The same tendency was observed; a higher joint strength of approximately 65 MPa was observed at laser start and end positions, and a lower joint strength of approximately 60 MPa was observed at the center of the welded materials. Finally, the welded materials produced at offset distance 0.3 mm showed a different tendency: a low joint strength of approximately 51 MPa was obtained at the laser starting point, and then the joint strength increased slightly to 58 MPa at the center part. Therefore, the joint strength decreased slightly before the laser end point. All the different types of welded materials exhibited stable joint strengths under these welding conditions, in addition to an offset distance of 0 mm. A decrease in the joint strength of approximately 10 MPa was confirmed. It is considered that a slight deviation of the laser irradiating position occurred, which caused the laser spot to irradiate aluminum side more than the steel after 40 mm during welding. Owing to the high reflection of the laser beam, the energy input to the steel side decreased, and consequently, the joint strength decreased. It is confirmed that the welded material exhibited a stable joint strength distribution in this study. However, welded materials with joint strengths exceeding the tensile strength of the raw materials were not obtained this time. Hereinafter, these welded materials are referred to as 40 MPa (offset distance of 0 mm) welded material, 60 MPa (0.1 mm) welded material, 65 MPa (0.2 mm) welded material, and 55 MPa (0.3 mm) welded material.

<figure><img src="image_1300.png" /><figcaption>Fig. 7 Distribution of joint strength for all types of welded materials.</figcaption></figure>

Table 2 lists the average joint strength of each welded material. The joint strengths of the welded materials at offset distances 0, 0.1, 0.2, and 0.3 mm were 42.5, 59.6, 64.8 and 55.2 MPa, respectively. Compared to the results in Fig. 4, the joint strengths at offset distances 0 and 0.1 mm were approximately the same, however, those at 0.2 and 0.3 mm decreased slightly.

<table><caption>Table 2 Average joint strength of welded materials.</caption><tr><td>Offset distance [mm]</td><td>0</td><td>0.1</td><td>0.2</td><td>0.3</td></tr><tr><td>Average joint strength [MPa]</td><td>42.5</td><td>59.6</td><td>64.8</td><td>55.2</td></tr></table>

Fracture in formability test. First, photograph of the fracture during Erichsen test is shown in Fig. 8. The fracture is indicated in red arrows and circles in the figure. In the 40MPa welded materials, the fracture occurred at the weld bead at the center of the punch part. For 55, 60, and 65 MPa welded materials, the fractures also occurred on the weld bead at the center of punch part.
joint strength decreased slightly to approximately 59 MPa at the center of the welded materials and then returned to approximately 61 MPa at the laser end position. The welded materials with an offset distance of 0.2 mm exhibited the highest joint strength among all welded materials. The same tendency was observed; a higher joint strength of approximately 65 MPa was observed at laser start and end positions, and a lower joint strength of approximately 60 MPa was observed at the center of the welded materials. Finally, the welded materials produced at offset distance 0.3 mm showed a different tendency: a low joint strength of approximately 51 MPa was obtained at the laser starting point, and then the joint strength increased slightly to 58 MPa at the center part. Therefore, the joint strength decreased slightly before the laser end point. All the different types of welded materials exhibited stable joint strengths under these welding conditions, in addition to an offset distance of 0 mm. A decrease in the joint strength of approximately 10 MPa was confirmed. It is considered that a slight deviation of the laser irradiating position occurred, which caused the laser spot to irradiate aluminum side more than the steel after 40 mm during welding. Owing to the high reflection of the laser beam, the energy input to the steel side decreased, and consequently, the joint strength decreased. It is confirmed that the welded material exhibited a stable joint strength distribution in this study. However, welded materials with joint strengths exceeding the tensile strength of the raw materials were not obtained this time. Hereinafter, these welded materials are referred to as 40 MPa (offset distance of 0 mm) welded material, 60 MPa (0.1 mm) welded material, 65 MPa (0.2 mm) welded material, and 55 MPa (0.3 mm) welded material.

<figure><img src="image_1304.png" /><figcaption>Fig. 7 Distribution of joint strength for all types of welded materials.</figcaption></figure>

Table 2 lists the average joint strength of each welded material. The joint strengths of the welded materials at offset distances 0, 0.1, 0.2, and 0.3 mm were 42.5, 59.6, 64.8 and 55.2 MPa, respectively. Compared to the results in Fig. 4, the joint strengths at offset distances 0 and 0.1 mm were approximately the same, however, those at 0.2 and 0.3 mm decreased slightly.

<table><caption>Table 2 Average joint strength of welded materials.</caption><tr><td>Offset distance [mm]</td><td>0</td><td>0.1</td><td>0.2</td><td>0.3</td></tr><tr><td>Average joint strength [MPa]</td><td>42.5</td><td>59.6</td><td>64.8</td><td>55.2</td></tr></table>

Fracture in formability test. First, photograph of the fracture during Erichsen test is shown in Fig. 8. The fracture is indicated in red arrows and circles in the figure. In the 40MPa welded materials, the fracture occurred at the weld bead at the center of the punch part. For 55, 60, and 65 MPa welded materials, the fractures also occurred on the weld bead at the center of punch part.
Observing the fractured parts, all the fractures occurred parallel to the weld bead near the aluminum side. During the Erichsen test, the materials at head of the punch were in an equibiaxial tensile state. Parallel fracture indicated the lack of joint strength resulted in the fractures in all types of welded materials.

<figure><img src="image_1301.png" /><figcaption>Fig. 8 Fractures in Erichsen tests.</figcaption></figure>

Fig. 9 shows the fracture of the welded materials during the flat punch stretch test. Evidently, the fracture on the 40 MPa welded materials was parallel to the weld bead, similar to that in case of the Erichsen test. Whereas 55 MPa welded materials, the fractures occurred parallel to weld bead on the punch shoulder parts of the welded materials. Similarly, the fracture on 60 and 65 MPa welded materials also occurred parallel to the weld bead on the punch shoulder parts of welded materials. Similar to Erichsen test results, the center of materials was in an equibiaxial tensile state and the lack of joint strength resulted in the fracture in the 40 MPa materials. However, the fractures on the punch shoulder part, which is parallel to the weld bead, indicated that the lack of ductility was the primary reason for occurrence of fractures.

<figure><img src="image_1302.png" /><figcaption>Fig. 9 Fractures in flat punch stretch tests.</figcaption></figure>

The fractures observed in the hole expansion test are shown in Fig. 10. The 40, 55, 60, and 65 MPa welded materials exhibited the same fracture pattern, wherein penetrating fractures occurred parallel to the weld bead on the hole edge. According to the deformation states, the materials were almost in a uniaxial tensile state at the hole edge, and the lack of joint strength resulted in the fracture during the hole expansion test.
Observing the fractured parts, all the fractures occurred parallel to the weld bead near the aluminum side. During the Erichsen test, the materials at head of the punch were in an equibiaxial tensile state. Parallel fracture indicated the lack of joint strength resulted in the fractures in all types of welded materials.

<figure><img src="image_1305.png" /><figcaption>Fig. 8 Fractures in Erichsen tests.</figcaption></figure>

Fig. 9 shows the fracture of the welded materials during the flat punch stretch test. Evidently, the fracture on the 40 MPa welded materials was parallel to the weld bead, similar to that in case of the Erichsen test. Whereas 55 MPa welded materials, the fractures occurred parallel to weld bead on the punch shoulder parts of the welded materials. Similarly, the fracture on 60 and 65 MPa welded materials also occurred parallel to the weld bead on the punch shoulder parts of welded materials. Similar to Erichsen test results, the center of materials was in an equibiaxial tensile state and the lack of joint strength resulted in the fracture in the 40 MPa materials. However, the fractures on the punch shoulder part, which is parallel to the weld bead, indicated that the lack of ductility was the primary reason for occurrence of fractures.

<figure><img src="image_1306.png" /><figcaption>Fig. 9 Fractures in flat punch stretch tests.</figcaption></figure>

The fractures observed in the hole expansion test are shown in Fig. 10. The 40, 55, 60, and 65 MPa welded materials exhibited the same fracture pattern, wherein penetrating fractures occurred parallel to the weld bead on the hole edge. According to the deformation states, the materials were almost in a uniaxial tensile state at the hole edge, and the lack of joint strength resulted in the fracture during the hole expansion test.
<figure><img src="image_1303.png" /><figcaption>Fig. 10 Fractures in hole expansion tests.</figcaption></figure>

Variations in Formability. To confirm the changes in formability during the Erichsen and flat punch stretch tests, the punch load-punch stroke curves are shown in Fig. 11; where the cross marks indicate the breaking load on each welded material. Fig. 11 (a) shows the punch load-punch stroke curves obtained during the Erichsen tests. The 40 MPa welded materials exhibited a breaking punch load of approximately 1.5kN and was the lowest among all the welded materials. Further, the slope of this welded material was slightly smaller than that of the other welded materials. For the 55 and 60 MPa welded materials, the breaking loads were approximately 2.3kN each. The 65 MPa welded materials indicated a breaking load of approximately 2kN. Although the breaking load of the 65MPa welded materials was lower than of the 55 and 60 MPa welded materials, the difference between the breaking forces was only approximately 0.3kN and it could be considered to be same as other two welded materials. This was because individual differences occurred during welding. Apart from the results of the 40 MPa welded materials, the slopes of all the welded materials were the same during the Erichsen tests. Fig. 11 (b) shows the punch load-punch stroke curves during the flat punch stretch tests. Similar to the Erichsen test, the 40 MPa welded materials had the lowest breaking load of approximately 4 kN. The breaking load increased to approximately 5.8 kN when the joint strength increased to 55 MPa. The 60 MPa welded materials exhibited approximately the same breaking load as that of the 55 MPa welded materials. In contrast to the Erichsen test, in case of the 65 MPa welded materials, the breaking load was almost 1kN higher than that of the 55 and 60 MPa welded materials. Although a difference in the breaking load was observed, the slope of the punch load-punch stroke curves for all the welded materials were the same during the flat punch stretch test. Thus, it was confirmed that as the joint strength increased, the breaking load also increased during the flat punch stretch test.

Correlation between the formability and joint strength. The results of the formability tests are presented in Fig. 12. The Erichsen value and limit dome height were both approximately 2.3mm and the limit hole-expansion ratio was only 4.5% for the 40 MPa welded materials and was minimum value this study. The 55 MPa welded materials had approximately the same Erichsen value and limit dome height of approximately 3.5mm; the limit hole-expansion ratio was approximately 9%. When the joint strength increased to 60MPa, the Erichsen value increased slightly to 3.9mm and the limit dome height remained at the same level compared to that of the 55 MPa case. However, limit hole-expansion ratio increased significantly to approximately 11% and was the highest value among all the welded materials. The 65 MPa welded materials yielded an Erichsen value of 2.9 mm and the limit dome height was approximately 4mm. Further, the limit hole-expansion ratio was approximately 9.2%. However, several values of the formability at higher joint strengths were lower than those of the other welded materials. It is considered that the higher the joint strength resulted to higher Erichsen value, limit dome height, and limiting hole expansion rate.
<figure><img src="image_1307.png" /><figcaption>Fig. 10 Fractures in hole expansion tests.</figcaption></figure>

Variations in Formability. To confirm the changes in formability during the Erichsen and flat punch stretch tests, the punch load-punch stroke curves are shown in Fig. 11; where the cross marks indicate the breaking load on each welded material. Fig. 11 (a) shows the punch load-punch stroke curves obtained during the Erichsen tests. The 40 MPa welded materials exhibited a breaking punch load of approximately 1.5kN and was the lowest among all the welded materials. Further, the slope of this welded material was slightly smaller than that of the other welded materials. For the 55 and 60 MPa welded materials, the breaking loads were approximately 2.3kN each. The 65 MPa welded materials indicated a breaking load of approximately 2kN. Although the breaking load of the 65MPa welded materials was lower than of the 55 and 60 MPa welded materials, the difference between the breaking forces was only approximately 0.3kN and it could be considered to be same as other two welded materials. This was because individual differences occurred during welding. Apart from the results of the 40 MPa welded materials, the slopes of all the welded materials were the same during the Erichsen tests. Fig. 11 (b) shows the punch load-punch stroke curves during the flat punch stretch tests. Similar to the Erichsen test, the 40 MPa welded materials had the lowest breaking load of approximately 4 kN. The breaking load increased to approximately 5.8 kN when the joint strength increased to 55 MPa. The 60 MPa welded materials exhibited approximately the same breaking load as that of the 55 MPa welded materials. In contrast to the Erichsen test, in case of the 65 MPa welded materials, the breaking load was almost 1kN higher than that of the 55 and 60 MPa welded materials. Although a difference in the breaking load was observed, the slope of the punch load-punch stroke curves for all the welded materials were the same during the flat punch stretch test. Thus, it was confirmed that as the joint strength increased, the breaking load also increased during the flat punch stretch test.

Correlation between the formability and joint strength. The results of the formability tests are presented in Fig. 12. The Erichsen value and limit dome height were both approximately 2.3mm and the limit hole-expansion ratio was only 4.5% for the 40 MPa welded materials and was minimum value this study. The 55 MPa welded materials had approximately the same Erichsen value and limit dome height of approximately 3.5mm; the limit hole-expansion ratio was approximately 9%. When the joint strength increased to 60MPa, the Erichsen value increased slightly to 3.9mm and the limit dome height remained at the same level compared to that of the 55 MPa case. However, limit hole-expansion ratio increased significantly to approximately 11% and was the highest value among all the welded materials. The 65 MPa welded materials yielded an Erichsen value of 2.9 mm and the limit dome height was approximately 4mm. Further, the limit hole-expansion ratio was approximately 9.2%. However, several values of the formability at higher joint strengths were lower than those of the other welded materials. It is considered that the higher the joint strength resulted to higher Erichsen value, limit dome height, and limiting hole expansion rate.
<figure><img src="image_1304.png" /><figcaption>Fig. 11 Punch load-punch strokes curves of Erichsen tests and flat punch stretch tests.</figcaption></figure>

<figure><img src="image_1305.png" /><figcaption>Fig. 12 Correlation of formability and joint strength.</figcaption></figure>

## Summary

This study welded aluminum/steel dissimilar metal TWBs in the butt form using JIS A1050-O aluminum and SPCC steel via a new laser welding method. This laser welding method was performed under compression in a similar form to solid-phase welding. Four welded materials were produced at different joint strengths, and formability tests were conducted. Using butt laser welding, the welded materials with a stable joint strength distribution were used for the formability test. Regardless of the joint strength, in the Erichsen test, the fractures of all types of welded materials occurred parallel to the welded bead at the center of the punch owing to the lack of joint strength. By contrast, two fracture patterns were confirmed during the flat-punch stretch test. Fractures of the welded materials with low joint strengths were occurred at the center of the punch head. When the joint strength increased, a fracture on welded material was observed on the punch shoulder. The fracture on the punch head was results of lack of joint strength. Whereas fracture on the punch shoulder results of lack of ductility. The lack of joint strength also resulted in a penetrating fracture that occurred on the weld bead for all types of welded materials during the hole-expansion test. Welded material in higher joint strength obtained higher punch load and fracture occurred at lower punch load on welded material in low joint strength. It was confirmed that the formability improved with an increase in the joint strength; however, the causes of the fracture were considered to be the low joint strength of the bead and lack of ductility. The joint strength only changed by 15MPa among the 55, 60, and 65 MPa welded materials. Thus, formability did not change significantly in this study, and a higher joint strength is required for further studies. Microstructures near weld bead should be investigated for further studies.
<figure><img src="image_1308.png" /><figcaption>Fig. 11 Punch load-punch strokes curves of Erichsen tests and flat punch stretch tests.</figcaption></figure>

<figure><img src="image_1309.png" /><figcaption>Fig. 12 Correlation of formability and joint strength.</figcaption></figure>

## Summary

This study welded aluminum/steel dissimilar metal TWBs in the butt form using JIS A1050-O aluminum and SPCC steel via a new laser welding method. This laser welding method was performed under compression in a similar form to solid-phase welding. Four welded materials were produced at different joint strengths, and formability tests were conducted. Using butt laser welding, the welded materials with a stable joint strength distribution were used for the formability test. Regardless of the joint strength, in the Erichsen test, the fractures of all types of welded materials occurred parallel to the welded bead at the center of the punch owing to the lack of joint strength. By contrast, two fracture patterns were confirmed during the flat-punch stretch test. Fractures of the welded materials with low joint strengths were occurred at the center of the punch head. When the joint strength increased, a fracture on welded material was observed on the punch shoulder. The fracture on the punch head was results of lack of joint strength. Whereas fracture on the punch shoulder results of lack of ductility. The lack of joint strength also resulted in a penetrating fracture that occurred on the weld bead for all types of welded materials during the hole-expansion test. Welded material in higher joint strength obtained higher punch load and fracture occurred at lower punch load on welded material in low joint strength. It was confirmed that the formability improved with an increase in the joint strength; however, the causes of the fracture were considered to be the low joint strength of the bead and lack of ductility. The joint strength only changed by 15MPa among the 55, 60, and 65 MPa welded materials. Thus, formability did not change significantly in this study, and a higher joint strength is required for further studies. Microstructures near weld bead should be investigated for further studies.
## Acknowledgment

This study was funded by the Amada Foundation (AF-2023055-X1). We are very grateful for their support.

## References

[1] M. Kleiner, M. Geiger, A. Klaus, Manufacturing of Lightweight Components by Metal Forming, CIRP Ann. 52-2 (2003) 521-542. https://doi.org/10.1016/S0007-8506(07)60202-9

[2] J. Hirsch, Aluminium in Innovative Light-Weight Car Design, Mater. Trans. 55-5 (2011) 818-824. https://doi.org/10.2320/matertrans.L-MZ201132

[3] T. Tanaka, T. Morishige, T. Hirata, Comprehensive analysis of joint strength for dissimilar friction stir welds of mild steel to aluminum alloys, Scr. Mater. 61-7 (2009) 756-759. https://doi.org/10.1016/j.scriptamat.2009.06.022

[4] T. Tanaka, T. Hirata, N. Shinomiya, N. Shirakawa, Analysis of material flow in the sheet forming of friction-stir welds on alloys of mild steel and aluminum, J. Mater. Process. Technol. 226 (2015) 115-124. https://doi.org/10.1016/j.jmatprotec.2015.06.030

[5] X. Cao, X. Zhou, H. Wang, Z. Luo, J. Duan, Microstructures and mechanical properties of laser offset welded 5052 aluminum to press-hardened steel, J. Mater. Res. Technol. 9-3 (2020) 5378-5390. https://doi.org/10.1016/j.jmrt.2020.03.064

[6] R. Itani, T. Iizuka, Joint Strength of SPCC/A5052P-H Joint Welded by Laser Butt Welding with Compression, Key Eng. Mater. 554-557 (2013) 86-92. https://doi.org/10.4028/www.scientific.net/KEM.554-557.86

[7] T. Iizuka, S. Kajikawa, N. Takakura, N. Hatanaka, Fundamental formability of SPC/A1100 hybrid sheet welded by butt laser welding, Special Edition: 10th International Conference on Technology of Plasticity, ICTP 2011. (2011) 651-656.

[8] J. Jin, T. Iizuka, Combined-cycle corrosion testing of steel/6000 series aluminum alloys joined by friction welding, ESAFORM 2021. MS05(Joining) (2021). https://doi.org/10.25518/esaform21.3665
Acknowledgment

This study was funded by the Amada Foundation (AF-2023055-X1). We are very grateful for their support.

References

[1] M. Kleiner, M. Geiger, A. Klaus, Manufacturing of Lightweight Components by Metal Forming, CIRP Ann. 52-2 (2003) 521-542. https://doi.org/10.1016/S0007-8506(07)60202-9

[2] J. Hirsch, Aluminium in Innovative Light-Weight Car Design, Mater. Trans. 55-5 (2011) 818-824. https://doi.org/10.2320/matertrans.L-MZ201132

[3] T. Tanaka, T. Morishige, T. Hirata, Comprehensive analysis of joint strength for dissimilar friction stir welds of mild steel to aluminum alloys, Scr. Mater. 61-7 (2009) 756-759. https://doi.org/10.1016/j.scriptamat.2009.06.022

[4] T. Tanaka, T. Hirata, N. Shinomiya, N. Shirakawa, Analysis of material flow in the sheet forming of friction-stir welds on alloys of mild steel and aluminum, J. Mater. Process. Technol. 226 (2015) 115-124. https://doi.org/10.1016/j.jmatprotec.2015.06.030

[5] X. Cao, X. Zhou, H. Wang, Z. Luo, J. Duan, Microstructures and mechanical properties of laser offset welded 5052 aluminum to press-hardened steel, J. Mater. Res. Technol. 9-3 (2020) 5378-5390. https://doi.org/10.1016/j.jmrt.2020.03.064

[6] R. Itani, T. Iizuka, Joint Strength of SPCC/A5052P-H Joint Welded by Laser Butt Welding with Compression, Key Eng. Mater. 554-557 (2013) 86-92. https://doi.org/10.4028/www.scientific.net/KEM.554-557.86

[7] T. Iizuka, S. Kajikawa, N. Takakura, N. Hatanaka, Fundamental formability of SPC/A1100 hybrid sheet welded by butt laser welding, Special Edition: 10th International Conference on Technology of Plasticity, ICTP 2011. (2011) 651-656.

[8] J. Jin, T. Iizuka, Combined-cycle corrosion testing of steel/6000 series aluminum alloys joined by friction welding, ESAFORM 2021. MS05(Joining) (2021). https://doi.org/10.25518/esaform21.3665
# In-process tool pose measurement in incremental sheet forming

TERLAU Marina¹,ª*, VON FREYBERG Axel¹,ᵇ and FISCHER Andreas¹,ᶜ

¹University of Bremen, Bremen Institute for Metrology, Automation and Quality Science, Linzer Straße 13, 28359 Bremen, Germany

ªm.terlau@bimaq.de, ᵇa.freyberg@bimaq.de, ᶜandreas.fischer@bimaq.de

**Keywords:** Incremental Sheet Forming, Tool Pose Measurement, Shadow Imaging

**Abstract.** Robotic incremental sheet forming is flexible, but involves significant forming path deviations, demanding an in-process tool pose measuring system. To achieve a 50 µm positional and 0.05° orientational measuring uncertainty, a triangulation system using multiple shadow imaging sensors is proposed. LEDs with different wavelengths are attached to the tool holder and cast a shadow of the sensor's mask though a color filter on the camera chip behind it. The LED position is obtained by processing the shadow images of at least two sensors. Conducted experiments demonstrate that the filters effectively separate the shadows, ensuring cross-sensitivities as low as the random error of measuring a single LED position. The unpredictable scatter in the systematic error dominates the LED position measurement uncertainty. However, a Monte Carlo simulation shows the feasibility of achieving the required uncertainty for tool pose measurement.

**Introduction**

Robotic incremental sheet forming (ISF) offers a cost-effective alternative for producing large sheet metal components in limited quantities [1]. However, the robot's low stiffness causes load-induced deformations, leading to significant path deviations [2]. Accurate tool pose prediction is challenging due to dynamic manufacturing conditions [3]. Thus, in-process tool pose measurement is preferred. To cover deviations along the kinematic chain, a direct contactless measurement is needed, which is independent of the robot kinematics and enables real-time compensation.

To achieve the fast and contactless in-process measurement of the 6-DOF tool pose, i. e. position and orientation, an optical measurement system is demanded, which works in single shot, is able to cover the machining volume of 1.0 m × 1.0 m × 0.2 m, and provides a sufficient measurement uncertainty of position and orientation of 50 µm and 0.05°, respectively.

During robot calibration the end-effector pose was measured by laser trackers [4], but they determined the tool orientation not in a single shot. Applying photogrammetry, robot end-effectors were tracked and controlled [5, 6]. The robot joint stiffness model was determined using 3D digital image correlation [7]. Although camera based methods cover a large measurement volume in a single shot with low measurement uncertainties [8], usually costly high-resolution cameras are required. This leads to high data amount which complicates real-time path correction. Additionally, the information in the image is spread over just a few pixels.

To increase the information content, shadow imaging introduced by Grenet et al. [9] is proposed for tool pose measurement. Thereby, the position of a light source is measured from the shadow, which the light source produces on a camera chip by passing through a mask. Analyzing the shadow images gives the direction to the light source, and triangulating the directions of at least two sensors provides the light source position. Studies confirm the capability to detect the 3D position of one light source [10]. However, the simultaneous measurement of at least three light source positions is necessary to calculate the tool pose. Therefore it needs to be clarified, in what extent shadow imaging sensors are capable of extracting each single light source position, how

<figure><img src="image_1306.png" /></figure>
# In-process tool pose measurement in incremental sheet forming

TERLAU Marina¹,ª*, VON FREYBERG Axel¹,ᵇ and FISCHER Andreas¹,ᶜ

¹University of Bremen, Bremen Institute for Metrology, Automation and Quality Science, Linzer Straße 13, 28359 Bremen, Germany

ªm.terlau@bimaq.de, ᵇa.freyberg@bimaq.de, ᶜandreas.fischer@bimaq.de

**Keywords:** Incremental Sheet Forming, Tool Pose Measurement, Shadow Imaging

**Abstract.** Robotic incremental sheet forming is flexible, but involves significant forming path deviations, demanding an in-process tool pose measuring system. To achieve a 50 µm positional and 0.05° orientational measuring uncertainty, a triangulation system using multiple shadow imaging sensors is proposed. LEDs with different wavelengths are attached to the tool holder and cast a shadow of the sensor's mask though a color filter on the camera chip behind it. The LED position is obtained by processing the shadow images of at least two sensors. Conducted experiments demonstrate that the filters effectively separate the shadows, ensuring cross-sensitivities as low as the random error of measuring a single LED position. The unpredictable scatter in the systematic error dominates the LED position measurement uncertainty. However, a Monte Carlo simulation shows the feasibility of achieving the required uncertainty for tool pose measurement.

**Introduction**

Robotic incremental sheet forming (ISF) offers a cost-effective alternative for producing large sheet metal components in limited quantities [1]. However, the robot's low stiffness causes load-induced deformations, leading to significant path deviations [2]. Accurate tool pose prediction is challenging due to dynamic manufacturing conditions [3]. Thus, in-process tool pose measurement is preferred. To cover deviations along the kinematic chain, a direct contactless measurement is needed, which is independent of the robot kinematics and enables real-time compensation.

To achieve the fast and contactless in-process measurement of the 6-DOF tool pose, i. e. position and orientation, an optical measurement system is demanded, which works in single shot, is able to cover the machining volume of 1.0 m × 1.0 m × 0.2 m, and provides a sufficient measurement uncertainty of position and orientation of 50 µm and 0.05°, respectively.

During robot calibration the end-effector pose was measured by laser trackers [4], but they determined the tool orientation not in a single shot. Applying photogrammetry, robot end-effectors were tracked and controlled [5, 6]. The robot joint stiffness model was determined using 3D digital image correlation [7]. Although camera based methods cover a large measurement volume in a single shot with low measurement uncertainties [8], usually costly high-resolution cameras are required. This leads to high data amount which complicates real-time path correction. Additionally, the information in the image is spread over just a few pixels.

To increase the information content, shadow imaging introduced by Grenet et al. [9] is proposed for tool pose measurement. Thereby, the position of a light source is measured from the shadow, which the light source produces on a camera chip by passing through a mask. Analyzing the shadow images gives the direction to the light source, and triangulating the directions of at least two sensors provides the light source position. Studies confirm the capability to detect the 3D position of one light source [10]. However, the simultaneous measurement of at least three light source positions is necessary to calculate the tool pose. Therefore it needs to be clarified, in what extent shadow imaging sensors are capable of extracting each single light source position, how

<figure><img src="image_1310.png" /></figure>
large is the cross-influence of the different light source channels, and what is the resulting achievable measurement uncertainty of the 6-DOF tool pose.

Hence, the aim of this article is to assess the capability of shadow imaging for measuring the 6D tool pose during robotic ISF. In this context, the cross-sensitivities between different light sources are investigated and combined with the examined uncertainty of the LED position. Finally, the tool pose measurement uncertainty is evaluated using a Monte Carlo simulation.

For this purpose, the principle of the tool pose measurement by determining the positions of three light sources is introduced first. The experimental setups, investigating the uncertainty in light source position measurement and cross-sensitivities among the light sources is addressed, and the outcomes from these investigations are subsequently presented and discussed. Lastly, a conclusion and future perspectives are provided.

## Measuring Principle

Light source position measurement.

For tool pose measurement, the several light source positions are measured separately but simultaneously. To measure a single light source position utilizing the shadow imaging principle, multiple sensors are employed for the 3D position measurement. In each sensor, the light source creates a shadow of a mask on a camera chip. From the shadow position extracted by image processing, each sensor $n = 1 ... N$ provides a direction $r_{M,n}$ to the light source. Together with the sensor positions $s_n$ (known from the calibration, also in the machine coordinate system (MCS) M), the lines from each sensor to the light source position are obtained as $s_n + t_n \cdot r_{M,n}$ with $t_n$ as function variable. In the ideal case, all lines intersect at the sought-after position of the light source. In real 3D measurements, the lines from the sensors do not intersect at a single point, so that the light source position is determined from the point $\hat{l}_M$ that is closest to all lines (least summed squared distances):

$$ \min_{l_M} \left( \sum_{n=1}^{N} \left( \frac{\left| (l_M - s_n) \times r_{M,n} \right|}{\left| r_{M,n} \right|} \right)^2 \right). \quad (1) $$

The direction vector $r_{M,n}$ in the MCS is obtained by a coordinate transformation of the detected direction vector $r_{S,n}$ in the sensor coordinate system S. This transformation is performed by applying a rotation matrix $R_{MS,n}$, which is obtained from the sensor's calibration:

$$ r_{M,n} = R_{MS,n} \cdot r_{S,n}. \quad (2) $$

Note that any potential misalignment between the mask and the camera is reduced during the sensor setup and thus disregarded. According to Fig. 1, the vector $r_{S,n}$ follows from the shadow position ($\xi_{i,n}, \zeta_{i,n}$) on the camera chip, the calibrated distance $h_n$ between mask and camera chip, and the known reference shadow position ($\xi_{i,0,n}, \zeta_{i,0,n}$) where the light source is centered in front of the camera:

$$ r_{S,n} = \begin{bmatrix} \xi_{i,0,n} - \xi_{i,n} \\ h_n \\ \zeta_{i,0,n} - \zeta_{i,n} \end{bmatrix}. \quad (3) $$
large is the cross-influence of the different light source channels, and what is the resulting achievable measurement uncertainty of the 6-DOF tool pose.

Hence, the aim of this article is to assess the capability of shadow imaging for measuring the 6D tool pose during robotic ISF. In this context, the cross-sensitivities between different light sources are investigated and combined with the examined uncertainty of the LED position. Finally, the tool pose measurement uncertainty is evaluated using a Monte Carlo simulation.

For this purpose, the principle of the tool pose measurement by determining the positions of three light sources is introduced first. The experimental setups, investigating the uncertainty in light source position measurement and cross-sensitivities among the light sources is addressed, and the outcomes from these investigations are subsequently presented and discussed. Lastly, a conclusion and future perspectives are provided.

## Measuring Principle

Light source position measurement.

For tool pose measurement, the several light source positions are measured separately but simultaneously. To measure a single light source position utilizing the shadow imaging principle, multiple sensors are employed for the 3D position measurement. In each sensor, the light source creates a shadow of a mask on a camera chip. From the shadow position extracted by image processing, each sensor $n = 1 ... N$ provides a direction $r_{M,n}$ to the light source. Together with the sensor positions $s_n$ (known from the calibration, also in the machine coordinate system (MCS) M), the lines from each sensor to the light source position are obtained as $s_n + t_n \cdot r_{M,n}$ with $t_n$ as function variable. In the ideal case, all lines intersect at the sought-after position of the light source. In real 3D measurements, the lines from the sensors do not intersect at a single point, so that the light source position is determined from the point $\hat{l}_M$ that is closest to all lines (least summed squared distances):

$$ \min_{l_M} \left( \sum_{n=1}^{N} \left( \frac{\left| (l_M - s_n) \times r_{M,n} \right|}{\left| r_{M,n} \right|} \right)^2 \right). \quad (1) $$

The direction vector $r_{M,n}$ in the MCS is obtained by a coordinate transformation of the detected direction vector $r_{S,n}$ in the sensor coordinate system S. This transformation is performed by applying a rotation matrix $R_{MS,n}$, which is obtained from the sensor's calibration:

$$ r_{M,n} = R_{MS,n} \cdot r_{S,n}. \quad (2) $$

Note that any potential misalignment between the mask and the camera is reduced during the sensor setup and thus disregarded. According to Fig. 1, the vector $r_{S,n}$ follows from the shadow position $(\xi_{i,n}, \zeta_{i,n})$ on the camera chip, the calibrated distance $h_n$ between mask and camera chip, and the known reference shadow position $(\xi_{i,0,n}, \zeta_{i,0,n})$ where the light source is centered in front of the camera:

$$ r_{S,n} = \begin{bmatrix} \xi_{i,0,n} - \xi_{i,n} \\ h_n \\ \zeta_{i,0,n} - \zeta_{i,n} \end{bmatrix}. \quad (3) $$
<figure><img src="image_1307.png" /><figcaption>Fig. 1. Shadow imaging principle for each sensor. The sensor index n is omitted here. The light source at its position $l_M$ casts the mask's shadow onto a camera chip. The shadow position $(\xi_i, \zeta_i)$ in the $(\xi, \zeta)$-image plane is where the shadow of the mask center $s$, denoted by a black cross, is observed. The vector components $r_\xi, r_\eta$ and $r_\zeta$ in sensor coordinates give the direction to the light source.</figcaption></figure>

Tool pose measurement.

To obtain the tool pose, the separate measurement of three light source positions is necessary. To distinguish the signals during the measurement and avoid overlapping shadows, light sources with different wavelength are used in this article which is feasible in single shot measurements and for various tool orientations.

The tool pose is described by the tool position $p_0$, and the tool orientation is defined by the Euler-angles $(\alpha_T, \beta_T, \gamma_T)$. Thereby, the Euler-angles form the rotation matrix $R_{MT}$ so that each position $l_{T,k}$ of a light source $k = 1...K$ in tool coordinates known from a calibration is expressed in machine coordinates as follows:

$$l_{M,k} = R_{MT} \cdot l_{T,k} + p_0. \qquad (4)$$

Since the light source position $l_{M,k}$ in machine coordinates is measured by the shadow imaging sensors, subtracting the $(k+1)$-th light source position from the $k$-th

$$(l_{M,k} - l_{M,k+1}) = R_{MT} \cdot (l_{T,k} - l_{T,k-1}) \qquad (5)$$

eliminates the tool position and enables solving for the rotation matrix $R_{MT}$ using at least three light sources. The elements $r_{uv}$ in the rotation matrix provide the tool orientation angles

$$\alpha_T = \operatorname{atan2}(r_{23}, r_{33}); \quad \beta_T = \operatorname{atan2}(-r_{13}, \sqrt{r_{23}^2 + r_{33}^2}); \quad \gamma_T = \operatorname{atan2}(r_{12}, r_{11}). \qquad (6)$$

Utilizing the determined rotation matrix $R_{MT}$ and solving Eq. (4) for $p_0$, each light source contributes an estimate for calculating the tool position

$$p_0 = \frac{1}{K} \cdot (\sum_{k=1}^{K} (l_{M,k} - R_{MT} \cdot l_{T,k})) \qquad (7)$$

as the average of the result of the K light sources.
<figure><img src="image_1311.png" /><figcaption>Fig. 1. Shadow imaging principle for each sensor. The sensor index n is omitted here. The light source at its position $l_M$ casts the mask's shadow onto a camera chip. The shadow position $(\xi_i, \zeta_i)$ in the $(\xi, \zeta)$-image plane is where the shadow of the mask center $s$, denoted by a black cross, is observed. The vector components $r_\xi, r_\eta$ and $r_\zeta$ in sensor coordinates give the direction to the light source.</figcaption></figure>

Tool pose measurement.

To obtain the tool pose, the separate measurement of three light source positions is necessary. To distinguish the signals during the measurement and avoid overlapping shadows, light sources with different wavelength are used in this article which is feasible in single shot measurements and for various tool orientations.

The tool pose is described by the tool position $p_0$, and the tool orientation is defined by the Euler-angles $(\alpha_T, \beta_T, \gamma_T)$. Thereby, the Euler-angles form the rotation matrix $R_{MT}$ so that each position $l_{T,k}$ of a light source $k = 1...K$ in tool coordinates known from a calibration is expressed in machine coordinates as follows:

$$l_{M,k} = R_{MT} \cdot l_{T,k} + p_0. \qquad (4)$$

Since the light source position $l_{M,k}$ in machine coordinates is measured by the shadow imaging sensors, subtracting the $(k+1)$-th light source position from the $k$-th

$$(l_{M,k} - l_{M,k+1}) = R_{MT} \cdot (l_{T,k} - l_{T,k-1}) \qquad (5)$$

eliminates the tool position and enables solving for the rotation matrix $R_{MT}$ using at least three light sources. The elements $r_{uv}$ in the rotation matrix provide the tool orientation angles

$$\alpha_T = \operatorname{atan2}(r_{23}, r_{33}); \quad \beta_T = \operatorname{atan2}(-r_{13}, \sqrt{r_{23}^2 + r_{33}^2}); \quad \gamma_T = \operatorname{atan2}(r_{12}, r_{11}). \qquad (6)$$

Utilizing the determined rotation matrix $R_{MT}$ and solving Eq. (4) for $p_0$, each light source contributes an estimate for calculating the tool position

$$p_0 = \frac{1}{K} \cdot \left( \sum_{k=1}^{K} (l_{M,k} - R_{MT} \cdot l_{T,k}) \right) \qquad (7)$$

as the average of the result of the K light sources.
Method

Shadow imaging sensor.

The basic shadow imaging sensor consists of a DMM 37UX273-ML monochrome board camera and a mask located 20 mm in front of the camera chip, and the light source is realized by any surface-mounted device LED type 0805. The camera resolution is 1440 px × 1080 px with a pixel size of 3.45 µm. The mask shown in Fig. 2 comprises vertical and horizontal grid segments that are alternately arranged, and each orientation provides one component of the shadow position. Each grid segment is 2.0 mm × 1.5 mm with 100 µm wide stripes so that continuous visibility of at least one grid is ensured. The inclusion of 8-bit binary codes in the initial transparent stripe creates an index for each grid, aiding in determining its position relative to the mask center.

<figure><img src="image_1308.png" /><figcaption>Fig. 2. Mask cutout for the shadow imaging sensors with opaque (black) and transparent (white) parts. Grid borders are marked by purple lines and the mask center is shown by the yellow cross. Red squares denote code bits of the grid segment index. The shown axes ξ and ζ are on the camera plane whereas the distance dₐ between the mask center and the stripe a, exemplarily indicated for the stripe a = 23, is known in the mask plane.</figcaption></figure>

To calculate the direction vector to an LED from a captured image, the shadow position must be evaluated in the image, which is explained in detail in [10]. Here, it is assumed, that the LED light is sufficiently distinguished so that the image processing is robust against interfering LEDs. During image processing, the alternately arranged grid segments are separated first. Then, the stripes per grid are localized by approximating a limited gaussian function to the smoothened intensity profile of each bright stripe. Thus, the peak position µₐ is calculated for each stripe a that serves as stripe location in the camera plane. For calculating the absolute shadow position, the mask's stripe coordinates relative to its center are derived using the index of a grid segment in the image. To determine the horizontal shadow position ξᵢ, an estimate

$$ \xi_{i,a} = \mu_a + d_a \cdot f \qquad (9) $$

is calculated for each vertical stripe a from the stripe location µₐ, the horizontal mask coordinate dₐ of the stripe and the magnification f of the image, i. e. the factor between mask features and corresponding shadow features, and the estimates are averaged afterwards. Respectively, for the vertical shadow position ζᵢ, horizontal stripes provide shadow position estimates. Thus, the shadow position (ξᵢ, ζᵢ) is obtained by means of processing the shadow images, and the direction vector to the LED can be calculated.
Method

Shadow imaging sensor.

The basic shadow imaging sensor consists of a DMM 37UX273-ML monochrome board camera and a mask located 20 mm in front of the camera chip, and the light source is realized by any surface-mounted device LED type 0805. The camera resolution is 1440 px × 1080 px with a pixel size of 3.45 µm. The mask shown in Fig. 2 comprises vertical and horizontal grid segments that are alternately arranged, and each orientation provides one component of the shadow position. Each grid segment is 2.0 mm × 1.5 mm with 100 µm wide stripes so that continuous visibility of at least one grid is ensured. The inclusion of 8-bit binary codes in the initial transparent stripe creates an index for each grid, aiding in determining its position relative to the mask center.

<figure><img src="image_1312.png" /><figcaption>Fig. 2. Mask cutout for the shadow imaging sensors with opaque (black) and transparent (white) parts. Grid borders are marked by purple lines and the mask center is shown by the yellow cross. Red squares denote code bits of the grid segment index. The shown axes ξ and ζ are on the camera plane whereas the distance dₐ between the mask center and the stripe a, exemplarily indicated for the stripe a = 23, is known in the mask plane.</figcaption></figure>

To calculate the direction vector to an LED from a captured image, the shadow position must be evaluated in the image, which is explained in detail in [10]. Here, it is assumed, that the LED light is sufficiently distinguished so that the image processing is robust against interfering LEDs. During image processing, the alternately arranged grid segments are separated first. Then, the stripes per grid are localized by approximating a limited gaussian function to the smoothened intensity profile of each bright stripe. Thus, the peak position µₐ is calculated for each stripe a that serves as stripe location in the camera plane. For calculating the absolute shadow position, the mask's stripe coordinates relative to its center are derived using the index of a grid segment in the image. To determine the horizontal shadow position ξᵢ, an estimate

$$ \xi_{i,a} = \mu_a + d_a \cdot f \qquad (9) $$

is calculated for each vertical stripe a from the stripe location µₐ, the horizontal mask coordinate dₐ of the stripe and the magnification f of the image, i. e. the factor between mask features and corresponding shadow features, and the estimates are averaged afterwards. Respectively, for the vertical shadow position ζᵢ, horizontal stripes provide shadow position estimates. Thus, the shadow position (ξᵢ, ζᵢ) is obtained by means of processing the shadow images, and the direction vector to the LED can be calculated.
Experimental setups.

The position measurement uncertainty for a single LED is examined using a minimal setup with three shadow imaging sensors, as presented in Fig. 3a. The uncertainty is investigated in the measuring volume of sensor 1 at position (0 mm, 0 mm, 0 mm) with a y-range (axial) of 500 mm, an x-range (horizontal lateral) of 300 mm and a z-range (vertical lateral) of 200 mm. This volume begins at a distance of 300 mm in front of sensor 1 and is divided into two sub-regions, where sensor 2 at (-550 mm, 425 mm, 0 mm) and sensor 3 at (-550 mm, 675 mm, 0 mm) are utilized for triangulation, respectively. The green LED (WENGN02-C1M) listed in Table 1 is directed in a - 45° angle so that it is visible from both sensor perspectives.

<figure><img src="image_1309.png" /><figcaption>Fig. 3. Setups used for experimental investigation of the LED position measuring uncertainty contribution. a) Examination of the systematic and random error in measuring the 3D position of a single LED in a volume of 500 mm × 300 mm × 200 mm. b) Setup to reveal cross-sensitivities between two LEDs.</figcaption></figure>

When the experiment is conducted, a coordinate measuring machine (CMM) Leitz PMM-F 30.20.7 positions the LED and at every location, the sensors capture ten images with an exposure time of 25 ms and a reference position is provided by the CMM. After calibration, the LED is repositioned across multiple points with a distance of 10 mm along each axis to analyze both systematic and random errors.

The cross-sensitivities between LEDs with different wavelength are investigated using a second setup where a red, a green and an ultraviolet (UV) LED is used. Here, according to Fig. 3b, only one sensor but two LEDs are used and a color filter is positioned in front of the camera that is transmissive for only one LED, the main LED, while the second LED is interfering the image data. The LEDs and the corresponding filter configurations are given in Table 1.

<table><caption>Table 1. LEDs used for cross-sensitivity investigation and filter configurations applied to transmit the respective LED light.</caption><thead><tr><th colspan="3">LED</th><th>filter configuration</th></tr><tr><th>name</th><th>wavelength [nm]</th><th>beam angle [°]</th><th>description</th></tr></thead><tbody><tr><td>WENUV1-CM</td><td>421 (ultraviolet)</td><td>120</td><td>color glass BG3 (Schott) &amp; color film in magenta</td></tr><tr><td>WENGN02-C1M</td><td>520 (green)</td><td>140</td><td>color glass VG9 (Schott) &amp; color film in green</td></tr><tr><td>WENRD09-C1M</td><td>625 (red)</td><td>140</td><td>color film in red</td></tr></tbody></table>

For the experiment, it is assumed that a tool holder with a diameter of 150 mm is used and that the LEDs are positioned every 60° on the surface. Thus, an average condition with two adjacent LEDs oriented in angles of +30° and -30° is represented in the experiment. The main LED is on a fixed position in a measuring distance of 500 m and a lateral position of 37.5 mm from the center.
Experimental setups.

The position measurement uncertainty for a single LED is examined using a minimal setup with three shadow imaging sensors, as presented in Fig. 3a. The uncertainty is investigated in the measuring volume of sensor 1 at position (0 mm, 0 mm, 0 mm) with a y-range (axial) of 500 mm, an x-range (horizontal lateral) of 300 mm and a z-range (vertical lateral) of 200 mm. This volume begins at a distance of 300 mm in front of sensor 1 and is divided into two sub-regions, where sensor 2 at (-550 mm, 425 mm, 0 mm) and sensor 3 at (-550 mm, 675 mm, 0 mm) are utilized for triangulation, respectively. The green LED (WENGN02-C1M) listed in Table 1 is directed in a - 45° angle so that it is visible from both sensor perspectives.

<figure><img src="image_1313.png" /><figcaption>Fig. 3. Setups used for experimental investigation of the LED position measuring uncertainty contribution. a) Examination of the systematic and random error in measuring the 3D position of a single LED in a volume of 500 mm × 300 mm × 200 mm. b) Setup to reveal cross-sensitivities between two LEDs.</figcaption></figure>

When the experiment is conducted, a coordinate measuring machine (CMM) Leitz PMM-F 30.20.7 positions the LED and at every location, the sensors capture ten images with an exposure time of 25 ms and a reference position is provided by the CMM. After calibration, the LED is repositioned across multiple points with a distance of 10 mm along each axis to analyze both systematic and random errors.

The cross-sensitivities between LEDs with different wavelength are investigated using a second setup where a red, a green and an ultraviolet (UV) LED is used. Here, according to Fig. 3b, only one sensor but two LEDs are used and a color filter is positioned in front of the camera that is transmissive for only one LED, the main LED, while the second LED is interfering the image data. The LEDs and the corresponding filter configurations are given in Table 1.

<table><caption>Table 1. LEDs used for cross-sensitivity investigation and filter configurations applied to transmit the respective LED light.</caption><thead><tr><th colspan="2">LED</th><th>filter configuration</th></tr><tr><th>name</th><th>wavelength [nm]</th><th>beam angle [°]</th><th>description</th></tr></thead><tbody><tr><td>WENUV1-CM</td><td>421 (ultraviolet)</td><td>120</td><td>color glass BG3 (Schott) &amp; color film in magenta</td></tr><tr><td>WENGN02-C1M</td><td>520 (green)</td><td>140</td><td>color glass VG9 (Schott) &amp; color film in green</td></tr><tr><td>WENRD09-C1M</td><td>625 (red)</td><td>140</td><td>color film in red</td></tr></tbody></table>

For the experiment, it is assumed that a tool holder with a diameter of 150 mm is used and that the LEDs are positioned every 60° on the surface. Thus, an average condition with two adjacent LEDs oriented in angles of +30° and -30° is represented in the experiment. The main LED is on a fixed position in a measuring distance of 500 m and a lateral position of 37.5 mm from the center.
The interfering LED is moved stepwise by the CMM along the x-axis in a range of -100 mm to +100 mm with respect to the main. In vertical direction, the distance between the LEDs is 37.5 mm which leads to a vertical shift between the shadows of both LEDs of one grid height. During the movement ten images are recorded every 0.5 mm with an exposure time of 50 ms.

Monte Carlo simulation.

To estimate the tool pose measurement uncertainty, a Monte Carlo simulation is applied. Initially, the tool position and orientation in the MCS, and three true LED positions in the tool coordinate system on the tool holder at alternating heights of 0 mm and 100 mm are defined. Then, the LED positions are transformed into the MCS, and the simulated LED position measurement error is added to each true LED position. The tool pose error is calculated for 10000 sets of simulated LED position measurements to enable a proper statistical evaluation. The procedure is repeated for 1000 random tool poses, whereby the tool positions are spread over the entire measurement volume and the orientation is in a range of ± 45° for αT and βT, and of ± 30° for γT.

To simulate the LED position measurement error, contributions to the uncertainty, systematic and random errors in single LED measurement, and cross-sensitivity between LEDs, are integrated based on their statistical distribution across the measuring volume. The systematic error is composed of a predictable tendential course and an unpredictable scatter. The scattering error is determined on multiple paths in the measurement volume and a standard deviation of all error values is calculated. The random error's standard deviation is the propagation of a fluctuating shadow position which depends on the angle of view and is modelled from the experimental results. Thus, the random measurement error is generated from the standard deviation that corresponds to a random position in the measurement volume. Regarding the cross-sensitivity, the experimentally detected LED position measurement error is used to assess the standard deviation of the shadow position, which is propagated to a random position in the measuring volume. Here, only the effect of the interfering LED leading to the major error is considered.

## Results

Systematic error.

The systematic error is evaluated using the three-sensor-setup by calculating the error between the average measured position and the reference position. The observation of the systematic error Δ(xL), mainly affected by sensor 1, is presented in Fig. 4a and shows a strong parabolic course overlaid by a scatter that is increasing to larger angles of view. The parabolic course is predictable, so the scatter of the systematic error Δ(xL) caused by varying magnification values is evaluated on paths along the z-axis. The frequency distribution of the remaining scattering error Δc(xL) on all paths, shown in Fig. 4b, follows a normal distribution with a standard deviation of 33 µm. Accordingly, the scatters of the systematic errors Δ(yL) and Δ(zL), also included in Fig. 4b, are extracted on paths along the z- and x-axis which leads to standard deviations of 29 µm and 25 µm, respectively. Therefore, the systematic scatter is more than the half of the allowed tool position uncertainty.

Random error.

The random LED position measurement error is evaluated based on the three-sensor-setup as the standard deviation of the evaluated LED positions. Fig. 5a shows the standard deviation of the measured xL-LED position component along the x-axis at zL,ref = 0 mm. The standard deviation σ(xL) increases with the angle of view between sensor 1 and the xL,ref position component. The strong angle-dependent increase is primarily caused by the propagation of the magnification uncertainty u(f) to the shadow position component ξi of sensor 1, see Eq. 9. As a result, the zL,ref position component has hardly any influence on the standard deviation σ(xL). The secondary effect is the increase of the LED position standard deviation σ(xL) with the axial distance yL,ref. Assuming the ideal sensor setup as described previously, including that the rotation
The interfering LED is moved stepwise by the CMM along the x-axis in a range of -100 mm to +100 mm with respect to the main. In vertical direction, the distance between the LEDs is 37.5 mm which leads to a vertical shift between the shadows of both LEDs of one grid height. During the movement ten images are recorded every 0.5 mm with an exposure time of 50 ms.

Monte Carlo simulation.

To estimate the tool pose measurement uncertainty, a Monte Carlo simulation is applied. Initially, the tool position and orientation in the MCS, and three true LED positions in the tool coordinate system on the tool holder at alternating heights of 0 mm and 100 mm are defined. Then, the LED positions are transformed into the MCS, and the simulated LED position measurement error is added to each true LED position. The tool pose error is calculated for 10000 sets of simulated LED position measurements to enable a proper statistical evaluation. The procedure is repeated for 1000 random tool poses, whereby the tool positions are spread over the entire measurement volume and the orientation is in a range of ± 45° for α<sub>T</sub> and β<sub>T</sub>, and of ± 30° for γ<sub>T</sub>.

To simulate the LED position measurement error, contributions to the uncertainty, systematic and random errors in single LED measurement, and cross-sensitivity between LEDs, are integrated based on their statistical distribution across the measuring volume. The systematic error is composed of a predictable tendential course and an unpredictable scatter. The scattering error is determined on multiple paths in the measurement volume and a standard deviation of all error values is calculated. The random error's standard deviation is the propagation of a fluctuating shadow position which depends on the angle of view and is modelled from the experimental results. Thus, the random measurement error is generated from the standard deviation that corresponds to a random position in the measurement volume. Regarding the cross-sensitivity, the experimentally detected LED position measurement error is used to assess the standard deviation of the shadow position, which is propagated to a random position in the measuring volume. Here, only the effect of the interfering LED leading to the major error is considered.

## Results

Systematic error.

The systematic error is evaluated using the three-sensor-setup by calculating the error between the average measured position and the reference position. The observation of the systematic error Δ(x<sub>L</sub>), mainly affected by sensor 1, is presented in Fig. 4a and shows a strong parabolic course overlaid by a scatter that is increasing to larger angles of view. The parabolic course is predictable, so the scatter of the systematic error Δ(x<sub>L</sub>) caused by varying magnification values is evaluated on paths along the z-axis. The frequency distribution of the remaining scattering error Δ<sub>c</sub>(x<sub>L</sub>) on all paths, shown in Fig. 4b, follows a normal distribution with a standard deviation of 33 µm. Accordingly, the scatters of the systematic errors Δ(y<sub>L</sub>) and Δ(z<sub>L</sub>), also included in Fig. 4b, are extracted on paths along the z- and x-axis which leads to standard deviations of 29 µm and 25 µm, respectively. Therefore, the systematic scatter is more than the half of the allowed tool position uncertainty.

Random error.

The random LED position measurement error is evaluated based on the three-sensor-setup as the standard deviation of the evaluated LED positions. Fig. 5a shows the standard deviation of the measured x<sub>L</sub>-LED position component along the x-axis at z<sub>L,ref</sub> = 0 mm. The standard deviation σ(x<sub>L</sub>) increases with the angle of view between sensor 1 and the x<sub>L,ref</sub> position component. The strong angle-dependent increase is primarily caused by the propagation of the magnification uncertainty u(f) to the shadow position component ξ<sub>i</sub> of sensor 1, see Eq. 9. As a result, the z<sub>L,ref</sub> position component has hardly any influence on the standard deviation σ(x<sub>L</sub>). The secondary effect is the increase of the LED position standard deviation σ(x<sub>L</sub>) with the axial distance y<sub>L,ref</sub>. Assuming the ideal sensor setup as described previously, including that the rotation
matrix $R_{MS,1}$ is a zero matrix and that the uncertainty of the $y_L$ component is negligible, the uncertainty

$$u(x_L) = u(\xi_i) \cdot \frac{y_{L,ref}}{h} \qquad (10)$$

is the shadow position uncertainty $u(\xi_i)$ scaled by the relation between the axial distance $y_{L,ref}$ and the distance $h$ between mask and camera. The standard deviations $\sigma(y_L)$ and $\sigma(z_L)$ show an according course, but the standard deviations are slightly smaller for the $y_L$-component because the angle of view is smaller, and the standard deviations are particularly small for the $z_L$-component since the information provided by two perspectives is averaged.

<figure><img src="image_1310.png" /><figcaption>Fig. 4. Systematic error of the measured LED position. a) Systematic error $\Delta(x_L)$ evaluated on paths along the x-axis vertically centered in front of sensor 1. b) Frequency distribution of the systematic error values after the correction of the tendential course.</figcaption></figure>

<figure><img src="image_1311.png" /><figcaption>Fig. 5. Random error of the LED position. a) Standard deviation of the measured LED position component $x_L$ evaluated on paths along the x-axis at $z_{L,ref} = 0$ mm. b) Frequency distribution of 10000 simulated random error values $\Delta_V$ following the empirical model.</figcaption></figure>

For establishing an empirical model for the position dependent random error, the LED position standard deviation $u(x_L)$ is extracted on the path at $y_{L,ref} = 675$ mm, which is centered in front of sensor 3, rescaled to the shadow position standard deviation and approximated by a parabola in dependence of the angle of view. The same empirical model is applied for the $y_L$- and $z_L$-
matrix $R_{MS,1}$ is a zero matrix and that the uncertainty of the $y_L$ component is negligible, the uncertainty

$$u(x_L) = u(\xi_i) \cdot \frac{y_{L,ref}}{h} \qquad (10)$$

is the shadow position uncertainty $u(\xi_i)$ scaled by the relation between the axial distance $y_{L,ref}$ and the distance $h$ between mask and camera. The standard deviations $\sigma(y_L)$ and $\sigma(z_L)$ show an according course, but the standard deviations are slightly smaller for the $y_L$-component because the angle of view is smaller, and the standard deviations are particularly small for the $z_L$-component since the information provided by two perspectives is averaged.

<figure><img src="image_1314.png" /><figcaption>Fig. 4. Systematic error of the measured LED position. a) Systematic error $\Delta(x_L)$ evaluated on paths along the x-axis vertically centered in front of sensor 1. b) Frequency distribution of the systematic error values after the correction of the tendential course.</figcaption></figure>

<figure><img src="image_1315.png" /><figcaption>Fig. 5. Random error of the LED position. a) Standard deviation of the measured LED position component $x_L$ evaluated on paths along the x-axis at $z_{L,ref} = 0$ mm. b) Frequency distribution of 10000 simulated random error values $\Delta_V$ following the empirical model.</figcaption></figure>

For establishing an empirical model for the position dependent random error, the LED position standard deviation $u(x_L)$ is extracted on the path at $y_{L,ref} = 675$ mm, which is centered in front of sensor 3, rescaled to the shadow position standard deviation and approximated by a parabola in dependence of the angle of view. The same empirical model is applied for the $y_L$- and $z_L$-
component, but the respective lateral and axial LED position components for Eq. 10 are adapted to the laterally measuring sensor. Since the $z_L$-component is covered from both sensor perspectives, both respective sensors provide a random error that is averaged then.

To further investigate the statistical distribution of the random error in the entire measuring volume, uniformly distributed positions are generated and random error values $\Delta_V$ that follow a normal distribution with the model-based standard deviation are simulated. After 10000 simulations, the frequency distribution of random errors $\Delta_V$ shown in Fig. 5b results. The standard deviation $\sigma(\Delta_V(x_L))$ of random error values of the LED position component $x_L$ in the entire measuring volume is 3.5 µm, and for the $y_L$- and $z_L$-component, the standard deviation is $\sigma(\Delta_V(y_L)) = 2.7$ µm and $\sigma(\Delta_V(z_L)) = 1.4$ µm.

### Cross-sensitivities.

Experiments with the setup shown in Fig. 3b provide an estimation on the cross-sensitivities between LEDs of different colors. The main LED position component $x_{L,main}$ is evaluated from the shadow position component $\xi_i$ assuming $x_{L,main} = 0$ mm as mean position, an ideal sensor setup and involving the axial position $y_{L,ref}$ from the CMM. The deviations of the mean main LED position per position of the interfering LED, presented in Fig. 6 for all combinations of LEDs, show that the deviation remains below 15 µm which is promising for tool pose measurement.

<figure><img src="image_1312.png" /><figcaption>Fig. 6. Measured lateral positions of fixed main LEDs while an interfering LED is moved above the main LED. The deviation of the main LED position $x_{L,main}$ is the error due to cross-sensitivities between the LEDs. a) Red main LED, b) green main LED, c) UV main LED.</figcaption></figure>

Furthermore, for the red main LED shown in Fig. 6a, a periodic course of the main LED position is present for both interfering LEDs. This periodicity occurs due to slight transmissivity of the color filter for the interfering light, causing the shadows of both LEDs to superpose. Two slightly shifted overlapping stripe shadows result in a shifted stripe shadow position and thus a shifted measured LED position. For the green interfering LED, the shift of the main LED $x_{L,main}$ varies also in the amplitude as the interfering LED moves. The amplitude increases with a larger overlap between vertical grid segment shadows and a higher intensity of the interfering shadow.

The error due to cross-sensitivities is normally distributed along the captured path. For the red main LED, the green interfering LED leads to the higher error with a standard deviation of 6.5 µm. While the red LED interferes the measurement of the green main LED in a distinct periodic course with a total standard deviation of 5.2 µm, the UV LED movement results in a low noisy error, see Fig. 6b. The cross-sensitivity error of the UV main LED shown in Fig. 6c is barely detectable with a standard deviation of 2.0 µm for the green interfering LED while the red interfering LED has a
component, but the respective lateral and axial LED position components for Eq. 10 are adapted to the laterally measuring sensor. Since the $z_L$-component is covered from both sensor perspectives, both respective sensors provide a random error that is averaged then.

To further investigate the statistical distribution of the random error in the entire measuring volume, uniformly distributed positions are generated and random error values $\Delta_V$ that follow a normal distribution with the model-based standard deviation are simulated. After 10000 simulations, the frequency distribution of random errors $\Delta_V$ shown in Fig. 5b results. The standard deviation $\sigma(\Delta_V(x_L))$ of random error values of the LED position component $x_L$ in the entire measuring volume is 3.5 µm, and for the $y_L$- and $z_L$-component, the standard deviation is $\sigma(\Delta_V(y_L)) = 2.7$ µm and $\sigma(\Delta_V(z_L)) = 1.4$ µm.

### Cross-sensitivities.

Experiments with the setup shown in Fig. 3b provide an estimation on the cross-sensitivities between LEDs of different colors. The main LED position component $x_{L,main}$ is evaluated from the shadow position component $\xi_i$ assuming $x_{L,main} = 0$ mm as mean position, an ideal sensor setup and involving the axial position $y_{L,ref}$ from the CMM. The deviations of the mean main LED position per position of the interfering LED, presented in Fig. 6 for all combinations of LEDs, show that the deviation remains below 15 µm which is promising for tool pose measurement.

<figure><img src="image_1316.png" /><figcaption>Fig. 6. Measured lateral positions of fixed main LEDs while an interfering LED is moved above the main LED. The deviation of the main LED position $x_{L,main}$ is the error due to cross-sensitivities between the LEDs. a) Red main LED, b) green main LED, c) UV main LED.</figcaption></figure>

Furthermore, for the red main LED shown in Fig. 6a, a periodic course of the main LED position is present for both interfering LEDs. This periodicity occurs due to slight transmissivity of the color filter for the interfering light, causing the shadows of both LEDs to superpose. Two slightly shifted overlapping stripe shadows result in a shifted stripe shadow position and thus a shifted measured LED position. For the green interfering LED, the shift of the main LED $x_{L,main}$ varies also in the amplitude as the interfering LED moves. The amplitude increases with a larger overlap between vertical grid segment shadows and a higher intensity of the interfering shadow.

The error due to cross-sensitivities is normally distributed along the captured path. For the red main LED, the green interfering LED leads to the higher error with a standard deviation of 6.5 µm. While the red LED interferes the measurement of the green main LED in a distinct periodic course with a total standard deviation of 5.2 µm, the UV LED movement results in a low noisy error, see Fig. 6b. The cross-sensitivity error of the UV main LED shown in Fig. 6c is barely detectable with a standard deviation of 2.0 µm for the green interfering LED while the red interfering LED has a
minor influence. It is assumed that the vertical position component is affected accordingly. However, the cause of the LED position error is the shadow position error so that the position error will increase with an increasing axial distance between sensor and LED.

Tool pose measurement.

To assess the feasibility for tool pose measurement using shadow imaging, the revealed uncertainty contributions are combined by means of a Monte Carlo simulation. In summary, the systematic scatter contributes the strongest to the LED position measurement uncertainty, followed by the error due to cross-sensitivities, and the random error has the lowest impact.

The frequency distribution of the resulting tool position and orientation measurement error is shown in Fig. 7a and Fig. 7b, respectively, for one exemplary tool pose. It is evident that the majority of the position errors is in the allowed range of ± 50 µm and also the orientation error is mostly in the required range of ± 0.05°. In fact, over all 1000 tool poses, at least 92 % of the simulated error values per position or orientation component are within the required range.

<figure><img src="image_1313.png" /><figcaption>Fig. 7. Frequency distributions of 10000 tool pose errors applied to one exemplary tool pose, divided in the respective a) tool position components ($p_{0,x}$, $p_{0,y}$, $p_{0,z}$) and b) tool orientation components ($\alpha_T$, $\beta_T$, $\gamma_T$).</figcaption></figure>

Furthermore, the results show that the tool position component $p_{0,x}$ has the highest uncertainty. The reason for this is that the LED position measurement uncertainty of the $x_L$-component is the highest while the tool orientation range is limited. Even the root of the mean squared error (RMSE), calculated for all simulated tool poses is the highest for the tool position component $p_{0,x}$ with 26 µm, while the RMSEs of the components $p_{0,y}$ and $p_{0,z}$ are each 21 µm on average. The frequency distribution of the tool orientation error demonstrates that the error of the component $\beta_T$ has the lowest uncertainty which is confirmed by the other tool poses. The average RMSE is 0.017° while the components $\alpha_T$ and $\gamma_T$ both show an average RSME of 0.021°.

In conclusion, the results of the Monte Carlo simulations show that tool pose measurement using shadow imaging is feasible with the required measuring uncertainty since the majority of the simulated tool position and orientation errors is in the aimed uncertainty range and the evaluated RMSEs are around the half of the required measuring uncertainty.

## Summary

To achieve a position and orientation measurement uncertainty of 50 µm and 0.05°, respectively, required for tool pose measurement during ISF, a triangulation system based on shadow imaging sensors measuring positions of LEDs attached to the tool holder, is introduced. The contributions to LED position measurement uncertainty, including cross-sensitivities between different LEDs, are examined. To finally assess the feasibility of tool pose measurement, the tool pose error resulting from the LED position uncertainty was investigated applying a Monte Carlo simulation.
minor influence. It is assumed that the vertical position component is affected accordingly. However, the cause of the LED position error is the shadow position error so that the position error will increase with an increasing axial distance between sensor and LED.

Tool pose measurement.

To assess the feasibility for tool pose measurement using shadow imaging, the revealed uncertainty contributions are combined by means of a Monte Carlo simulation. In summary, the systematic scatter contributes the strongest to the LED position measurement uncertainty, followed by the error due to cross-sensitivities, and the random error has the lowest impact.

The frequency distribution of the resulting tool position and orientation measurement error is shown in Fig. 7a and Fig. 7b, respectively, for one exemplary tool pose. It is evident that the majority of the position errors is in the allowed range of ± 50 µm and also the orientation error is mostly in the required range of ± 0.05°. In fact, over all 1000 tool poses, at least 92 % of the simulated error values per position or orientation component are within the required range.

<figure><img src="image_1317.png" /><figcaption>Fig. 7. Frequency distributions of 10000 tool pose errors applied to one exemplary tool pose, divided in the respective a) tool position components ($p_{0,x}$, $p_{0,y}$, $p_{0,z}$) and b) tool orientation components ($\alpha_T$, $\beta_T$, $\gamma_T$).</figcaption></figure>

Furthermore, the results show that the tool position component $p_{0,x}$ has the highest uncertainty. The reason for this is that the LED position measurement uncertainty of the $x_L$-component is the highest while the tool orientation range is limited. Even the root of the mean squared error (RMSE), calculated for all simulated tool poses is the highest for the tool position component $p_{0,x}$ with 26 µm, while the RMSEs of the components $p_{0,y}$ and $p_{0,z}$ are each 21 µm on average. The frequency distribution of the tool orientation error demonstrates that the error of the component $\beta_T$ has the lowest uncertainty which is confirmed by the other tool poses. The average RMSE is 0.017° while the components $\alpha_T$ and $\gamma_T$ both show an average RSME of 0.021°.

In conclusion, the results of the Monte Carlo simulations show that tool pose measurement using shadow imaging is feasible with the required measuring uncertainty since the majority of the simulated tool position and orientation errors is in the aimed uncertainty range and the evaluated RMSEs are around the half of the required measuring uncertainty.

## Summary

To achieve a position and orientation measurement uncertainty of 50 µm and 0.05°, respectively, required for tool pose measurement during ISF, a triangulation system based on shadow imaging sensors measuring positions of LEDs attached to the tool holder, is introduced. The contributions to LED position measurement uncertainty, including cross-sensitivities between different LEDs, are examined. To finally assess the feasibility of tool pose measurement, the tool pose error resulting from the LED position uncertainty was investigated applying a Monte Carlo simulation.
The Monte Carlo simulation revealed that shadow imaging sensors are capable of measuring the tool pose with a sufficient measurement uncertainty. From the experimental results on the contributions to the LED position uncertainty, it stands out that the scatter in the systematic error resulting from variations in the evaluated magnification primarily influences the uncertainty budget, and that the lowest contribution is the random error caused by image noise. The effect of cross-sensitivities is reduced to a sufficient level, comparable to the random error, by applying the respective color filters.

Although the Monte Carlo simulation proved the feasibility of measuring the tool pose with the proposed measuring principle, an experimental validation is still pending and will be subject of future work. Furthermore, the reduction of the measurement duration and the processing time, to demonstrate the capability of real-time tool pose measurement, will be covered in further studies.

## References

[1] W. Ji, L. Wang: Industrial robotic machining: a review. Int J Adv Manuf Technol 103(1-4):1239-1255, 2019. https://doi.org/10.1007/s00170-019-03403-z

[2] H. Zu, X. Chen, Z. Chen, Z. Wang, X. Zhang: Positioning accuracy improvement method of industrial robot based on laser tracking measurement. Measurement: Sensors 18:100235, 2021. https://doi.org/10.1016/j.measen.2021.100235

[3] G. Xiong, Z.-L. Li, Y. Ding, L. Zhu: A closed-loop error compensation method for robotic flank milling. Robotics and Computer-Integrated Manufacturing 63:101928, 2020. https://doi.org/10.1016/j.rcim.2019.101928

[4] A. Nubiola, I. A. Bonev: Absolute calibration of an ABB IRB 1600 robot using a laser tracker. Robotics and Computer-Integrated Manufacturing 29(1):236-245, 2013. https://doi.org/10.1016/j.rcim.2012.06.004

[5] T. Shu, S. Gharaaty, W. Xie, A. Joubair, I. A. Bonev: Dynamic path tracking of industrial robots with high accuracy using photogrammetry sensor. IEEE/ASME Trans. Mechatron. 23(3):1159-1170, 2018. https://doi.org/10.1109/TMECH.2018.2821600

[6] J. Tang, T. Zhou, E. Zakeri, T. Shu, W.-F. Xie: Photogrammetry-based Dynamic Path Tracking of Industrial Robots Using Adaptive Neuro-PID Control Method and Robust Kalman Filter. 2023 9th International Conference on Automation, Robotics and Applications (ICARA), Abu Dhabi, United Arab Emirates, 10.02.2023 - 12.02.2023. https://doi.org/10.1109/ICARA56516.2023.10125681

[7] J. Lin, Y. Li, Y. Xie, J. Hu, J. Min: Joint stiffness identification of industrial serial robots using 3D digital image correlation techniques. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236(1):536-551, 2022. https://doi.org/10.1177/09544062211002878

[8] T. Luhmann: Close range photogrammetry for industrial applications. ISPRS Journal of Photogrammetry and Remote Sensing 65(6):558-569, 2010. https://doi.org/10.1016/j.isprsjprs.2010.06.003

[9] E. Grenet, P. Masa, E. Franzi, D. Hasler: Measurement system of a light source in space 14.07.2011

[10] M. Terlau, A. von Freyberg, D. Stöbener, A. Fischer: Shadow-Imaging-Based Triangulation Approach for Tool Deflection Measurement. Sensors (Basel) 23(20):2023. https://doi.org/10.3390/s23208593
The Monte Carlo simulation revealed that shadow imaging sensors are capable of measuring the tool pose with a sufficient measurement uncertainty. From the experimental results on the contributions to the LED position uncertainty, it stands out that the scatter in the systematic error resulting from variations in the evaluated magnification primarily influences the uncertainty budget, and that the lowest contribution is the random error caused by image noise. The effect of cross-sensitivities is reduced to a sufficient level, comparable to the random error, by applying the respective color filters.

Although the Monte Carlo simulation proved the feasibility of measuring the tool pose with the proposed measuring principle, an experimental validation is still pending and will be subject of future work. Furthermore, the reduction of the measurement duration and the processing time, to demonstrate the capability of real-time tool pose measurement, will be covered in further studies.

## References

[1] W. Ji, L. Wang: Industrial robotic machining: a review. Int J Adv Manuf Technol 103(1-4):1239-1255, 2019. https://doi.org/10.1007/s00170-019-03403-z

[2] H. Zu, X. Chen, Z. Chen, Z. Wang, X. Zhang: Positioning accuracy improvement method of industrial robot based on laser tracking measurement. Measurement: Sensors 18:100235, 2021. https://doi.org/10.1016/j.measen.2021.100235

[3] G. Xiong, Z.-L. Li, Y. Ding, L. Zhu: A closed-loop error compensation method for robotic flank milling. Robotics and Computer-Integrated Manufacturing 63:101928, 2020. https://doi.org/10.1016/j.rcim.2019.101928

[4] A. Nubiola, I. A. Bonev: Absolute calibration of an ABB IRB 1600 robot using a laser tracker. Robotics and Computer-Integrated Manufacturing 29(1):236-245, 2013. https://doi.org/10.1016/j.rcim.2012.06.004

[5] T. Shu, S. Gharaaty, W. Xie, A. Joubair, I. A. Bonev: Dynamic path tracking of industrial robots with high accuracy using photogrammetry sensor. IEEE/ASME Trans. Mechatron. 23(3):1159-1170, 2018. https://doi.org/10.1109/TMECH.2018.2821600

[6] J. Tang, T. Zhou, E. Zakeri, T. Shu, W.-F. Xie: Photogrammetry-based Dynamic Path Tracking of Industrial Robots Using Adaptive Neuro-PID Control Method and Robust Kalman Filter. 2023 9th International Conference on Automation, Robotics and Applications (ICARA), Abu Dhabi, United Arab Emirates, 10.02.2023 - 12.02.2023. https://doi.org/10.1109/ICARA56516.2023.10125681

[7] J. Lin, Y. Li, Y. Xie, J. Hu, J. Min: Joint stiffness identification of industrial serial robots using 3D digital image correlation techniques. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236(1):536-551, 2022. https://doi.org/10.1177/09544062211002878

[8] T. Luhmann: Close range photogrammetry for industrial applications. ISPRS Journal of Photogrammetry and Remote Sensing 65(6):558-569, 2010. https://doi.org/10.1016/j.isprsjprs.2010.06.003

[9] E. Grenet, P. Masa, E. Franzi, D. Hasler: Measurement system of a light source in space 14.07.2011

[10] M. Terlau, A. von Freyberg, D. Stöbener, A. Fischer: Shadow-Imaging-Based Triangulation Approach for Tool Deflection Measurement. Sensors (Basel) 23(20):2023. https://doi.org/10.3390/s23208593
# Thermomechanical reverse flow forming of AISI 304L

ARIAN Bahman¹, a *, HOMBERG Werner¹, KERSTING Lukas², b, TRÄCHTLER Ansgar², ROZO VASQUEZ Julian³, c and WALTHER Frank³

¹Paderborn University, Forming and Machining Technology (LUF), Germany

²Fraunhofer Institute for Mechatronic Systems Design (IEM), Germany

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

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

**Keywords:** Reverse Flow Forming, α'-Martensite, Grading Strategies, Property-Control

**Abstract.** In manufacturing, property-control ensures efficient part production. However, in reverse flow forming, current practices focus on geometry-control rather than property-control. To address the complexity of the process and tool-machine interaction, process control is crucial for defined component properties. This study focuses on controlling local α'-martensite content in reverse flow forming of seamless AISI 304L steel tubes. Strategies and systems are presented to influence α'-martensite content, creating unique microstructure profiles for 1D- and 2D-Gradings, with tangible component outcomes.

**Introduction**

Flow forming excels in precision production of rotationally symmetrical parts, but using semi-finished metastable austenitic steel (AISI 304L) poses challenges due to strain-induced α'-martensite formation [1]. Disturbances like eccentricity and batch variations induce arbitrary microstructural profiles, complicating reproducibility [2]. Manufacturing faces heightened demands for materials, tools, and processes driven by customer expectations for reliability, recyclability, crash safety, and lightweight suitability [3, 4]. The main production objective is defect-free components with local property adjustments, facilitated by closed-loop property-control. Funded by DFG, experimental investigations focus on better control of α'-martensite content during reverse flow forming, aiming for reproducible production with imperceptible microstructure profiles. This innovation enables invisible “barcodes” for product labeling, revolutionizing counterfeiting prevention. Developing process strategies for local α'-martensite manipulation while maintaining external dimensions, using actuator and sensory concepts, is crucial. The current research emphasis is on producing invisible 1D- and 2D-Gradings, as shown in Fig. 1, in an innovative combination of axial and angular grading.

<figure><img src="image_1314.png" /><figcaption>Fig. 1. Differentiation of grading types</figcaption></figure>

<figure><img src="image_1315.png" /></figure>
# Thermomechanical reverse flow forming of AISI 304L

ARIAN Bahman¹, a *, HOMBERG Werner¹, KERSTING Lukas², b, TRÄCHTLER Ansgar², ROZO VASQUEZ Julian³, c and WALTHER Frank³

¹Paderborn University, Forming and Machining Technology (LUF), Germany

²Fraunhofer Institute for Mechatronic Systems Design (IEM), Germany

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

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

**Keywords:** Reverse Flow Forming, α'-Martensite, Grading Strategies, Property-Control

**Abstract.** In manufacturing, property-control ensures efficient part production. However, in reverse flow forming, current practices focus on geometry-control rather than property-control. To address the complexity of the process and tool-machine interaction, process control is crucial for defined component properties. This study focuses on controlling local α'-martensite content in reverse flow forming of seamless AISI 304L steel tubes. Strategies and systems are presented to influence α'-martensite content, creating unique microstructure profiles for 1D- and 2D-Gradings, with tangible component outcomes.

**Introduction**

Flow forming excels in precision production of rotationally symmetrical parts, but using semi-finished metastable austenitic steel (AISI 304L) poses challenges due to strain-induced α'-martensite formation [1]. Disturbances like eccentricity and batch variations induce arbitrary microstructural profiles, complicating reproducibility [2]. Manufacturing faces heightened demands for materials, tools, and processes driven by customer expectations for reliability, recyclability, crash safety, and lightweight suitability [3, 4]. The main production objective is defect-free components with local property adjustments, facilitated by closed-loop property-control. Funded by DFG, experimental investigations focus on better control of α'-martensite content during reverse flow forming, aiming for reproducible production with imperceptible microstructure profiles. This innovation enables invisible “barcodes” for product labeling, revolutionizing counterfeiting prevention. Developing process strategies for local α'-martensite manipulation while maintaining external dimensions, using actuator and sensory concepts, is crucial. The current research emphasis is on producing invisible 1D- and 2D-Gradings, as shown in Fig. 1, in an innovative combination of axial and angular grading.

<figure><img src="image_1318.png" /><figcaption>Fig. 1. Differentiation of grading types</figcaption></figure>

<figure><img src="image_1319.png" /></figure>
## Reverse Flow Forming

Flow forming is an incremental process offering various advantages in terms of flexibility and efficiency [5]. A characteristic feature for the process is an intended wall thickness reduction $\Delta w$ of semi-finished tubes, which leads to component elongation $\Delta l$ due to volume constancy, accompanied by excellent shape, dimensional accuracy and outstanding surface qualities [6]. Flow formed tubes therefore meet rigorous standards, including those set by the aerospace industry, and are widely used in high-performance components such as drive shafts for jet engines and helicopters [7]. In this paper, the emphasis is on reverse flow forming shown in Fig. 2, a process in which the material flows counter to the axial motion of the roller tools. These roller tools are capable of both radial and axial movement, and they rotate around their own axis due to contact friction with the rotating tube.

<figure><img src="image_1316.png" /><figcaption>Fig. 2. Reverse flow forming process principle</figcaption></figure>

## Experimental Setup

The experiments were carried out on a setup shown in Fig. 3 including a PLB 400 spinning machine from Leifeld Metal Spinning GmbH (Ahlen, Germany) reaching a drive power up to 11 kW and a maximum spindle speed of 950 rpm. The machine is equipped with a hydraulically driven cross support, which has two axes capable of generating a maximum force of 35 kN.

<figure><img src="image_1317.png" /><figcaption>Fig. 3. Machine and actuator configuration with a) and b) showing different viewing angles</figcaption></figure>

The machine setup employs a single-roller tool configuration to accommodate thermal actuator systems and sensors for process control, as outlined in [8]. The sensor concept, developed at Forming and Machining Technology (LUF), will not be the primary focus of this paper. Featuring
## Reverse Flow Forming

Flow forming is an incremental process offering various advantages in terms of flexibility and efficiency [5]. A characteristic feature for the process is an intended wall thickness reduction $\Delta w$ of semi-finished tubes, which leads to component elongation $\Delta l$ due to volume constancy, accompanied by excellent shape, dimensional accuracy and outstanding surface qualities [6]. Flow formed tubes therefore meet rigorous standards, including those set by the aerospace industry, and are widely used in high-performance components such as drive shafts for jet engines and helicopters [7]. In this paper, the emphasis is on reverse flow forming shown in Fig. 2, a process in which the material flows counter to the axial motion of the roller tools. These roller tools are capable of both radial and axial movement, and they rotate around their own axis due to contact friction with the rotating tube.

<figure><img src="image_1320.png" /><figcaption>Fig. 2. Reverse flow forming process principle</figcaption></figure>

## Experimental Setup

The experiments were carried out on a setup shown in Fig. 3 including a PLB 400 spinning machine from Leifeld Metal Spinning GmbH (Ahlen, Germany) reaching a drive power up to 11 kW and a maximum spindle speed of 950 rpm. The machine is equipped with a hydraulically driven cross support, which has two axes capable of generating a maximum force of 35 kN.

<figure><img src="image_1321.png" /><figcaption>Fig. 3. Machine and actuator configuration with a) and b) showing different viewing angles</figcaption></figure>

The machine setup employs a single-roller tool configuration to accommodate thermal actuator systems and sensors for process control, as outlined in [8]. The sensor concept, developed at Forming and Machining Technology (LUF), will not be the primary focus of this paper. Featuring
a robust counter-holder designed to support the mandrel and an absolute value encoder, the machine can perform angle-dependent operations within the process. The thermal heating actuator consists of a custom-developed inductor that conforms to the shape of the semi-finished tube and can heat a local angular area. The automated cryogenic cooling system, detailed in [9] and illustrated in Fig. 4, serves as a thermal actuator for localized cooling. It enables computer-assisted and reproducible cooling in both axial and/or angular directions. The cryogenic nozzle focuses a -196 °C stream of liquid nitrogen, simultaneously averting the Leidenfrost phenomenon [10].

<figure><img src="image_1318.png" /><figcaption>Fig. 4. Automated cryogenic cooling system</figcaption></figure>

The material for the semi-finished tubes is AISI 304L (X2CrNi18-9), a TRIP steel with strain- and/or temperature-induced α'-martensite formation [11]. Detection methods include offline tools like Feritscope and online options like the 3MA-II sensor as addressed in [8] and [12]. The potential for α'-martensite varies with chemical composition, emphasizing the need for property-control.

## Grading Strategies

The novel grading strategies aim for 1D- and 2D-graded structures with locally adjusted α'-martensite content useful for functional or sensory purposes in high-performance components.

### 1D-Grading Strategies:

These circumferential gradings (see Fig. 1) can be performed isothermal only using mechanical actuators or thermomechanical by including thermal actuators. Isothermal strategies create 1D-Gradings through deformation, controlled by process parameters like feed rate *f* and infeed *r*. Thermomechanical strategies, as shown in [9], use a cryogenic cooling system to increase α'-martensite locally or an induction heating system to suppress it. The thermal actuators locally temper the tube, creating a ring of either cool or hot temperature during the process (Fig. 5).

<figure><img src="image_1319.png" /><figcaption>Fig. 5. Thermomechanical strategy for 1D-Grading</figcaption></figure>

### 2D-Grading Strategies:

For these annular gradings (Fig. 1) isothermal or thermomechanical strategies are possible. Isothermal 2D-Gradings, using an absolute value encoder, involve alternating the radial
a robust counter-holder designed to support the mandrel and an absolute value encoder, the machine can perform angle-dependent operations within the process. The thermal heating actuator consists of a custom-developed inductor that conforms to the shape of the semi-finished tube and can heat a local angular area. The automated cryogenic cooling system, detailed in [9] and illustrated in Fig. 4, serves as a thermal actuator for localized cooling. It enables computer-assisted and reproducible cooling in both axial and/or angular directions. The cryogenic nozzle focuses a -196 °C stream of liquid nitrogen, simultaneously averting the Leidenfrost phenomenon [10].

<figure><img src="image_1322.png" /><figcaption>Fig. 4. Automated cryogenic cooling system</figcaption></figure>

The material for the semi-finished tubes is AISI 304L (X2CrNi18-9), a TRIP steel with strain- and/or temperature-induced α'-martensite formation [11]. Detection methods include offline tools like Feritscope and online options like the 3MA-II sensor as addressed in [8] and [12]. The potential for α'-martensite varies with chemical composition, emphasizing the need for property-control.

## Grading Strategies

The novel grading strategies aim for 1D- and 2D-graded structures with locally adjusted α'-martensite content useful for functional or sensory purposes in high-performance components.

### 1D-Grading Strategies:

These circumferential gradings (see Fig. 1) can be performed isothermal only using mechanical actuators or thermomechanical by including thermal actuators. Isothermal strategies create 1D-Gradings through deformation, controlled by process parameters like feed rate *f* and infeed *r*. Thermomechanical strategies, as shown in [9], use a cryogenic cooling system to increase α'-martensite locally or an induction heating system to suppress it. The thermal actuators locally temper the tube, creating a ring of either cool or hot temperature during the process (Fig. 5).

<figure><img src="image_1323.png" /><figcaption>Fig. 5. Thermomechanical strategy for 1D-Grading</figcaption></figure>

### 2D-Grading Strategies:

For these annular gradings (Fig. 1) isothermal or thermomechanical strategies are possible. Isothermal 2D-Gradings, using an absolute value encoder, involve alternating the radial
positioning of the roller tool to create a visible 2D-Grading on the tube surface (Fig. 6 a) penetration and b) exit process) with a defined grading angle, such as 90° (Stage 1).

<figure><img src="image_1320.png" /><figcaption>Fig. 6. Mechanical actuator strategy for 2D-Grading with a) penetration and b) exit process</figcaption></figure>

After the initial stage (Stage 1), two strategies can render the 2D-Grading invisible. The first (Stage 2 A) involves turning until the 2D-Grading surface is reached, while the second (Stage 2 B) employs multiple circumferential passes. In contrast, the thermomechanical strategy achieves invisibility in a single stage, using thermal actuators to create an angular temperature gradient. Combining mechanical and thermomechanical strategies is feasible, exploring potential synergies. Liquid nitrogen could enhance α'-martensite formation during 2D-Deformation, while induction heating in the second stage could reduce α'-martensite formation, preventing local resolution loss.

## Results and Discussion

### Thermomechanical 1D-Grading:

Cryogenic cooling and induction heating (Fig. 5) were employed for 1D-Grading. Cooling/heating the tube surface to approx. -40 °C and 100 °C while forming. Parameters included a 2 mm infeed, 0.1 mm/s feed rate and 30 rpm rotational speed *n*. Both tubes underwent analysis for α'-martensite content and wall thickness. Tempering influenced α'-martensite content without impacting wall thickness. Both exhibited an average 0.68 mm wall thickness reduction over the axial deformation length. Fig. 7 compares α'-martensite distribution, highlighting the differences between cryogenic cooling (Fig. 7 a)) and induction heating (Fig. 7 b)).

<figure><img src="image_1321.png" /><figcaption>Fig. 7. Thermomechanical 1D-Grading: Distribution of α'-martensite for a) cryogenic cooling and b) induction heating with *r* = 2 mm, *f* = 0.1 mm/s, *n* = 30 rpm and *v* = *f*/*n* = 0.2 mm/rev</figcaption></figure>

Non-tempered areas contained 40% α'-martensite, increased to 80% with cryogenic cooling, and reduced to 1% with induction heating. Tempering of 20 mm in both cases showed thermal actuators achieving a 40% difference in α'-martensite with consistent wall thickness reduction.

### Isothermal 2D-Grading:
positioning of the roller tool to create a visible 2D-Grading on the tube surface (Fig. 6 a) penetration and b) exit process) with a defined grading angle, such as 90° (Stage 1).

<figure><img src="image_1324.png" /><figcaption>Fig. 6. Mechanical actuator strategy for 2D-Grading with a) penetration and b) exit process</figcaption></figure>

After the initial stage (Stage 1), two strategies can render the 2D-Grading invisible. The first (Stage 2 A) involves turning until the 2D-Grading surface is reached, while the second (Stage 2 B) employs multiple circumferential passes. In contrast, the thermomechanical strategy achieves invisibility in a single stage, using thermal actuators to create an angular temperature gradient. Combining mechanical and thermomechanical strategies is feasible, exploring potential synergies. Liquid nitrogen could enhance α'-martensite formation during 2D-Deformation, while induction heating in the second stage could reduce α'-martensite formation, preventing local resolution loss.

## Results and Discussion

### Thermomechanical 1D-Grading:

Cryogenic cooling and induction heating (Fig. 5) were employed for 1D-Grading. Cooling/heating the tube surface to approx. -40 °C and 100 °C while forming. Parameters included a 2 mm infeed, 0.1 mm/s feed rate and 30 rpm rotational speed *n*. Both tubes underwent analysis for α'-martensite content and wall thickness. Tempering influenced α'-martensite content without impacting wall thickness. Both exhibited an average 0.68 mm wall thickness reduction over the axial deformation length. Fig. 7 compares α'-martensite distribution, highlighting the differences between cryogenic cooling (Fig. 7 a)) and induction heating (Fig. 7 b)).

<figure><img src="image_1325.png" /><figcaption>Fig. 7. Thermomechanical 1D-Grading: Distribution of α'-martensite for a) cryogenic cooling and b) induction heating with $r = 2$ mm, $f = 0.1$ mm/s, $n = 30$ rpm and $v = f/n = 0.2$ mm/rev</figcaption></figure>

Non-tempered areas contained 40% α'-martensite, increased to 80% with cryogenic cooling, and reduced to 1% with induction heating. Tempering of 20 mm in both cases showed thermal actuators achieving a 40% difference in α'-martensite with consistent wall thickness reduction.

### Isothermal 2D-Grading:
In Stage 1 a visible 2D-Grading of 90° was performed using 2 mm infeed $r$, axial feed rate $f$ (X-direction Fig. 3) of 0.1 mm/s, radial feed rate $f_r$ (Y-direction) of 10 mm/s and rotational speed $n$ of 5 rpm (Fig. 8 a)). To enhance surface quality, the axial feed rate was reduced (Fig. 8 b)). The shape of the entry (Fig. 8 c)) and exit region (Fig. 8 d)) result from the geometry of the roller tool and the grading angle of 124.62° (Fig. 8 b)) exceeds the desired 90°, attributed to the exit process.

<figure><img src="image_1322.png" /><figcaption>Fig. 8. 2D-Deformation: Using a) suboptimal, b) optimized parameters; c) entry, d) exit region</figcaption></figure>

2D-Deformation measurements included $\alpha$'-martensite and wall thickness profiles in axial (X-direction) and angular directions (Fig. 9). At the center (30 mm X-position, 180°), both wall thickness reduction (approx. 0.5 mm) and $\alpha$'-martensite content (approx. 48%) peak (Fig. 9 a)-d)).

<figure><img src="image_1323.png" /><figcaption>Fig. 9. 2D-Deformation: $\alpha$'-martensite distribution a) axial, c) angular; wall thickness profile b) axial, d) angular using $r = 2$ mm, $f = 0.017$ mm/s, $f_r = 10$ mm/s, $n = 5$ rpm and $v = 0.2$ mm/rev</figcaption></figure>

After the 2D-Deformation in Stage 1, the tube is turned in Stage 2 A (Fig. 10 a)-b)). Post-turning, $\alpha$'-martensite measurements at various angles (Fig. 10 c)-d)) reveal approx. 0.40% in non-graded areas and 41% in 2D-graded areas. The 2D-Grading is successful and entirely invisible.
In Stage 1 a visible 2D-Grading of 90° was performed using 2 mm infeed $r$, axial feed rate $f$ (X-direction Fig. 3) of 0.1 mm/s, radial feed rate $f_r$ (Y-direction) of 10 mm/s and rotational speed $n$ of 5 rpm (Fig. 8 a)). To enhance surface quality, the axial feed rate was reduced (Fig. 8 b)). The shape of the entry (Fig. 8 c)) and exit region (Fig. 8 d)) result from the geometry of the roller tool and the grading angle of 124.62° (Fig. 8 b)) exceeds the desired 90°, attributed to the exit process.

<figure><img src="image_1326.png" /><figcaption>Fig. 8. 2D-Deformation: Using a) suboptimal, b) optimized parameters; c) entry, d) exit region</figcaption></figure>

2D-Deformation measurements included $\alpha$'-martensite and wall thickness profiles in axial (X-direction) and angular directions (Fig. 9). At the center (30 mm X-position, 180°), both wall thickness reduction (approx. 0.5 mm) and $\alpha$'-martensite content (approx. 48%) peak (Fig. 9 a)-d)).

<figure><img src="image_1327.png" /><figcaption>Fig. 9. 2D-Deformation: $\alpha$'-martensite distribution a) axial, c) angular; wall thickness profile b) axial, d) angular using $r = 2$ mm, $f = 0.017$ mm/s, $f_r = 10$ mm/s, $n = 5$ rpm and $v = 0.2$ mm/rev</figcaption></figure>

After the 2D-Deformation in Stage 1, the tube is turned in Stage 2 A (Fig. 10 a)-b)). Post-turning, $\alpha$'-martensite measurements at various angles (Fig. 10 c)-d)) reveal approx. 0.40% in non-graded areas and 41% in 2D-graded areas. The 2D-Grading is successful and entirely invisible.
<figure><img src="image_1324.png" /><figcaption>Fig. 10. 2D-Grading: a) 2D-Deformation (Stage 1), b) after turning (Stage 2 A)</figcaption></figure>

An alternative to Stage 2 A is Stage 2 B, using multiple flow forming passes to make the 2D-Deformation invisible (Fig. 11). Fig. 11 a) shows the initial 2D-Deformation, and Fig. 11 b) illustrates the tubes appearance with an increasing number of passes (1-4). Results indicate that an initial 2D-Grading with a 2 mm infeed depth (Stage 1) requires four passes with a 2 mm infeed and a feed speed v of 0.2 mm/rev until becoming invisible. Unlike Stage 2 A, Stage 2 B has no material loss and results in additional tube hardening, providing application-specific advantages.

<figure><img src="image_1325.png" /><figcaption>Fig. 11. 2D-Grading: a) 2D-Deformation (Stage 1), b) after multiple consecutive passes 1-4 (Stage 2 B) to make the 2D-Deformation invisible</figcaption></figure>

Fig. 12 depicts α'-martensite distribution and wall thickness profiles in axial and angular directions. The center remains at 30 mm (X-position) and 180° (angle). In Stage 2 B, aiming for 2D-Deformation invisibility, local α'-martensite resolution is compromised. As passes increase starting at approx. 45% α'-martensite content and 0.6 mm wall thickness reduction, curves smooth until similar values at approx. 95% α'-martensite and 2 mm wall thickness reduction emerge.
<figure><img src="image_1328.png" /><figcaption>Fig. 10. 2D-Grading: a) 2D-Deformation (Stage 1), b) after turning (Stage 2 A)</figcaption></figure>

An alternative to Stage 2 A is Stage 2 B, using multiple flow forming passes to make the 2D-Deformation invisible (Fig. 11). Fig. 11 a) shows the initial 2D-Deformation, and Fig. 11 b) illustrates the tubes appearance with an increasing number of passes (1-4). Results indicate that an initial 2D-Grading with a 2 mm infeed depth (Stage 1) requires four passes with a 2 mm infeed and a feed speed $v$ of 0.2 mm/rev until becoming invisible. Unlike Stage 2 A, Stage 2 B has no material loss and results in additional tube hardening, providing application-specific advantages.

<figure><img src="image_1329.png" /><figcaption>Fig. 11. 2D-Grading: a) 2D-Deformation (Stage 1), b) after multiple consecutive passes 1-4 (Stage 2 B) to make the 2D-Deformation invisible</figcaption></figure>

Fig. 12 depicts α'-martensite distribution and wall thickness profiles in axial and angular directions. The center remains at 30 mm (X-position) and 180° (angle). In Stage 2 B, aiming for 2D-Deformation invisibility, local α'-martensite resolution is compromised. As passes increase starting at approx. 45% α'-martensite content and 0.6 mm wall thickness reduction, curves smooth until similar values at approx. 95% α'-martensite and 2 mm wall thickness reduction emerge.
<figure><img src="image_1326.png" /><figcaption>Fig. 12. 2D-Grading: α'-martensite distribution a) axial, c) angular; wall thickness profile b) axial, d) angular for 2D-Deformation (Stage 1) followed by multiple passes (Stage 2 B)</figcaption></figure>

Fig. 13 a) shows the tube produced using the thermomechanical 2D-Grading strategy, employing cryogenic cooling and induction heating systems to create a temperature gradient during tube forming. Measurements in Fig. 13 b) and c) reveal α'-martensite content ranging from about 83% (cooled area) to 2% (heated area) angularly, ensuring uniform wall thickness.

<figure><img src="image_1327.png" /><figcaption>Fig. 13. Thermomechanical 2D-Grading: a) produced tube; b)-c) angular measurement points</figcaption></figure>
<figure><img src="image_1330.png" /><figcaption>Fig. 12. 2D-Grading: α'-martensite distribution a) axial, c) angular; wall thickness profile b) axial, d) angular for 2D-Deformation (Stage 1) followed by multiple passes (Stage 2 B)</figcaption></figure>

Fig. 13 a) shows the tube produced using the thermomechanical 2D-Grading strategy, employing cryogenic cooling and induction heating systems to create a temperature gradient during tube forming. Measurements in Fig. 13 b) and c) reveal α'-martensite content ranging from about 83% (cooled area) to 2% (heated area) angularly, ensuring uniform wall thickness.

<figure><img src="image_1331.png" /><figcaption>Fig. 13. Thermomechanical 2D-Grading: a) produced tube; b)-c) angular measurement points</figcaption></figure>
Cryogenic cooling cools the tube surface to around -40 °C, while induction heating raises it to about 100 °C to suppress α'-martensite formation. Cooling and heating occur at defined angular regions during rotation, with cryogenic cooling targeting a 90° angular position and induction heating focusing on a 270° position (Fig. 14 b)). Flow forming included a 2 mm infeed, a feed rate of 0.1 mm/s, and a rotational speed *n* of 30 rpm. Wall thickness reduction, approx. 0.65 mm, remained unaffected, resulting in a completely invisible 2D-Grading in this single-stage strategy. In Fig. 14 a), α'-martensite content rises from approx. 45% to 74% until it reaches the center of the heated area at X-position 100 mm, then drops to approx. 2% due to inadvertent cooling of adjacent areas. Successful suppression of α'-martensite formation is shown in an axial range of 20 mm. Fig. 14 b) displays the centers of cooled and heated areas, along with approx. 180° angular ranges where α'-martensite content fluctuates due to cooling and heating effects. The size of these ranges is influenced by factors such as cooling/heating duration, liquid nitrogen flow rate, and induction power. Managing local α'-martensite resolution is complex due to heat conduction.

<figure><img src="image_1328.png" /><figcaption>Fig. 14. Thermomechanical 2D-Grading: α'-martensite distribution a) axial and b) angular</figcaption></figure>

Combining the isothermal (Stage 1 and Tage 2 B) and thermomechanical strategies for 2D-Grading offers a solution to address local α'-martensite resolution challenges. The 2D-Deformation takes place (Stage 1) while the area is cooled by the cryogenic cooling system (Fig. 15 a)). In the subsequent stage, the tube exhibiting the visible 2D-Deformation in Fig. 15 b) undergoes multiple passes, heated by the induction heating system, resulting in an invisible 2D-Grading (Fig. 15 c)-d)). Once again, tempering did not affect the wall thickness reduction.

<figure><img src="image_1329.png" /><figcaption>Fig. 15. Combined 2D-Grading strategy: a)-b) cryogenic 2D-Deformation, c)-d) heated passes</figcaption></figure>

Fig. 16 a) and c) show an increase in α'-martensite content compared to the isothermal strategy (Fig. 16 b) and d)). An improvement of the local resolution of α'-martensite content was also visible, without sacrificing resolution through multiple flow forming passes. This approach offers enhanced control over angular α'-martensite distribution, as the resolution is no longer solely dependent on thermal conduction.
Cryogenic cooling cools the tube surface to around -40 °C, while induction heating raises it to about 100 °C to suppress α'-martensite formation. Cooling and heating occur at defined angular regions during rotation, with cryogenic cooling targeting a 90° angular position and induction heating focusing on a 270° position (Fig. 14 b)). Flow forming included a 2 mm infeed, a feed rate of 0.1 mm/s, and a rotational speed *n* of 30 rpm. Wall thickness reduction, approx. 0.65 mm, remained unaffected, resulting in a completely invisible 2D-Grading in this single-stage strategy. In Fig. 14 a), α'-martensite content rises from approx. 45% to 74% until it reaches the center of the heated area at X-position 100 mm, then drops to approx. 2% due to inadvertent cooling of adjacent areas. Successful suppression of α'-martensite formation is shown in an axial range of 20 mm. Fig. 14 b) displays the centers of cooled and heated areas, along with approx. 180° angular ranges where α'-martensite content fluctuates due to cooling and heating effects. The size of these ranges is influenced by factors such as cooling/heating duration, liquid nitrogen flow rate, and induction power. Managing local α'-martensite resolution is complex due to heat conduction.

<figure><img src="image_1332.png" /><figcaption>Fig. 14. Thermomechanical 2D-Grading: α'-martensite distribution a) axial and b) angular</figcaption></figure>

Combining the isothermal (Stage 1 and Tage 2 B) and thermomechanical strategies for 2D-Grading offers a solution to address local α'-martensite resolution challenges. The 2D-Deformation takes place (Stage 1) while the area is cooled by the cryogenic cooling system (Fig. 15 a)). In the subsequent stage, the tube exhibiting the visible 2D-Deformation in Fig. 15 b) undergoes multiple passes, heated by the induction heating system, resulting in an invisible 2D-Grading (Fig. 15 c)-d)). Once again, tempering did not affect the wall thickness reduction.

<figure><img src="image_1333.png" /><figcaption>Fig. 15. Combined 2D-Grading strategy: a)-b) cryogenic 2D-Deformation, c)-d) heated passes</figcaption></figure>

Fig. 16 a) and c) show an increase in α'-martensite content compared to the isothermal strategy (Fig. 16 b) and d)). An improvement of the local resolution of α'-martensite content was also visible, without sacrificing resolution through multiple flow forming passes. This approach offers enhanced control over angular α'-martensite distribution, as the resolution is no longer solely dependent on thermal conduction.
<figure><img src="image_1330.png" /></figure>

<figure><img src="image_1331.png" /></figure>

<figure><img src="image_1332.png" /></figure>

<figure><img src="image_1333.png" /><figcaption>Fig. 16. Comparing α'-martensite distribution a)-b) axial, c)-d) angular with a) and c) showing the combined 2D-Grading strategy, while b) and d) display the isothermal 2D-Grading strategy</figcaption></figure>

## Conclusions and Outlook

In conclusion, exploring functionally grade flow forming components with both 1D- (axial) and 2D- (axial and angular) Gradings has provided valuable insights. Various strategies, including isothermal, thermomechanical, and combined approaches, were examined to influence local α'-martensite content and wall thickness profiles. Cryogenic cooling effectively increased α'-martensite content locally, while induction heating efficiently suppressed it. It was shown that these thermal strategies could be applied dynamically and combined for simultaneous cooling and heating, maximizing temperature gradients in locally displaced areas (e.g., to create a ring of hot and cool temperature). Mechanical strategies offer precise adjustment of grading range but may require two-stage designs for invisible 2D-Gradings. Combining isothermal and thermomechanical strategies enhances α'-martensite content significantly while optimizing and ensuring local resolution. Future research aims to advance to 3D-Gradings, influencing α'-martensite content in radial (resp. thickness) direction. These ongoing efforts stand as a testament to the commitment to advancing the understanding and application of functionally graded components in the realm of flow forming.

## Acknowledgements

The authors would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for their support of the depicted research within the priority program SPP 2183 "Property controlled deformation processes", through project no. 424335026 "Property control during spinning of metastable austenites".
<figure><img src="image_1334.png" /></figure>

<figure><img src="image_1335.png" /></figure>

<figure><img src="image_1336.png" /></figure>

<figure><img src="image_1337.png" /><figcaption>Fig. 16. Comparing α'-martensite distribution a)-b) axial, c)-d) angular with a) and c) showing the combined 2D-Grading strategy, while b) and d) display the isothermal 2D-Grading strategy</figcaption></figure>

## Conclusions and Outlook

In conclusion, exploring functionally grade flow forming components with both 1D- (axial) and 2D- (axial and angular) Gradings has provided valuable insights. Various strategies, including isothermal, thermomechanical, and combined approaches, were examined to influence local α'-martensite content and wall thickness profiles. Cryogenic cooling effectively increased α'-martensite content locally, while induction heating efficiently suppressed it. It was shown that these thermal strategies could be applied dynamically and combined for simultaneous cooling and heating, maximizing temperature gradients in locally displaced areas (e.g., to create a ring of hot and cool temperature). Mechanical strategies offer precise adjustment of grading range but may require two-stage designs for invisible 2D-Gradings. Combining isothermal and thermomechanical strategies enhances α'-martensite content significantly while optimizing and ensuring local resolution. Future research aims to advance to 3D-Gradings, influencing α'-martensite content in radial (resp. thickness) direction. These ongoing efforts stand as a testament to the commitment to advancing the understanding and application of functionally graded components in the realm of flow forming.

## Acknowledgements

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

[1] M. Haridas, G. Gopal, A. Ramesh, R. K. Katta, "Modelling and simulation of single and multi-pass flow forming to investigate the influence of process parameters on part accuracy," *IJMR*, vol. 11, no. 3, 2016, Art. no. 79473. https://doi.org/10.1504/IJMR.2016.079473

[2] M. S. Mohebbi, A. Akbarzadeh, "Experimental study and FEM analysis of redundant strains in flow forming of tubes," *Journal of Materials Processing Technology*, vol. 210, no. 2, pp. 389-395, 2010. https://doi.org/10.1016/j.jmatprotec.2009.09.028

[3] D. Y. Yang et al., "Flexibility in metal forming," *CIRP Annals*, vol. 67, no. 2, pp. 743-765, 2018. https://doi.org/10.1016/j.cirp.2018.05.004

[4] M. Bambach, T. Meurer, W. Homberg, S. Duncan, "Editorial to special issue "Property-controlled forming processes"," *Advances in Industrial and Manufacturing Engineering*, vol. 4, p. 100068, 2022. https://doi.org/10.1016/j.aime.2022.100068

[5] M. Runge, *Spinning and Flow forming: spinning and flow forming technology, product design, equipment, control systems*. Landsberg/Lech: Moderne Industrie, 1994.

[6] M. Sivanandini, S. S. Dhami, and B. S. Pabla, "Flow Forming Of Tubes-A Review," *International Journal of Scientific & Engineering Research*, no. 3, 2012, Art. no. 5. [Online]. Available: https://www.ijser.org/researchpaper/Flow-Forming-Of-Tubes-A-Review.pdf

[7] J. Savoie and M. Bissinger, "Case Studies and Applications of Flowforming to Aircraft Engine Component Manufacturing," *KEM*, vol. 344, pp. 443-450, 2007. https://doi.org/10.4028/www.scientific.net/KEM.344.443

[8] B. Arian, *Produktkennzeichnung durch lokal definierte Einstellung von ferromagnetischen Eigenschaften beim Drückwalzen von metastabilen Stahlwerkstoffen: Ideen Form geben: 36. ASK Umformtechnik : 26.-27. Oktober 2022, Eurogress Aachen : Tagungsband*, 1st ed. Aachen: Verlagshaus Mainz GmbH, 2022.

[9] B. Arian and Materials Research Proceedings (Materials Research Forum LLC), Eds., *Cryogenic reverse flow forming of AISI 304L: Material Forming*, 2023, https://doi.org/10.21741/9781644902479-219

[10] Y. Guo et al., "Delayed Leidenfrost Effect of a Cutting Droplet on a Microgrooved Tool Surface," *Langmuir: the ACS journal of surfaces and colloids*, early access. https://doi.org/10.1021/acs.langmuir.3c00592.

[11] M. Jambor, T. Vojtek, P. Pokorný, and M. Šmíd, "Effect of Solution Annealing on Fatigue Crack Propagation in the AISI 304L TRIP Steel," *Materials (Basel, Switzerland)*, early access. https://doi.org/10.3390/ma14061331.

[12] M. Riepold, B. Arian, J. Rozo Vasquez, W. Homberg, F. Walther, and A. Trächtler, "Model approaches for closed-loop property control for flow forming," *Advances in Industrial and Manufacturing Engineering*, vol. 3, p. 100057, 2021. https://doi.org/10.1016/j.aime.2021.100057
## References

[1] M. Haridas, G. Gopal, A. Ramesh, R. K. Katta, "Modelling and simulation of single and multi-pass flow forming to investigate the influence of process parameters on part accuracy," *IJMR*, vol. 11, no. 3, 2016, Art. no. 79473. https://doi.org/10.1504/IJMR.2016.079473

[2] M. S. Mohebbi, A. Akbarzadeh, "Experimental study and FEM analysis of redundant strains in flow forming of tubes," *Journal of Materials Processing Technology*, vol. 210, no. 2, pp. 389-395, 2010. https://doi.org/10.1016/j.jmatprotec.2009.09.028

[3] D. Y. Yang et al., "Flexibility in metal forming," *CIRP Annals*, vol. 67, no. 2, pp. 743-765, 2018. https://doi.org/10.1016/j.cirp.2018.05.004

[4] M. Bambach, T. Meurer, W. Homberg, S. Duncan, "Editorial to special issue "Property-controlled forming processes"," *Advances in Industrial and Manufacturing Engineering*, vol. 4, p. 100068, 2022. https://doi.org/10.1016/j.aime.2022.100068

[5] M. Runge, *Spinning and Flow forming: spinning and flow forming technology, product design, equipment, control systems*. Landsberg/Lech: Moderne Industrie, 1994.

[6] M. Sivanandini, S. S. Dhami, and B. S. Pabla, "Flow Forming Of Tubes-A Review," *International Journal of Scientific & Engineering Research*, no. 3, 2012, Art. no. 5. [Online]. Available: https://www.ijser.org/researchpaper/Flow-Forming-Of-Tubes-A-Review.pdf

[7] J. Savoie and M. Bissinger, "Case Studies and Applications of Flowforming to Aircraft Engine Component Manufacturing," *KEM*, vol. 344, pp. 443-450, 2007. https://doi.org/10.4028/www.scientific.net/KEM.344.443

[8] B. Arian, *Produktkennzeichnung durch lokal definierte Einstellung von ferromagnetischen Eigenschaften beim Drückwalzen von metastabilen Stahlwerkstoffen: Ideen Form geben: 36. ASK Umformtechnik : 26.-27. Oktober 2022, Eurogress Aachen : Tagungsband*, 1st ed. Aachen: Verlagshaus Mainz GmbH, 2022.

[9] B. Arian and Materials Research Proceedings (Materials Research Forum LLC), Eds., *Cryogenic reverse flow forming of AISI 304L: Material Forming*, 2023, https://doi.org/10.21741/9781644902479-219

[10] Y. Guo et al., "Delayed Leidenfrost Effect of a Cutting Droplet on a Microgrooved Tool Surface," *Langmuir: the ACS journal of surfaces and colloids*, early access. https://doi.org/10.1021/acs.langmuir.3c00592.

[11] M. Jambor, T. Vojtek, P. Pokorný, and M. Šmíd, "Effect of Solution Annealing on Fatigue Crack Propagation in the AISI 304L TRIP Steel," *Materials (Basel, Switzerland)*, early access. https://doi.org/10.3390/ma14061331.

[12] M. Riepold, B. Arian, J. Rozo Vasquez, W. Homberg, F. Walther, and A. Trächtler, "Model approaches for closed-loop property control for flow forming," *Advances in Industrial and Manufacturing Engineering*, vol. 3, p. 100057, 2021. https://doi.org/10.1016/j.aime.2021.100057
# Effects of machine hammer peening on case-hardened 16MnCr5 gear analogue shafts

DADGAR Mohammad<fnref n="1" />, a*, GRESCHERT René<fnref n="2" />, b, MÜLLER Martina<fnref n="1" />, c,
SKLENAK Sebastian<fnref n="2" />, d, HERRIG Tim<fnref n="1" />, e, BRIMMERS Jens<fnref n="2" />, f and
BERGS Thomas<fnref n="1" />, 3, g

**Keywords:** Machine Hammer Peening, Surface Structuring, Strain Hardening, Gear

**Abstract.** Gears are integral to many mechanical systems, including industrial machinery and automotive transmissions. Subject to significant mechanical and tribological stresses from rotational forces and torque transmission, gears often face challenges like surface wear and fatigue. Enhancing the durability and performance of gears is therefore vital, and this is where manufacturing processes such as Machine Hammer Peening (MHP) come into play. As an incremental forming process, MHP has the potential to substantially increase the mechanical and tribological load capacities of gears. The objective of this study is to assess how MHP can enhance the surface characteristics of case-hardened 16MnCr5 (1.7131) gear analogue shafts, focusing on the reduction of surface roughness and the increase in surface hardness. Such improvements contribute to improved wear resistance, which can significantly extend the lifespan of the gears, ensuring more reliable performance in demanding operational conditions.

**Introduction**

Machine Hammer Peening (MHP) is an advanced incremental material forming process, primary employed for the mechanical surface treatment of workpieces [1]. In MHP, a semi-spherical carbide hammer head delivers repetitive strikes to the workpiece, with high-frequency oscillations of a plunger driven by an actuator [2]. Such actions cause plastic deformation, modifying the microstructure of the surface boundary layer and potentially triggering local phase transformations. MHP effectively improves surface characteristics by inducing strain hardening and increasing hardness [3]. A key aspect of MHP is its ability to induce residual compressive stresses within the edge zone [4], which substantially strengthens the mechanical integrity of the material. Additionally, MHP reduces surface roughness, leading to improved frictional behavior of the treated surface. Fig. 1(a) shows a schematic illustration of the MHP tool, detailing key process parameters such as hammer frequency *f*, hammer head diameter *d*, stroke distance *h*, step over distance *s*, and impact angle $\beta_i$. Fig. 1(b) displays the MHP tool as it is mounted on a robot, highlighting the integration of advanced robotics to achieve precise positioning and control during the peening process.

<figure><img src="image_1334.png" /></figure>

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

<footnote n="2">²Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Steinbachstr. 19, 52074 Aachen, Germany</footnote>

<footnote n="3">³Fraunhofer Institute for Production Technology (IPT), Steinbachstr. 17, 52074 Aachen, Germany</footnote>

<footnote>a.m.dadgar@mti.rwth-aachen.de, b.r.greschert@wzl.rwth-aachen.de,</footnote>

<footnote>c.m.mueller@mti.rwth-aachen.de, d.s.sklenak@wzl.rwth-aachen.de,</footnote>

<footnote>e.t.herrig@mti.rwth-aachen.de, f.j.brimmers@wzl.rwth-aachen.de, g.t.bergs@mti.rwth-aachen.de</footnote>
# Effects of machine hammer peening on case-hardened 16MnCr5 gear analogue shafts

DADGAR Mohammad<fnref n="1" />, a*, GRESCHERT René<fnref n="2" />, b, MÜLLER Martina<fnref n="1" />, c,
SKLENAK Sebastian<fnref n="2" />, d, HERRIG Tim<fnref n="1" />, e, BRIMMERS Jens<fnref n="2" />, f and
BERGS Thomas<fnref n="1" />, 3, g

**Keywords:** Machine Hammer Peening, Surface Structuring, Strain Hardening, Gear

**Abstract.** Gears are integral to many mechanical systems, including industrial machinery and automotive transmissions. Subject to significant mechanical and tribological stresses from rotational forces and torque transmission, gears often face challenges like surface wear and fatigue. Enhancing the durability and performance of gears is therefore vital, and this is where manufacturing processes such as Machine Hammer Peening (MHP) come into play. As an incremental forming process, MHP has the potential to substantially increase the mechanical and tribological load capacities of gears. The objective of this study is to assess how MHP can enhance the surface characteristics of case-hardened 16MnCr5 (1.7131) gear analogue shafts, focusing on the reduction of surface roughness and the increase in surface hardness. Such improvements contribute to improved wear resistance, which can significantly extend the lifespan of the gears, ensuring more reliable performance in demanding operational conditions.

**Introduction**

Machine Hammer Peening (MHP) is an advanced incremental material forming process, primary employed for the mechanical surface treatment of workpieces [1]. In MHP, a semi-spherical carbide hammer head delivers repetitive strikes to the workpiece, with high-frequency oscillations of a plunger driven by an actuator [2]. Such actions cause plastic deformation, modifying the microstructure of the surface boundary layer and potentially triggering local phase transformations. MHP effectively improves surface characteristics by inducing strain hardening and increasing hardness [3]. A key aspect of MHP is its ability to induce residual compressive stresses within the edge zone [4], which substantially strengthens the mechanical integrity of the material. Additionally, MHP reduces surface roughness, leading to improved frictional behavior of the treated surface. Fig. 1(a) shows a schematic illustration of the MHP tool, detailing key process parameters such as hammer frequency *f*, hammer head diameter *d*, stroke distance *h*, step over distance *s*, and impact angle $\beta_i$. Fig. 1(b) displays the MHP tool as it is mounted on a robot, highlighting the integration of advanced robotics to achieve precise positioning and control during the peening process.

<figure><img src="image_1338.png" /></figure>

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

<footnote n="2">²Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Steinbachstr. 19, 52074 Aachen, Germany</footnote>

<footnote n="3">³Fraunhofer Institute for Production Technology (IPT), Steinbachstr. 17, 52074 Aachen, Germany</footnote>

<footnote>a.m.dadgar@mti.rwth-aachen.de, b.r.greschert@wzl.rwth-aachen.de,</footnote>

<footnote>c.m.mueller@mti.rwth-aachen.de, d.s.sklenak@wzl.rwth-aachen.de,</footnote>

<footnote>e.t.herrig@mti.rwth-aachen.de, f.j.brimmers@wzl.rwth-aachen.de, g.t.bergs@mti.rwth-aachen.de</footnote>
<figure><img src="image_1335.png" /><figcaption>Fig. 1: (a) Schematic illustration of MHP tool with its key process parameters; (b) MHP system setup mounted on a robot.</figcaption></figure>

As a precise edge zone machining technique, MHP introduces a high level of control in the creation of surfaces with uniform structures and reduced roughness [5]. This level of precision provides a notable advantage over conventional method of shot peening, which may not consistently produce uniform surfaces and often risks increasing surface roughness [1]. Moreover, compared to other surface treatment methods like laser shock peening (LSP), which can introduce unwanted thermal residual tensile stresses and melting edges that may lead to cracking [6], the cold forming process of MHP inherently avoids these detrimental effects. The unique benefits of MHP, alongside the advantages it shares with traditional techniques, make it a valuable process in the maintenance and enhancement of industrial components. This is especially relevant in gear systems, where the consistent surface finish and the prevention of crack initiation are of paramount importance [7].

Gears are vital components within various mechanical systems, facing significant mechanical and tribological stresses. These stresses often lead to surface wear and fatigue, adversely affecting both the durability and operational efficiency of gear systems [8]. Inducing residual compressive stresses in the edge zone is an established technique to reinforce fatigue strength and the durability of these components [9]. Research focused on the fatigue strength of 16MnCr5 materials under different residual stress scenarios revealed that the presence of residual compressive stresses, particularly in surface-near layers where cracks are prone to initiate, substantially extends component service life [10]. These insights affirm the effectiveness of MHP as an effective post-processing technique for case-hardened 16MnCr5 (1.7131) gears. By enhancing their service life and ensuring reliability, MHP proves to be an indispensable method, especially in applications that entail severe operating conditions.

To date, the application of MHP in machining case-hardened gears made of 16MnCr5 has been limited, with only foundational research exploring the relationship between the MHP process parameters and the resultant surface integrity, encompassing roughness, hardness, microstructure, and residual stresses. Building on the crucial insights from the preliminary research [11,12], which identified optimal MHP process parameters, this study delves into the effects of varied MHP strategies on enhancing the lifespan of gear analogue shaft specimens. The research is driven by
<figure><img src="image_1339.png" /><figcaption>Fig. 1: (a) Schematic illustration of MHP tool with its key process parameters; (b) MHP system setup mounted on a robot.</figcaption></figure>

As a precise edge zone machining technique, MHP introduces a high level of control in the creation of surfaces with uniform structures and reduced roughness [5]. This level of precision provides a notable advantage over conventional method of shot peening, which may not consistently produce uniform surfaces and often risks increasing surface roughness [1]. Moreover, compared to other surface treatment methods like laser shock peening (LSP), which can introduce unwanted thermal residual tensile stresses and melting edges that may lead to cracking [6], the cold forming process of MHP inherently avoids these detrimental effects. The unique benefits of MHP, alongside the advantages it shares with traditional techniques, make it a valuable process in the maintenance and enhancement of industrial components. This is especially relevant in gear systems, where the consistent surface finish and the prevention of crack initiation are of paramount importance [7].

Gears are vital components within various mechanical systems, facing significant mechanical and tribological stresses. These stresses often lead to surface wear and fatigue, adversely affecting both the durability and operational efficiency of gear systems [8]. Inducing residual compressive stresses in the edge zone is an established technique to reinforce fatigue strength and the durability of these components [9]. Research focused on the fatigue strength of 16MnCr5 materials under different residual stress scenarios revealed that the presence of residual compressive stresses, particularly in surface-near layers where cracks are prone to initiate, substantially extends component service life [10]. These insights affirm the effectiveness of MHP as an effective post-processing technique for case-hardened 16MnCr5 (1.7131) gears. By enhancing their service life and ensuring reliability, MHP proves to be an indispensable method, especially in applications that entail severe operating conditions.

To date, the application of MHP in machining case-hardened gears made of 16MnCr5 has been limited, with only foundational research exploring the relationship between the MHP process parameters and the resultant surface integrity, encompassing roughness, hardness, microstructure, and residual stresses. Building on the crucial insights from the preliminary research [11,12], which identified optimal MHP process parameters, this study delves into the effects of varied MHP strategies on enhancing the lifespan of gear analogue shaft specimens. The research is driven by