Relating wear stages in sheet metal forming based on short- and long-term force signal variations

Phase 1 or the elastic phase begins with the first occurrence of a cutting force \(F_S\). The counter punch force \(F_G\), which is (in theory) kept constant throughout the cutting process, has been present since the beginning of the cutting process and is countered in phase 1 by the continuously increasing cutting force \(F_S\). After the cutting force \(F_S\) has exceeded the counter punch force \(F_G\), the cutting punch and counter punch begin to move downwards, causing elastic deformation of the sheet metal material. Phase 1 ends when the maximum elastic deformation of the sheet material or its shear flow limit is exceeded. Phase 2, also known as the cutting phase, begins with the onset of plastic flow of the sheet material. It is characterized by the penetration of the cutting punch as a result of a further increase in the cutting force \(F_S\). Two opposing mechanisms act on the cutting force during this phase. As the forming process continues, sliding dislocations accumulate at obstacles in the crystal lattice of the sheet material and lead to work hardening in the cutting gap (Klocke, 2014). As a result, the deformation resistance and the required cutting force increase. As a second effect, the force-transmitting residual material cross section in the cutting area of the sheet material decreases continuously due to the progressive cutting process until the material is completely penetrated (Schmidt et al., 2006). Until the maximum cutting force \(F_{S,\max }\) is reached, the effect of work hardening is dominant. After the maximum cutting force \(F_{S,\max }\) is reached, the decrease of the remaining cross section is predominant and the cutting force decreases rapidly. Phase 2 is finished when the maximum plastic deformation of the sheet material is exceeded and the material breaks. The plateau within the cutting force curve shown in Fig. 1 represents the residual cutting force \(F_S\) required to compensate for the counter punch force \(F_G\) after phase 2 has ended. Phase 3, the fracture phase, and phase 4, the oscillating phase, are characteristic for the shearing process, but do not occur in the idealized cutting force-time curve of the fine-blanking process (Schmidt et al., 2006).

The wear of tool components does not proceed linearly with time, but follows a non-linear pattern. It starts in the early run-in phase with an unstable wear rate, continues in the middle phase with a stable low wear rate and ends in the third phase, which is characterized by accelerated wear leading to the failure of the punch (Behrens et al., 2016) (see Fig. 2). Initially, the surfaces of the punch and the workpiece are in contact. When a sliding motion begins, an enormous stress is applied to the very small area of the interfering surface asperities, causing them to fail and the abrasive wear phase begins. This abrasive wear phase is the first phase, the running-in phase, where the abrasion increases rapidly and deteriorates the surface of the punch very quickly. Under heat and pressure, these abrasive particles stick to the surface and lead to the more stable phase of adhesive wear. The force and the stresses during fine-blanking increase due to the strong adhesion and the altered tribology of the punch, resulting in an accelerated wear rate in the third stage. The third phase is usually accompanied by fatigue wear and can lead to cracking and breakage of the punch (Lind et al., 2010).

The analysis of the stamping system requires an industry-like setup. Thus, a commercially available fine-blanking production line Feintool XFT 2500 Speed is used for this research. The fine-blanking process typically begins with a 1–20 mm thick and 50–250 mm wide metal coil being unrolled by a decoiler. To relieve the residual stresses, the metal sheet is fed into a leveler (Klocke, 2014). A lubricant film is subsequently applied on the metal sheet, which is followed by the actual blanking process. The press can be configured for up to 140 strokes/min.

In this study, all experiments were performed with the same speed of 50 strokes/min and lubrication setup, while the used lubricant changed throughout the experimental samples. X5CrNi18-10 is used as semi-finished product. In total, almost 12,000 strokes have been acquired with a sensor sample frequency of 10 kHz within individual experiments, see Table 1 for details and (Niemietz, 2022) for the raw data.

Figure 3 illustrates the steps of data processing. For preprocessing and artifact removal, drift and tilt correction is performed, assuming that the force should always be set to 0 at the beginning as well as at the end (drift correction) and that no increase in force should be visible when the tool is open (tilt correction), see Fig. 3.

To include domain knowledge in the feature extraction process, the signal is divided into logical segments based on the different phases of the forming process (see Fig. 3). The clamping (C) segment is characterized by the first peak and represents the time during which the sheet is clamped between the tool components. The blanking (B) segment is identified by the global maximum and refers to the actual blanking process. Finally, the segments pre-stripping (P) (minor vibrations that occur only to a limited extent during fine-blanking) and stripping (S) represent the process of stripping off the sheet from the punch and are characterized by the global minimum of the signal.

Features are extracted from the entire signal as well as from the individual segments using the Python library TSFEL (Barandas et al., 2020). An overview can be found in Table 2. In addition, six manually selected features that are easy for humans to interpret and reasonable from a domain perspective are examined. Namely, the maximum \(M^+\), the minimum \(M^-\), the mean M, and the index t of the total signal as well as the area under the curve of the blank and stripping segments \(I^b\) and \(I^e\), respectively, are selected (see Fig. 4).

For each test, the die components are examined at four characteristic edges (see Fig. 5) after approximately 1000, 2000, and 3000 strokes using SEM images at \(\times \) 100 magnification. Standard image processing methods are used to identify the damaged punch surface. Figure 6 shows the basic steps to isolate the coating-free area from the rest of the image. The first step is to increase the contrast of the SEM images and blur the images using a simple median blur method. Then, worn areas are detected by setting a global threshold for the gray level to classify each pixel as either worn or not worn. Due to geometric differences in the worn areas, some pixels are still not classified correctly. This is solved with a contour detection algorithm, and the detected area is filled in white. The relative amount of pixels in each image is calculated and set as a relative wear estimate in the last step. All image processing steps are performed using the Python image processing library OpenCV (Bradski, 2000). To obtain a wear approximation for each stroke executed, the values of the calculated wear estimate are linearly interpolated.

AEs are a type of artificial neural networks (ANN) that are used for dimension reduction and denoising among various other applications. They consist of a (commonly) nonlinear transformation to a low-dimensional representation space (encoding) and a back- transformation to the space of the data set (decoding). AEs learn appropriate low-dimensional representations.

Here, an AE is designed with three fully connected layers with fifteen, two and fifteen units using the Python Keras package. The hidden layer with two units results in the two-dimensional representation for each input time series. The ReLU activation function is used for the hidden layers and hyperbolic tangent (tanh) for the output layer of the decoder. The training of the AE is done through the optimizer adam by minimizing the mean squared error loss over 300 episodes with a batch-size of 50 and the input is the cleaned force raw data. In contrast to the PCA approach mentioned above, this method uses the raw sensor signal as input instead of a feature set to take advantage of the AEs’ ability to learn generic features themselves. Because tanh takes values between − 1 and 1, all signal values are scaled accordingly.

The application of dimension reduction techniques based either on feature sets (PCA, UMAP) or raw force data (AE) results in a multivariate sequence that contains much of the variation in the original data set. Next, the correlation between structural properties of the subspaces with the wear increase of the punch is computed to evaluate the suitability of each approach to estimate the wear state. In this study, four different estimators are derived, each of which resembles specific structural properties of the computed subspaces. All of the estimators are computed separately for each interval of tool-inspections listed in Table 1 and concatenated afterwards, while the transition between these distances is accounted for. The complete methodology is visualized in Fig. 7.

For experiments \(E_1\) and \(E_3\), irregularities have been recorded during the experiment execution. While during the first 700 strokes of \(E_1\) a lubrication error was recorded, a sequence of stroke data of about 1000 strokes are missing for \(E_3\). Therefore, in the following result evaluation, the performance of both experiments are considered with these obstacles in mind.

First, the Pearson correlation coefficients are computed for the principal components based on the four experiments, four feature sets, and five process segments considered in this study, see Fig. 8.

The first correlation matrix shows the correlations of the first three principal components of each experiment using the combined feature template with the manually selected features. For all experiments, the first component shows the highest correlation with the manually selected features, except for some outliers. Only experiment \(E_1\) shows a lower correlation with a part of the features. The lowest correlation is observed for the total amount of applied stripping force, represented by \(I^e\). Of particular interest are the correlations of the components with t, where t represents the stroke index and thus the sequence. They indicate the change of signals over time and represent the non-stationary behavior of the signal changes. The high correlations of the first component and only low correlations of the second and third components indicate that a large part of the non-stationary behavior of the data is captured in the first principal component. The second correlation matrix displays the average correlations between the principle components based on each feature template with the complete set of manually selected features for all experiments. Again, a common pattern between all experiments except for \(E_1\) can be identified, where most of the correlations are found in the first component, while the correlations of the other components are negligible. The third matrix shows the correlations for the principle components of each segment based on the combined feature template to the manually selected features for each experiment. All segments show similar correlation patterns for each experiment, while again \(E_1\) shows a different pattern, consistently for all considered segments. Additionally, the clamping segment shows a different correlation pattern with the selected features, but also consistent throughout all experiments \(E_1\) to \(E_4\).

The findings indicate that the lubrication error in \(E_1\) significantly skews the pattern observable in all other experiments and it is therefore expected that the wear estimation of \(E_1\) will perform poorly. A low correlation between the amount of applied pulling force during the stripping phase and the principle components derived from features computed from the complete signal indicates that local information is lost for all of the experiments and hints that considering local segments can be beneficial if such information is important. Additionally, since the correlation structure of the feature sets remains considerably stable throughout all considered feature templates, all feature spaces seem to cover the basic information of the manually selected features for each experiment equally. Lastly, the similarity between the correlation structure of the complete signal’s components and the components of the blanking segment is expected, since the complete signal is dominated by the blanking signal’s behavior. The difference in correlation structure of the pre-stripping and stripping segments indicates a general difference in included information within the subspaces.

To compare the explained variance ratio (EVR) of the principle components based on four feature sets for each experiment, Fig. 9 shows the cumulative EVR for the first 60 principle components. For each feature set, differences between each experiment can be observed, while the general pattern between the feature spaces remains the same, indicating that the amount of information in the feature spaces in total is similar after reduction in subspace with PCA.

After evaluating the correlation structure of the signals’ features, common patterns are identified in two-dimensional plots of the first two principal components on a qualitative basis. Figure 10 shows the two-dimensional plots of all data sets using the combined feature template of all models evaluated. Figure 11 shows the two-dimensional plots of only experiment \(E_2\) using PCA and UMAP with four different feature templates, and for all segments considered. Both plots show the significant correlation with time and stroke index. Figure 10 shows that UMAP and PCA have very different properties when the feature size is reduced to a few dimensions. Whereas PCA tends to maintain the global structure of the input feature set, UMAP can detect local differences in the data, often resulting in more and clearly separated clusters. The flat AE used in this study is still able to capture similar information to both algorithms, but tends to learn highly correlated features, especially for \(E_1\) and \(E_2\).

The different feature templates and their effects can be seen in Fig. 11. The spectral feature template shows strong similarities to the combined feature template, for both UMAP and PCA, indicating that most of the information in the spectral set dominates the representation of the combined feature set. Again, UMAP shows better cluster separability, while PCA is more coherent and shows fewer clusters overall. The different segments clamping, blanking, pre-stripping, and stripping show a large influence on the resulting plot. While the plot of the blanking segment bears a strong resemblance to the plot of the full signal, which is intuitive since the original signal is dominated by the blanking segment, the rest of the signal shows a very different structure with a different number of clusters or level of variation. This indicates that the information contained in the local structure of the original signal may contain additional information (see pre-stripping and stripping). It has already been pointed out in Sect. 2 that during the stripping phase, the different wear conditions have a considerable influence on the measured signal. In the first 1000 strokes, a strong deviation from one stroke to the next can be observed, which decreases until the end of the test run, see Fig. 11.

Figure 12 shows the UMAP plots of the last 1500 strokes of \(E_2\) and all templates sets. Here, the correlation with time and the change in local variance are shown by the red and yellow arrows. The plots show that the chosen dimensionality reduction methods result in considerably different low-dimensional representations, showing a consistent correlation with time, sometimes directly related to the amount of variation. In the next chapter, the relationship between the different representations, their variations and the approximated wear increase is examined and related to the dimensionality reduction method used, the feature templates, and the estimator approach.

Figure 13 shows the comparison between the four different feature sets evaluated in this work for all experiments and the estimates derived from UMAP and PCA embeddings. The results show that the performance of the approaches depends strongly on the experiment. Recall that experiment \(E_3\) lacks a critical amount of data from process execution, which seems to lead to poorer performance in contrast to the other experiments. When using the cumulative estimation of stroke variance and cumulative rolling-variance, the effect of varying feature templates is much smaller compared to the distance to reference points. Since the estimator for distance to reference points is more sensitive to global structure changes, while the other two are more sensitive to local structure in the input spaces, it can be concluded that a change in feature template mainly affects the global structure, whereas the local structure remains similar. The feature template Temp leads to slightly better results than the other feature templates in most experiments. For the other feature templates, the wear estimators perform similarly, with some exceptions. In general, the feature template Stat leads to the worst estimates. The feature templates Comb and Spec lead to very similar good estimates in most cases.

Figure 14 shows the performance of the estimators with respect to the local segments in the force signal. A first observation is the similarity of the results for experiments \(E_2\) and \(E_4\) and the significant deviations for the other two experiments. For \(E_2\) and \(E_4\), the best results for all projection methods were obtained with the distance to reference points measure and the stripping segment. For \(E_1\) and \(E_3\), on the other hand, other segments, e.g., clamping or pre-stripping, led to the best wear estimates. The same observations can be made for the results of the cumulative stroke-wise change. PCA shows very good performance for the stripping segments of \(E_2\) and \(E_4\), while no clear pattern is evident for UMAP in terms of segment suitability. Interestingly, AE performs well for the stripping segments, but best for the blanking segments for \(E_2\) and \(E_4\). From a fine-blanking perspective, the respective blanking and stripping segments are both stages in the fine-blanking process that are strongly affected by changes in wear condition. Therefore, good results for both segments are appropriate. Good results for the clamping and pre-stripping segments could indicate that the data are biased because, from a theoretical point of view, the segments in question should not contain detailed information on wear condition. In addition, AE seems to be particularly suitable for quantifying variations and changes in the blanking segment, compared to the other methods, which perform significantly worse for the blanking segments.

Figure 16 shows a comparison between the methods for computing the low-dimensional projection. Of particular interest is the comparison of performances between the feature engineering-based approaches PCA and UMAP on the one hand, and AE, which automatically learns to extract valuable features, on the other hand. In addition to these three methods, a baseline reference is given by a simple approximation of the wear increase using a linear function from 0 to the maximum wear value. First, on experiment \(E_1\), the linear approximation is almost always more accurate than all other estimators, indicating the influence of the skewed data resulting from the lubrication error in the beginning of experiment \(E_1\). In general, a better overall performance of the cumulative approaches can be observed, using the stroke-wise change and the rolling variance. The distance to reference points is better than the linear reference approximation only for some of the experiments and segments presented, namely for the original and stripping segments of \(E_2\) and \(E_4\). Regarding the cumulative stroke-wise change for both \(E_2\) and \(E_4\), AE performs best for the blanking, whereas PCA performs best for the stripping segment. Similar trends are observed for the combined estimator. UMAP generally performs worst for the cumulative stroke-wise change, while PCA and AE can achieve better results than the linear wear approximation.

Figure 16 compares the performance of the four estimation approaches for PCA, UMAP, and AE. For PCA, the distance to reference point estimator performs worst in all trials, while the combined and stroke-wise estimators perform best in most cases. This is in contrast to UMAP, where the distance to reference point estimator performs better than its competitors. This observation is consistent to the before mentioned properties of UMAP that allow UMAP to isolate local changes, while skewing global structure. Therefore, local structure gains more significance. In both methods, the rolling variance estimator is able to achieve good results in all trials, while it does not achieve the best results in any of the trials. For AE, the distance to reference point and the cumulative stroke-wise approaches perform worse than the other two methods in most cases. Figure 17 shows the approximate wear for each estimator for selected experiments and methods. Here, the combined estimator highly overlaps to the measured wear increase for PCA, while the distance to reference points estimator shows much better performance on UMAP.

The poor performance of the estimator for the distance to reference point on the stripping segments of \(E_1\) can be explained by the recorded lubrication error. A reduction in lubrication has a strong effect on the frictional forces during stripping and thus on the measured force signal. In Fig. 10, the scatter plot on the upper left shows the global distribution of the data and shows a strong deviation from the other experiments. Since the estimator for the distance to reference point mainly captures global structural properties, the poor performance of this estimator is understandable. On the other hand, the estimators based on stroke-wise change or variance do not seem to be negatively affected by the error. This is a very interesting fact, as it shows that the different estimators indeed handle severe local or global structural changes differently.