1 Introduction

In machining, grinding is often the final process step, making it responsible for the quality of the workpiece. Grinding wheel wear can negatively affect the machining result and cause higher surface roughness or grinding burn [1]. To avoid a decrease in process quality, monitoring the grinding wheel condition is essential. Due to the stochastic character of the process, development of suited monitoring approaches remains a topic of ongoing research. While concepts based on acoustic emission (AE) sensors and also dynamometers are most commonly researched, the potential of internal drive signals has been mostly overlooked, due to its limited bandwidth [2].

In general, there are two ways to monitor grinding wheel wear. One is to directly evaluate the grinding wheel condition with optical sensors, known as offline monitoring or direct measurement [3, 4]. The other is to indirectly estimate the wheel condition based on process signals like AE referred to as online monitoring or indirect measurement. Indirect measurement allows for immediate reactions without additional idle times. However, the monitoring accuracy heavily depends on sensors and algorithms used for wear estimation. Due to the complex correlation between measured signals and the grinding wheel condition, machine learning (ML) approaches are used predominantly. The most common approach is to extract features from process signals, select features and apply an ML-algorithm [5, 8,9,10,11,12, 18, 22, 23] to estimate a discrete tool state (uncritical/critical tool wear). An overview of artificial intelligence-based monitoring of grinding processes is given by Pandiyan et al. [2]. The review lists a total of 41 monitoring approaches of the grinding process based on AE sensors. Force sensors are used in 11 and vibration sensors in 12 cases. Current and power measurements are only researched in two cases as a part of sensor fusion approaches which also rely on other sensors.

A main reason for the prevalent use of AE sensors is their wide frequency band [7]. Grinding wheel condition monitoring based on AE signals in general reaches high accuracy between 90% [9] and 100% [8] in case of classification. However, the high dependency of the signals on the sensor location and the low interpretability of the signals are disadvantageous [13].

Force sensors allow for measuring grinding force, which in turn depends on the grinding wheel wear [14]. As they are easy to interpret, force measurements from piezo electric dynamometers are often used to analyze grinding wheel wear related to force [14, 15], but less often to predict the tool condition [6]. In general, piezo electric dynamometers are associated with high costs. As an alternative, Couey et al. [16] integrated a sensor to measure the displacement of an aerostatic spindle to estimate the grinding force. The system is able to detect changes in the normal force as small as 25 mN, to enable grinding wheel wear monitoring. Last, strain gauges, can be used to measure forces. Denkena et al. [17] applicate strain gauges to the spindle shaft and measured forces with a resolution of 3.7 N.

Moreover, there are less commonly used sensors like microphones. E.g. Cheng-Hsiung Lee et al. [18] used a Convolutional Neural Network to classify wear of grinding wheels. As an input they used filtered time series with a length of 1 s, comprising 44,100 samples. They achieved an accuracy of 97.44%.

Only few studies investigated solely internal signals of the machine tools control [19, 20]. None of them covers grinding wheel wear. Grimmert and Wiederkehr [21] worked on the topic of indirect force monitoring based on the spindle current of a grinding machine. They showed that in general tangential forces can be reconstructed with a Mean average error of 24.5 N.

In many cases, sensor fusion is applied, to use different sensors for tool condition estimation [22,23,24]. E.g. Guo et al. [24] used an LSTM to predict the grinding wheel wear. Signals from a dynamometer, an AE sensor and an accelerometer are used to estimate the grinding wheel wear. In contrast to the previous presented work grinding wheel wear is characterized continuously. The approach reaches a R² of 0.994. The benefit of sensor fusion is the potential to reduce uncertainty and increase precision [25]. Nevertheless, sensor fusion requires multiple sensors and suited algorithms, to handle high dimensional data [26].

Literature shows, the potential of utilizing internal control signals for process monitoring has not been investigated. In particular, the following points are still unknown:

  • Which machine learning models are suited to estimate grinding wheel wear based on control signals.

  • How accurate are control signal based monitoring approaches in comparison to approaches based on more accurate sensors like a dynamometer.

  • Which preprocessing steps are necessary to enable control signal based grinding wheel wear monitoring.

  • Which control signals are most relevant.

In this work, an approach is proposed to estimate the grinding wheel wear based on internal drive signals. The approach is explained in Sect. 2. Next, the experimental setup is described in Sect. 3. In Sect. 4 preprocessing and machine learning algorithms are introduced. The results are shown in Sect. 5. Finally, the findings are discussed in Sect. 6.

2 Approach

This work aims to estimate the grinding wheel wear based on drive signals. Due to the stochastic character of the process, ML algorithms are chosen for monitoring the grinding wheel wear. Moreover, the wear is treated as a continuous value instead of a discrete wear state. Consequently, regression models are used. Thereby, more information is provided in comparison to a classifier. The resulting model estimates the tool life volume.

The whole approach is depicted in Fig. 1. First, a dataset is recorded, which is mandatory to train and evaluate ML models. The data-acquisition covers force measurements and control signals, stored as two separate datasets. Both datasets are then preprocessed. The preprocessing is necessary to remove measurement noise. As an additional preprocessing step, the time series are transformed into feature space. This reduces the dimensionality of a single time series, to provide a suitable input feature vector for the ML models. The features are ranked with a feature ranking algorithm to enable feature selection. Subsequently different models are trained. For the training process, the model type itself, its hyperparameters, as well as the amount of selected input features are varied, to find the best performing ML model. As a result, the tool life volume is estimated by the model. Finally, the model with the lowest error is selected.

Fig. 1
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Overview over signal processing and tool life volume prediction

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3 Experimental setup and procedure

The experimental setup (Sect. 3.1) and procedure (Sect. 3.2) is introduced in the following.

3.1 Experimental setup and data acquisition

The experiments are carried out on a Walter HELITRONIC VISION 400 L grinding machine. A cuboid 100Cr6 workpiece (53 × 20 × 100 mm) is clamped in a hydraulic chuck, as shown in Fig. 2. The grinding wheel is ceramic bonded and the abrasive grain is Al2O3 corundum. To measure the forces, the chuck is fixed to a Kistler dynamometer 9257B. The data is recorded with an external measuring computer. In addition, control signals are recorded using the measurement software “Servo Guide” of the machine tools Fanuc control. This enables the recording of eight different control signals with a sampling rate of f = 1,000 Hz. The selected signals are listed in Table 1. The drive currents of the x- and y-axis as well as the motor spindle are selected, because they correspond to the acting forces, as already investigated in preliminary work on a different machine with similar drives [24]. Moreover, the spindle load torque is expected to reflect the tangential forces. Position errors as well as deviations of the spindles motor speed have shown promising results in the fields of condition monitoring [27]. Last, the position feedback for the x-axis is a prerequisite for the segmentation approach, explained in Sect. 4.1.

Fig. 2
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Experimental setup

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Table 1 Control signals as documented in the fanuc controls variable browser
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3.2 Experimental procedure

For the surface grinding process, the depth of cut is set to a constant value of ae = 0.5 mm. The width of cut equals the workpiece width (ap = 20 mm). The feed velocity of the process was set to vf = 300 mm/min and the cutting velocity to vc = 20 m/s which corresponds to a spindle speed of 3,820 min− 1.

With these process parameters, six process series are recorded. Each series contains a different number of repetitions of the same surface grinding process. The number of repetitions increases steadily: 10, 20, 40, 70, 80 and 100. After each series, the grinding wheel is removed from the machine tool and its condition is evaluated. For this purpose, a 2D/3D laser profile sensor Keyence LJ-V7020 is used scanning the surface of the grinding wheel. The results are evaluated with the software MountainsMap to determine the grinding wheel’s surface roughness values related to wear. Afterwards, the grinding tool is dressed. A total of 80 μm is removed from the radius of the grinding wheel. As a consequence, there is a negligible decrease of cutting velocity of 0.03 m/s with each series. However, the surface roughness did not show a significant correlation to the tool life volume (see Sect. 9, for a more detailed explanation). Nevertheless, between 100 and 110 process repetitions, grinding burn occurred and clogging became visible. As this condition requires the grinding wheel to be redressed in order to guarantee workpiece quality, 100 process repetitions are defined as the end of tool life.

4 Signal processing and machine learning algorithms

In the following, the signal processing and segmentation (Sect. 4.1) as well as the procedure of machine learning model training (Sect. 4.2) are presented.

4.1 Preprocessing

The preprocessing is subdivided into four steps: data cleaning, segmentation, feature extraction and feature ranking. Internal control signals and the recorded measurements of the dynamometer are pre-processed separately.

Starting with cleaning the dynamometer measurements, drift is removed by subtracting a linear function fitted with the help of the first and last second of the measured time series, where the grinding wheel is not engaged. Further on, a fifth order Butterworth low pass filter is used to filter frequencies above 2 kHz which is necessary to consider the limitations of the dynamometer due to its Eigen frequency. The drive signals are already filtered and free from drift, but idle times without axis movement have to be discarded. For this reason, the feed velocity vf  is derived from the feed axis position feedback. The feed velocity then is used to identify the relevant process time window based on a velocity threshold thv as shown in Fig. 3a.

Next, the signals are segmented into a start segment S1, a middle segment S2 and an end segment S3 for each process. The segmentation is illustrated in Fig. 3b and c for the drive signals. Only the middle segment has constant process conditions. During the start segment period, the depth of cut steadily increases, during the end segment, the depth of cut steadily decreases down to a value of 0.

In case of the internal drive signals, the spindle load torque (DTRQ) is used, to determine the points of time for the segmentation. The DTRQ is smoothened and its gradient ∆DTRQ is calculated (Fig. 3b). Segmentation indices are determined according to the threshold value thdtrq (-thdtrq< ∆DTRQ < thdtrq). The calculated segmentation indices are applied to all internal control signals, resulting in three different segments S1, S2 and S3.

Fig. 3
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Segmentation of control internal signals based on the numeric gradient of the spindle load torque

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A similar approach is taken for the segmentation of the dynamometer measurements: In particular, the measured force in y-direction Fy is used, which approximately corresponds to the tangential force, as depicted in Fig. 2. Only for segmentation process, the force signal is smoothed with a moving mean method, to prevent unstable numerical differentiation. Subsequently, the gradient ∆Fy is calculated numerically. A constant threshold value of thf = 0.5 N/s is applied to determine the cuts for segmentation. The segmentation is transferred to the other force signals Fx and Fz by choosing the same segmentation indices.

Based on the segmented signals, a feature vector is calculated to describe the signal statistically and to reduce its complexity from a time series to an n-dimensional vector, whereby n is the number of features. A summary of all features is given in Table 2. The preselection of the features, as listed in Table 2, is based on a cross section of different approaches, commonly used in literature (e.g [24, 28, 29]). The features are then calculated for each segment (S1-S3) and each signal, by applying the corresponding formula to the cropped timeseries. As a result, three sets of feature vectors are provided:

  1. a)

    vA: nA-dimensional feature vector calculated from force signals with nA = 135 (3 Segments, 15 statistical descriptions, 3 force directions).

  2. b)

    vB: nB-dimensional feature vector calculated from control signals with nB = 360 (3 Segments, 15 statistical descriptions, 8 control signals, Table 1).

  3. c)

    vC: nC-dimensional feature vector as a combination of vA and vB with nc = 495.

Last, all features of the feature vector vc are ranked, based on the F-test feature ranking algorithm. The algorithm uses the F-test to enable univariate feature ranking for regression based on a score s = -log(p), where p is the p-value according to the F-test [30]. The algorithm also requires the output values which should be predicted by the ML models. In this work, this is the tool life volume normalized by the width of cut, in the following referred to as specific tool life volume. The higher the score s, the higher is the information of the feature regarding to the desired output.

4.2 Machine learning algorithms

The different machine learning algorithms are trained with a feature vector of variable size as an input. The output is the specific tool life volume. Subsequently, the variations as well as the machine learning approaches are explained in detail.

Table 2 Features
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Three different feature sets are evaluated: only force related features (Set FrF), only drive signal related features (DrF) and the combined features of both sets (CF). The different models used for the evaluation include a variation of Support Vector Machines (SVM) [36], Gaussian process regression (GPR) [31] and Regression Trees (RT) as well as a linear regression model (LR). An overview of all models is presented in Table 3.

Table 3 Overview of ML models
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All models are trained separately with the three different datasets A: FrF, B: DrF and C: CF. For validation during the training process, k-fold cross validation [32] was used with k = 5. The final evaluation of the machine learning models is based on the test set, which was not considered during the training. As error metrics, the Root Mean Square Error (RMSE) and the coefficient of determination R² are evaluated. First, an extended list of models is considered and evaluated based on the five-fold cross validation. Moreover, input sizes of the models are altered based on the ranked features. Because of the curse of dimensionality [35], the input size is an important hyperparameter. In this work, it is varied in three steps: (1) complete set of features (2) 50 features with highest rank and (3) 20 features with highest rank.

A total of 48 different models were trained for each input domain (force, drive signals, combined). The number results from the number of model types nmt = 16 (Table 3) multiplied by the number of input size variations niv = 3. In the following, the different models are referred to according to their Model ID and the input size depending on the different feature vectors: < Model ID>-< input size>, e.g. SVM-Q-50 is a Support Vector Machine with a quadratic kernel function and 50 input features.

Fig. 4
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Feature selection based on the F test algorithm

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5 Results

In the following, the calculated features are presented and evaluated (Sect. 5.1). To allow for conclusions on the topic of signal fusion, the correlations between forces and drive signals are analyzed (Sect. 5.2). Moreover, different machine learning algorithms are compared regarding their ability to estimate the specific tool life volume based on different signals (Sect. 5.3).

5.1 Features in the context of tool wear monitoring

The calculated features are evaluated by using the F- test as a feature ranking algorithm (Fig. 4). By evaluating the resulting p-value with respect to the specific tool life volume, highest values are achieved by features based on the force measured by the dynamometer. In particular the ten highest p-values all refer to the y- and z-forces which correspond to the tangential and normal forces during the grinding process. Expanding the scope to the twenty highest p-values, the Y-axis current IQ1 is the control signal with the highest impact compared to all other control signals.

5.2 Correlation between forces and drive signals

Focusing on the middle segment, evaluation of the different features shows that there is a negative correlation with a Pearson correlation coefficient [33] of -0.90 between the mean spindle torque and the mean force measured by the dynamometer in x-direction (Fig. 5). Similar, there is a negative correlation with a value of 0.74, between the mean values of the active current IQ and the force in x-direction. However, while a correlation close to 1 was found for features corresponding to mean, median, maximum and minimum values, this does not apply to features, corresponding to the distribution, like standard deviation, kurtosis, skewness or the peak-to-peak range. For example, the correlation between the standard deviation of DTRQ and Fx is only 0.05.

Fig. 5
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Correlation of DTRQ and force x

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The main reason for this is the low sampling frequency of the signal. Due to the Nyquist-Shannon theorem, drive signals frequency band is limited to 0 to 500 Hz. Though, the force amplitudes in the frequency band from 0 to 1,000 Hz remain constant for all experiments, Fig. 6. Only from 1,000 to 1,500 Hz the amplitudes steadily increase corresponding to the decline of specific tool life volume. In addition, there are significant changes from 1,500 to 2,000 Hz.

Fig. 6
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Frequencies measured by the dynamometer for different tool life volumes

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However, it has to be considered that the dynamometer leads to an increase of compliance, compared to an experimental setup without dynamometer. To examine the frequency response, a modal analysis has been conducted, as depicted in Fig. 7a. Therefore, different sensor positions have been evaluated.

For excitation in x-direction, Fig. 7b, the different sensors show qualitative similar curves. The higher compliance of sensor 1 (S1) may be explained by the workpieces cantilever length. For excitation in y-direction, as shown in Fig. 7, resonance frequencies at roughly f1 = 402 Hz and f2 = 555 Hz can be spotted. Moreover, a resonance frequency occurs at f3 = 1716 Hz. Compared to f1 and f2, f3 shows a noticeable difference between the amplitudes of sensor S1 and S3.

The experimental setup influences the compliance and therefore the dynamic forces, too. As a consequence, there is a deviation between measured force in this setup and the non-measurable force of a setup without dynamometer. But as Fig. 6 shows, force amplitudes are low for frequencies below 1,000 Hz. Consequently, the experimental setup does not significantly impact the control signals. Nevertheless, it has to be considered, that there is an error in the force measurement. For an accurate force measurement, compensation would be beneficial as described by Wan et al. [34]. For the presented approach, the error can be neglected, since the machine learning models aim for tool life volume prediction, only using the force measurements as an input. The coherence between tool life volume and measured force during grinding process is evident, including the frequency range from 1,000 Hz to 2,000 Hz. Consequently, the impact of the changed compliance is learned implicitly by the machine learning models, but is specific for the experimental setup.

Fig. 7
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Modal analysis (a) Experimental setup (b) compliance measured by sensor 1 and 3 in x-direction (c) compliance measured in y-direction

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5.3 Model and feature selection

For each input domain, the five models with the lowest RMSE based on the cross validation are selected and evaluated for the test dataset (Fig. 8, A1-A5, B1-B5, C1-C5). In Fig. 8, test error is plotted for the different datasets and models. Figure 8a shows the results of the ML models based on the dynamometer measurements (A). Overall, A1: GPR-R-135 (Gaussian process regression with rational quadratic kernel function, using all 135 input features), achieves lowest error, across all ML models and datasets. The RMSE is eA1 = 61.3 mm² and the R² value is r2A1 = 0.99. The majority of selected ML models relies on 50 input features. This aligns to the state of the art knowledge about the curse of dimensionality [35], which deals with the declining learning performance for high dimensional data. By analyzing the different model types, Gaussian process regression generally yields lower RMSE compared to other models like support vector machines.

Compared to the force measurement based models (A), the RMSE value eB (Fig. 8b) of the models trained with the control signals is not lower than eB1 = 104.9 mm², which is the test error of the Gaussian process regression with the Matern 5/2 kernel function and 50 input features (B1: GPR-M-50). The corresponding R² value is r2B1 = 0.98. Compared to the dynamometer measurements, the algorithm’s RMSE is 43.6 mm² higher. Since a single surface grinding process has a specific material removal rate of 26.5 mm², this corresponds to an increase of 1.7 processes. The dynamometer-based model A1: GPR-R-135 on average confuses processes within a range of its next 2.3 neighbors to each side, while the average range is 4.0 neighbors for the control signal based model B1: GPR-M-50.

Fig. 8
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Validation and test errors, depending on the machine learning model and the input features. (a) Models based on force-related features (b) models based on drive signal-related features, (c) models based on combined feature vector

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Figure 8c shows the evaluation of the combined feature vectors based models (C), which rely on both, force measurements and control signals. The results of the cross validation reveal the lowest validation error, compared to the previously discussed models. In particular, the validation error is 42.6 mm² for C2: GPR-M-50. However, test errors eC are as high as the test errors eB (lowest test error is eC1 = 102.5 mm2 for C1 and eC2 = 105.5 mm2 for C2). The difference between validation and test error is a strong indicator for overfitting. A larger training dataset would be a possible solution to avoid overfitting.

6 Summary and conclusion

This work shows, that it is possible to estimate grinding wheel wear based on drive signals. A preprocessing approach is proposed that automatically segments the control signals into three relevant segments. For each segment, features are calculated. The results are summarized in a feature vector. Next, the feature vector is sorted by a feature ranking algorithm. Based on the feature vector, different models were trained to estimate the tool life volume. The results show the following:

  • For drive signal-based grinding wheel wear monitoring, Gaussian process regression model A1 with a Matern 5/2 kernel an input size of 50 achieves the lowest error.

  • The R² value of A1 is 0.98, and the RMSE is 104.9 mm² (per millimeter grinding wheel width).

  • The drive current of the Y-axis, which corresponds to the normal force, was identified as most significant control signal regarding the identification of grinding wheel wear.

  • Lowest overall error was reached by the B1 model (Gaussian process regression, rational quadratic kernel, 135 input features) based on dynamometer measurements.

  • The R² value of the predicted specific tool live volume of B1 is 0.99, the RMSE is 61.3 mm² which is 41.6% lower than the best drive signal based model.

  • A main reason for the difference is the limited bandwidth of the control signals (0 to 500 Hz).

  • Sensor fusion of both signal sources had no positive impact on the result of the learning algorithms.

If high precision is desired for grinding wheel wear monitoring, use of a dynamometer is recommended. However, the presented approach enables drive signal based monitoring of grinding wheel wear. Still, a loss of precision must be taken into account. Whether or not to use drive signals depends on the grinding process and especially the expected tangential and normal forces. Sensor fusion on the other hand does not improve the systems accuracy, since the control signal are mostly redundant to the force measurement. Nevertheless, extending control data by signals containing information with higher bandwidths, e.g. an accelerometer, still is considered as a suitable approach.

7 Attachment

As described in Sect. 3.2, the evaluation of the surface roughness did not show a significant correlation tool life volume. Figure 9 shows the calculated reduced groove depth Svk, the reduced center height Spk and the core height Sk. None of these values could be used as an indicator for grinding wheel wear. Nevertheless, literature shows good results for different setups with different grinding wheels [3].

Fig. 9
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Surface roughness of the grinding wheel for different levels of grinding wheel wear

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