Introduction

On-site machining provides a valuable alternative when workpieces cannot be effectively handled on a conventional machine [1]. For instance, for the machining of large parts where the workpiece is already installed in its functional location. Such operations are non-standard and rely heavily on the operator’s experience to achieve a good surface finish. Indeed, many uncertainties surround the operation, such as unexpected material behavior and challenging machine installation conditions.

Mobile machine tools have lightweight designs which are quick to assemble to simplify the transportation and installation phases on site [1]. Thus, designers must strike a balance between portability and structural rigidity. Consequently, specific problems arise which have been addressed in the literature. Firstly, static deformations of mobile machines were modelled, allowing for better redesign of specific parts or establishing displacement compensation strategies [2, 3]. Secondly, kinematic imperfections arise from the installation phase of mobile machines in the on-site environment. Consequently, many robotized machine concepts have been proposed to simplify the installation and calibration processes on site [1]. Kinematic imperfections were modelled by Legoff et al. [4] in a comparative analysis between a mobile machine and a robotic arm for a milling operation of a large part. The authors concluded that the mobile machine tool was overall more performant due to the poor structural rigidity of the robotic arm. Vibrational problems are also a common source of error in on-site machining due to the changing nature of the machine’s surrounding environment. Law et al. [5,6,7] address the problem of chatter prediction in mobile milling using substructuring and component mode synthesis to predict the dynamics of mobile machines coupled with the dynamics of their surrounding environment. Indeed, on-site machining lacks the opportunity for pre-testing, consequently, the prediction of milling tool dynamics is a valuable insight which can be used before venturing into an unknown operation.

On-site operations are highly varied, in this context, the machining operator must be constantly alert to the inception of chatter. This issue is a popular topic in conventional machining, leading to continuous monitoring systems for chatter detection. Monitoring systems can be summarized in five key steps [8]: choice of sensors, signal processing, feature generation, feature extraction and classification.

For chatter detection, sensor choice can be decomposed into two types of approaches: direct or indirect [9]. Direct approaches rely on measurement of the vibration close to the tool-workpiece interface caused by chatter whereas indirect approaches concern all other types of sensors, such as force signals or internal sensor signals. Internal sensor signals are increasing in popularity as they avoid the use of further costly equipment. In the context of on-site machining, they also present a big advantage relative to installations times, which are a critical part of the operation. The most common approach to chatter detection in milling using internal sensor signals is to use the spindle drive signals [9,10,11,12].

Signal features can be decomposed into three types [8, 13]: frequency domain, time domain and time–frequency domain. For frequency domain features, the sampled signal must follow the Nyquist-Shannon theorem in respect to the chatter vibration frequency. The most common method used in chatter detection is to use high frequency sensors and to decompose the signal using the Fourier transform to differentiate chatter vibrations from normal operational vibrations [14]. Concerning time domain features, many statistical values have been used for chatter detection, such as standard deviation, root mean square, energy ratio, crest factor, skewness, kurtosis, etc. [10, 12, 15, 16]. More advanced methods include empirical mode decomposition [17, 18] where the signal is decomposed into intrinsic mode functions, some of which can be associated with chatter. Such statistical indicators can also be used in monitoring applications where signal acquisition frequency is low. For instance, Tseng et al. [19] monitor motor current signals in a CNC machine at a sampling frequency of 62 Hz for tool wear estimation in an end milling operation and Jeong et al. [20] use the feed motor signal, sampled at 130 Hz for cutting force estimation. Furthermore, another common time domain feature is to analyse periodic components of a signal at the normal forced vibration frequency [21]. One such method is to analyse chatter using Poincare maps [22, 23]. Finally, time–frequency domain features concern all the methods based on the wavelet transform which has also been extensively used for chatter identification [16, 18].

Chatter classification requires data to be labelled beforehand, the effectiveness of the classification method can then be evaluated by comparing the method’s outputs to the reference. Many chatter detection methods establish empirical thresholds on the selected features [13]. However, non-linear classification methods can also be used for optimising the boundary between stable and unstable cases. Such methods include neural networks [24, 25], hidden Markov models [26] and Support Vector Machines (SVM) [15, 18, 27]. SVM has been reported as being the most popular method for chatter classification in milling [13, 18].

This article investigates the potential of low-frequency internal sensors in a mobile CNC milling machine for chatter identification. The study is based on an experimental comparison of the internal sensor signals in comparison to a reference chatter state which is determined using a high frequency accelerometer signal. the article is organized as follows. First, a section is dedicated to the presentation of the mobile milling machine, the monitoring sensors, an overview of the milling operations and the initial data treatment. Second, the chatter identification method using the accelerometer is defined. Third, different time domain features are evaluated for chatter detection using the internal sensor signals. Finally, the internal sensors are used for instantaneous chatter detection using two classification methods, one linear and one non-linear using the C-SVM method.

Description of the Test Bench and Experimental Procedure

The focus of the present study is a mobile milling machine designed by Tacquet Industries, as seen in Fig. 1. The machine design is equivalent to a lightweight vertical three axis milling machine. The movement of the machine along each of the three axes is enabled by dovetail slides and trapezoidal lead screw systems. The operations are carried out in up-milling to compensate for the backlash in the lead screw system.

Fig. 1
figure 1

Mobile milling machine test bench setup

Full size image

The machine is bolted to a flat surface on a machining table. The table is made up of a bloc of granite and a metal plate which are supported by six pneumatic anti-vibration mounts. The anti-vibration mounts allow the whole test bench to be isolated from external vibrations, which can come from other machines in the building for instance. This setup allows the machine to be studied in a highly rigid environment. This is not always the case in on-site machining. This allows the study to focus on the chatter behaviour of the milling machine itself.

The spindle is equipped with a 2.8 kW BSM90N-3150AF brushless motor, and the axis motors are 0.75 kW BST80-IMOI02430-Z motors. The machine is numerically controlled and powered by a Geobrick Turbo PMAC 2. The control system allows an accuracy on the dynamic spindle position to within 0.4° when operating without load. The Geobrick controller has a peak current value of 16 A. When the total current consumption of the milling machine exceeds this value, the machine shuts down. These current overruns constitute an important limitation for the milling machine since they require immediate intervention by a technician and are time-consuming.

During milling operations, external vibrations and internal signals are simultaneously monitored. Vibrations are measured using a tri-axial Bruel & Kjaer 4535 B accelerometer which has a sensitivity of 10 mV/(m.s−2). The accelerometer is placed as close to the tool as possible, as illustrated in Fig. 1. The signal is acquired using a Compact DAQ system from National Instruments at a sampling rate of 25.6 kHz. The internal signals for spindle speed and motor current are measured via the Geobrick controller. The spindle speed is measured using an incremental encoder which is integrated with the spindle motor. This encoder has 2500 points per revolution with commutation which allows an accuracy of 1/10000th of a rotation. Spindle current is monitored using the internal signal of the control system. Spindle speed and current are measured via a remote PC using a LabVIEW program which communicates with the Geobrick using a Pcomm Server protocol. This protocol enables continuous low-frequency measurements at an acquisition rate of 40 Hz.

The present study focuses on surfacing operations. Each operation is carried out on an 80 mm long steel block of S235JR non-alloy structural steel. The steel block, is clamped to the machining table, as seen in Fig. 1. The milling tool is a Mitsubishi WWX400-080A07AR tool with 7 teeth and a diameter of 80 mm. The cutting inserts are general purpose Mitsubishi 6NMU1409080PNER-M which have a MP6130 steel coating. The inserts were frequently changed, before the appearance of any visible wear marks, to maintain consistent cutting conditions.

For each operation, first the tool cutting edge enters the material. As the tool advances in the feed direction, the radial immersion gradually increases. When the radial immersion reaches maximal value, then the tool is in the “Full Immersion” (FI) zone. This corresponds to the zone where the cutting conditions remain consistent. This zone is notably the focus of Section "Internal sensors feature selection by comparative analysis of the FI zone". After travelling the full length of the FI zone, the tool edge exits the material. As the tool continues further along the feed direction, the tool eventually completely exits the material. Figure 2 below depicts these steps. This process is further detailed in the presentation of the initial data treatment below and in Fig. 3.

Fig. 2
figure 2

Description of the operation steps

Full size image
Fig. 3
figure 3

Identification of the milling operation steps and the FI zone on the different sensor signals

Full size image

The radial immersion is kept constant for the entire set of experiments at 37 mm. Two feed per tooth (fz) values are considered: 0.1 mm, this value corresponds to ideal cutting conditions according to the tool manufacturer, and 0.05 mm, this value is often chosen in on site operations due to the limited power of the milling machine. The spindle speed (N) was varied from 900 to 1500 rpm with an interval of 100 rpm. For each spindle speed, depth of cut (ap) was incrementally increased by 0.5 mm until the machine’s power limits are reached. A total of 66 operations are carried out, as summarized in Table 1.

Table 1 Milling operations with experiment numbers
Full size table

Note that the limit depth of cut is different depending on the spindle speed value. Furthermore, the maximal depth of cut is lower for the experiments that are carried out with an fz value of 0.1 mm due to increased power consumption.). For each operation, the cutting steps (as mentioned previously) are identified. First the tool material entrance time is manually identified, then the following steps are deduced based on the feed and the operation geometry. Figure 3 shows an example of a signal recording corresponding operation number 7. The displayed signals are from the accelerometer (A), the motor current (I) and the spindle speed (N).

The full signal starts two seconds before the tool enters the material and ends two seconds after the tool exits the material. Consequently, the total signal duration is dependent on the machine feed.

Experimental Identification of the Chatter Phenomenon

The aim of this section is to identify the chatter phenomenon using accelerometer signals. For each operation, the accelerometer signal is analyzed in time and frequency domain using spectrogram diagrams. The FFTs are calculated along a sliding window of 0.5 s without overlap, resulting in a time resolution of 0.5 s. The frequency resolution is calculated as the ratio between the number of acquisition frequency and the number of samples. For ease of calculation, the number of samples is elevated to the next power of two, from 12,800 to 16,384. Hence the spectral frequency resolution is approximately 1.52 Hz.

Chatter presence is determined by a visual inspection of the spectrograms. Indeed, in an operation without chatter, the main vibrations in the system are from forced vibrations caused by the spindle action on the workpiece. In this scenario, operational vibrations should be found at the harmonics of the tooth passing frequency, H(fTP), or at the harmonics of the spindle rotation frequency when the tool has a significant runout, H(fSR). Chatter diagnosis is therefore carried out as follows: first, the vibration with the highest amplitude is examined, this corresponds to the highest peak in the spectrogram. If the peak frequency is different to fTP, then chatter is present in the operation. If the peak frequency is equal to fTP then the remaining peaks in the spectrogram are examined. If these have frequencies that are equal to harmonics of fSR then there is no chatter. Finally, if the main vibration is fTP and the secondary vibrations are different to harmonics of fSR then the chatter state is a “limit” case. In this case, chatter is observable but has not yet become the main source of vibrations in the operation. Furthermore, chatter vibrations in the X direction are consistently more severe than in the Y and Z directions. Hence, the X direction signal was retained for chatter monitoring. The spectrogram for experiments 7, 8, 9 and 10 are illustrated in Fig. 4 below as examples for each chatter scenario and for a current overrun case, in which chatter is also diagnosed.

Fig. 4
figure 4

Chatter diagnosis using the spectrogram method for experiments 7 to 10

Full size image

Furthermore, if chatter arises during the operation, the start and end times are manually identified, as illustrated in red in Fig. 4. These chatter boundaries are used as a reference chatter state vector when studying the internal sensors in Section "Instantaneous chatter detection using linear and non-linear classification".

The chatter frequencies that are observed during the milling operations vary between 93 and 140 Hz. Furthermore, the chatter frequency tends to remain identical for a specific spindle speed.

Note that the current overrun cases all contain chatter, as illustrated in in Fig. 4d. Indeed, increased current consumption is one of the common problems associated with chatter. Thus, it is probable that the current overrun and presence of chatter are linked, however, this topic is not covered in the scope of this article.

Internal Sensors Feature Selection by Comparative Analysis of the FI Zone

Whenever chatter is observed in the measurement, it generally appears just before the beginning of the FI zone and then dissipates once the tool edge exits the workpiece. Indeed, in these zones, chatter can easily build up due to the stationary nature of the FI zone. Thus, the chatter state can be classified as a function of the operational parameters ap, fz and N based solely on an analysis of the FI zone. Each experiment is classified into one of the three chatter scenarios: “none”, “limit” and “chatter”. The results are displayed in the diagrams in Fig. 5.

Fig. 5
figure 5

Chatter scenarios determined by visual inspection of the FI zone using the spectrogram method

Full size image

The aim of the current section is to determine features on the internal sensor signals which can discern these different chatter states. Milling experiments with current overruns are not considered in this analysis since data is not available to fully describe the FI zone.

Several studies [15, 16] have shown that chatter is correlated to significant changes in signal behavior, which can be highlighted by time domain statistical features. Hence, the signal section corresponding to the FI zone of current signal and the spindle speed signal is extracted and the following statistical features are calculated: standard deviation, maximum value, peak to peak, root mean squared, kurtosis, crest factor and energy ratio. These values are defined in the previously mentioned article by Večeř et al. [28]. Note that for the calculation of the energy ratio, the two first seconds of the signal, where the tool has not yet entered the material, are used as the reference signal. Feature selection is then carried out by comparing the feature values to their chatter state using diagrams such as those displayed in Figs. 6 and 7. In the scope of the present article, four features are retained: the spindle current energy ratio (Ier), the spindle current rms (Irms), these two feature values are displayed in two individual diagrams in Fig. 6. And the spindle current and spindle speed standard deviation (Istd, Nstd), these two features are displayed together in the same diagram in Fig. 7. Note that some of the experiment numbers have been highlighted in the figures for commentary. Indeed, these selected features separate the chatter class from the non-chatter class quite effectively, except for a few problematic cases. For instance, experiment 48 generally has very high feature value compared to the other experiments in the non-chatter class, which makes it difficult to classify.

Fig. 6
figure 6

Evaluation Ier and Irms as features for chatter recognition on the internal sensor signals based on FI zone analysis (legend is identical to Fig. 5)

Full size image
Fig. 7
figure 7

Coupled Istd and Nstd features for chatter recognition on the internal sensor signals (legend is identical to Fig. 5)

Full size image

In some cases, the feature values are complementary. For instance, experiments 60 and 63 have high feature value in Irms and thus their classification is ambiguous. However, in Istd, Nstd and Ier, feature value is lower and thus the experiment is more likely to belong to the non-chatter class. Inversely, experiment 22 has a high feature value in Ier, but has a low feature value in Istd, Nstd and Irms.

Furthermore, it is interesting to note that there seems to be a linear relationship between Istd and Nstd in Fig. 7 for the chatter cases. This observation is coherent with the fact that both spindle current and spindle speed are affected by the same underlying mechanical phenomenon. However, three experiments seem not to follow this rule: experiments 32, 65 and 34, where spindle current standard deviation is proportionally much higher than spindle speed standard deviation relative to the other cases. It is interesting to note that these three experiments are all carried out with the same spindle speed, at 1500 rpm. Consequently, it is possible that some other mechanical or electrical phenomenon is occurring during these operations, as this spindle speed value is close to the maximum of the mobile milling machine’s limits. However, the analysis of this phenomenon is not covered within the scope of the present article.

Finally, the limit chatter cases are distributed differently depending on the feature which is used. Indeed, in Ier, the limit cases seem to be equivalent to non-chatter cases, however, in Irms, Istd and Nstd, the limit chatter cases seem to be situated mostly in between chatter cases and non-chatter cases.

Instantaneous Chatter Detection Using Linear and Non-linear Classification

The objective of this section is to assess the potential of the selected features for instantaneous chatter detection. Thus, in this section, the features are computed along a sliding window on the internal sensor signals. This allows continuous monitoring over the course of the whole signal (not limited to the FI zone as in the previous section). The chosen window has a width of 20 data points, corresponding to 0.5 s. To evaluate the efficiency of this method, the features are compared to a reference chatter state. In this section, the reference state is defined using the chatter start and end times determined in Section "Experimental identification of the chatter phenomenon" using the accelerometer. An example of the computed sliding window feature and reference chatter state is presented in Fig. 8 for experiments 7 and 9. In this figure, I represents the spindle current signal, Istd represents the sliding window feature, the chatter start and end times are represented by the red lines and the chatter state is represented by the green and red markers on the feature signal.

Fig. 8
figure 8

Instantaneous chatter identification

Full size image

For the present analysis, the data is divided into two classes, “chatter” and “non-chatter” where the limit chatter cases considered previously are labelled as “non-chatter” and the current overrun cases are not considered for the evaluation of the method. The data treatment resulted in a total of 37,288 feature points, including 6025 points with chatter and 31,263 points without. This labelling method leads to an important number of overlapping points between the two classed as can be observed in Istd in Fig. 8.

Two classification methods are compared: a linear method, where thresholds are identified for each feature individually, and a non-linear method, where a C-SVM model is trained using all four features simultaneously. In the first method, the classification success rate of the stable and unstable cases is calculated for many threshold values. The best threshold value is then determined at the point where classification success is equal for both the stable points and chatter points, as illustrated in Fig. 9.

Fig. 9
figure 9

Method to empirically determine the best threshold for an individual feature

Full size image

The Table 2 summarises the threshold values and the success rate of the classification for each feature.

Table 2 Empirically derived thresholds and success rate for individual features
Full size table

Hence, the classification is overall quite successful using the linear method. The Istd feature is the most effective while the other features are quite similar in performance.

To optimise the boundary between the different classes, a C-SVM model was trained using sequential minimal optimization in the MATLAB environment. The model uses a radial basis function kernel to fit the data. For training the model 3000 points were randomly selected from both the chatter class and the non-chatter class. Thus the number of points taken from both classes is equal in order to limit the model bias [29]. An example of the C-SVM method which is calculated on two features only is displayed in in Fig. 10, where “sv” represent the support vectors which are used to compute the boundary, which is displayed as a black line. In this example, the chatter cases have a classification success rate of 93.2% and the non-chatter cases of 91.3%.

Fig. 10
figure 10

Optimal class identification using the C-SVM method

Full size image

However, when all four features are used together to train the C-SVM model, the success rate reached is 98% for the chatter points and 95% for the non-chatter points. Thus, the boundary between classes is much better defined. This shows that multiple features can be used together in a complementary fashion to increase the effectiveness of the model predictions for chatter detection.

Concluding Remarks and Perspectives

This article presents a chatter identification method using only low-frequency internal sensors of a numerically controlled mobile milling machine. The study focuses on a surface milling operation utilizing a single tool and material combination. Numerous operations are carried out at different spindle speeds, cutting depths and feeds per tooth. For each operation, vibrations are monitored using a high-frequency accelerometer placed on the machine head and chatter is diagnosed by a visual inspection of spectrogram diagrams calculated on the measured signals. Feature selection is carried out by doing a comparative analysis of the chatter state and many different feature values calculated on the FI zone of the internal sensor signals. Different time domain statistical features are calculated, and four features are selected as being the most efficient discerning chatter cases from non-chatter cases. The features are then applied in an instantaneous chatter identification process. Two methods for chatter classification are considered, a linear classification method based on empirically defined thresholds and a nonlinear SVM method which is trained on the feature data. The nonlinear method is shown to be overall more effective for classification of the data, resulting in a good agreement between chatter detection using the internal sensors and the accelerometer. The results are applicable to the specific mobile milling machine and are shown to be effective over a wide range of parameters. Generalization of the proposed method to other similar types of machines and validation of the method in on-site conditions is a topic which will be addressed in future work.