1.1 High-speed milling and chatter
Production yield is important for CNC machines. One way to increase production yield is by increasing the spindle speed in the milling process. By increasing the spindle speed, the material removal rate is increased proportionally, so is the production yield [1].
However, by increasing the cutting speed, new problem arises. Chatter is a phenomenon caused by the mechanical interactions between the cutting tool and the workpiece. This self-excited vibration [2] causes significant issues in machining, causing large vibrations, which limits productivity and may produce poor surface finish on the workpiece [3] [4]. Fig. 1 shows a comparison of surface finishes between chatter and chatter-free cutting. Fig. 2 illustrates the effect of chip thickness in chatter development.
Vibrations in the cutting process causes variations in chip thickness, and certain combination of spindle speed, feed rate, material, and cutting tool causes the chip thickness to drastically fluctuate like Fig. 2 (c). This is the origin of chatter.
The cause of chatter and its mechanical models are well-studied. The cutting process can be described with as a non-linear system [5], and a stability lobe diagram (SLD) was used to indicate which cutting conditions cause chatter [6]. Fourier series was used to obtain an analytical description of SLDs [7], and was later verified experimentally [8].
Fig. 1. Chatter leaving undesired marks on the surface of the workpiece [9]
Fig. 2. Illustration of how chatter develops due to abrupt change in chip thickness [2]
Many methods were proposed to calculate the SLD, including a previous research using transfer functions [10], and a method using multi-frequency solution [11]. Semi-discretization method was applied to solve the non-linear delayed differential equations describing chatter stability [12], and had been verified as accurate approach for SLD computations [13]. Fig. 3 shows a SLD with spindle speed on the x-axis and depth of cut on the y-axis. The region above the black curve is the chatter region, i.e. any cutting condition above the black curve is unstable.
Fig. 3. An example of a stability lobe diagram [14]
1.2 Chatter detection
The most straightforward way to avoid chatter is to obtain the SLD [15] [16] [17], and avoid cutting in the unstable range. However, several parameters have effects on the SLD, including the vibration modes of the CNC machine, the cutting tool, the material of the workpiece, and the wear of the cutting tool. In addition, cutting force signal is required to calculate the SLD, which typically requires a dynamometer. In this research, we utilize chatter detection methods that do not require a dynamometer.
In the past, many chatter detection methods were proposed using different signal processing methods. FFT of vibration signals were used to calculate the optimal cutting path [18]. FFT can also be calculated every 16 samples for quick detection [19]. Wavelet transform is a signal processing method that was also applied to chatter recognition [20].
Wavelet packet transform (WPT) is an extension of wavelet transform to get better
frequency resolution at certain frequency ranges, and was used in several previous works [21] [22] [23] [24] [25] [26] [27]. R-value was also used to monitor chatter by measuring the spindle drive current [28] [29]. Time domain cutting force signal [30], or its power spectrum density [31] can also be utilized. Hilbert-Huang transform has also been proven effective [32] [33] [34] [35] [36]. Fig. 4 (a) shows an example of FFT spectrum, and Fig.
4 (b) is the intrinsic mode functions (IMFs) decomposed from the time-domain vibration signals. Machine vision was also applied in combination with short-time Fourier transform (STFT) [37], or texture analysis using neural networks [38] [39].
(a) (b)
Fig. 4. (a) Spectrum of the vibration signal after FFT, (b) Intrinsic mode functions (IMFs) obtained from Hilbert-Huang transform [40]
After features are extracted with one of the signal processing methods, some researches set a fixed threshold as the boundary of chatter (unstable) and non-chatter (stable) signals [21] [31] [41] [42] [43]. A classification algorithm may be used to train a
algorithms such as support-vector machine (SVM) [21] [44] [45] [46], k-means [31], local outlier factor (LOF) [47], and artificial neural networks [41] [42] [43] were used in the past and were proven effective. Fig. 5 (a) and (b) shows examples of dataset classified with LOF and SVM, respectively.
(a) (b)
Fig. 5. Illustrations of LOF and SVM
(a) Each data point is assigned a local outlier factor (LOF) and outliers of the dataset can be identified [48]. (b) An illustration of data classified using support vector machine (SVM). The solid lines are support vectors separating the two classes – triangle and circle [49].
1.3 Aim of this research
Despite the large variety of existing chatter identification methods, there are two main issues. The first is that in most researches, the dataset used to validate the proposed method is small, usually consisting of less than 10 cuts. Comprehensive validation was done only in rare cases, e.g. Zhehe Yao, et al. tested their detection method with a dataset
consisting of 45 cuts [21]. Therefore, in most cases, the reader cannot obtain the actual accuracy of the given method, and it is near impossible to compare the effectiveness of different methods. For example, many researches claims that wavelet transform [50] [51], wavelet packet transform [52], or Hilbert-Huang transform [53] is a superior method compared to fast Fourier transform for chatter or machine fault identifications. However, the claims are usually based on a theoretical or empirical argument with little or no statistical evidence provided. We aim to resolve this issue by comparing different signal processing methods using the same dataset and common parameters such as window size.
In fact, as will be shown in chapter 5, some of our findings are completely opposite to such popular claims.
The second issue is that, even if a chatter identification method is tested on a large dataset, and the accuracy is available for comparison, it is unfair to compare the accuracy of two methods from different research teams. This is because the datasets used for validation are different, and some datasets probably consists many data at the boundary of stable and unstable region, and is thus more difficult to classify correctly.
With the rise of industry 4.0, the availability of large amount of data from manufacturing processes should be utilized to help training models in order to improve chatter detection accuracy. In this research, we will take advantage of the cutting data to truly test the signal processing methods and classification algorithms against the entire dataset, with spindle speed ranging from 4500 to 7000 rpm, and depth of cut from 0.2 to 1.0 mm. We believe this approach can help developing a standard procedure to train a model, and evaluate the true accuracy of the model in a fair way.
1.4 Structure of the thesis
This thesis consists of two main topics: feature extraction and classification algorithms. Chapter 2 briefly introduces the signal processing methods that will be compared in this research. Each signal processing method may generate one or more feature(s), and will be further processed by one of the classification algorithms discussed in chapter 3. Chapter 2 and 3 will mainly focus on the concepts, and the implementation details will be described in chapter 4, which is focused on the software implementation and optimizations of some of the algorithms.
Chapter 5 summarizes the results. Data collection procedure for the dataset used in this research is explained in detail. Then, the classification algorithms are compared when using the same feature extraction method. Since there are many parameters involved for each signal processing method, their parameters will be optimized. After optimization is completed within each signal processing method, all of the methods will be compared.
The amount of combination is large, because, for our model training platform developed in this research, any extracted feature can be combined with any classification algorithm.
Finally, since both the error rate and detection speed are critical for chatter detection, we will discuss how they are affected by window size, and the tradeoff involved.
Chapter 6 is the conclusion and we point out the potential direction for future researches. There is an appendix showing all the results from different models we trained which should make comparison easier.