Chatter identification in end milling process based on EEMD and nonlinear dimensionless indicators
Introduction
Chatter is a self-excited vibration accompanied by unstable, chaotic behavior and largely abnormal fluctuations of cutting tool. It arises in machining processes due to specific combinations of cutting parameters such as depth of cut and cutting speeds, imposing negative effects on the productivity because of poor surface quality, dimensional accuracy error, excessive noise, early tool wear, waste of materials and waste of energy [1]. To avoid chatter, conservative cutting parameters are usually selected, which of course becomes one of the main limitations of high productivity. Therefore, timely detection of the chatter onset is essential and crucial in machining process.
Early chatter detection allows operators to interfere in the machining process and avoid chatter damage. Extensive and significant research has been conducted on chatter detection in recent years [1], [2], [3], [4]. Various sensor signals have been used to monitor chatter, such as acceleration signal [5], [6], [7], cutting force [8], [9], [10], sound [11], [12], motor current [13], [14], torque signal [15]. It is worth noticing that Kuljanic et al. [16] designed a multi-sensor system composed of three or four sensors to detect chatter, achieving high levels of accuracy and of robustness against malfunctions. Signals acquired by these sensors are subjected to machining processing with the aim to generate certain features correlated (at least potentially) with machining conditions [4]. Different signal processing methodologies have been employed in time domain [6], [17], [18], [19], [20], frequency domain [9], [21], [22], [23], and time-frequency domain [9], [10], [12], [24], [25], [26], [27], [28], [29], [30], [31], to extract relevant and sensitive features about chatter.
Chatter is a complex nonlinear and non-stationary phenomenon in machining process and the loss of stability in milling process results in different types of bifurcations, including subcritical Hopf and period doubling bifurcations, as well as limit cycles, quasi-periodic and chaotic behavior [32], [33]. Therefore, traditional spectral methods based on Fourier transform is hampered due to the nonlinear and non-stationary nature of chatter signals and noisy spectrum. In addition, both short-time Fourier transform and S-transform are based on Fourier transform theory, which are more suitable for quasi-stationary signal. As for wavelet transform, it is difficult to determine the suitable wavelet base functions and decomposition levels, which have a significant influence on the analysis results.
Empirical mode decomposition (EMD) is a self-adaptive analysis method for nonlinear and non-stationary signals. The EMD method is based on the local characteristic time scales of a signal and may decompose a complicated signal function into a set of complete and almost orthogonal components named intrinsic mode functions (IMFs) [34]. It has been widely used in fault diagnosis of rotating machinery in recent years, for example, rolling bearing fault diagnosis [35], [36] and gear fault diagnosis [37]. Recently, EMD is being used in the area of machining process monitoring. Peng [38] adopted EMD based on time–frequency analysis for the detection of tool breakage in milling process. Raja et al. [39] used the HHT-based emitted sound signal analysis to monitor the tool flank wear. Li et al. [40] used EMD to extract the feature of chatter symptom in boring process. Liu et al. [13] decomposed the motor current signal into IMFs and extracted energy index and kurtosis index based on those IMFs for chatter detection. Cao et al. [41] combined the benefits of wavelet packet transform (WPT) and EMD to extract features according to the Hilbert-Huang spectrum for chatter detection. However, one of the major drawbacks of EMD is the mode mixing problem, which is defined as either a single IMF consisting of components of widely disparate scales, or a component of a similar scale residing in different IMFs [42]. To mitigate the problem of mode mixing in EMD, an improved method called ensemble empirical mode decomposition (EEMD) was presented recently [43]. EEMD is a noise-assisted data analysis method and by adding finite white noise to the analyzed signal, the EEMD method can eliminate the mode mixing problem automatically. Nevertheless, the application of EEMD for chatter detection/identification is rarely reported based on the authors' literature search.
Vibration analysis is widely used in machining condition monitoring to reveal the fundamental cutting mechanics. Due to the nonlinearity and non-stationary characteristic of milling process, EEMD should be a suitable tool to analyze the generated vibration signals during cutting. In this paper, an alternative method based on EEMD and nonlinear dimensionless indicators is proposed for chatter identification. With EEMD, the vibration signal is decomposed into a set of IMFs, and then IMFs containing rich chatter information are selected for feature extraction. Two nonlinear dimensionless indices, i.e., C0 complexity and power spectral entropy, are calculated in both time domain and frequency domain which can be used as indicators to identify the existence of chatter in milling process.
The rest of paper is organized as follows. Brief introduction of empirical mode decomposition and ensemble empirical mode decomposition are given in Section 2. Section 3 introduces two feature extraction methods for chatter identification. Section 4 presents the chatter identification methods in this paper. In Section 5, the experimental setup is described. In Section 6, the results and discussions of the proposed chatter identification method are given. Finally, the conclusive remarks are laid out in Section 7.
Section snippets
Brief introduction of empirical mode decomposition and ensemble empirical mode decomposition
The EMD method is a novel and adaptive decomposition method proposed by Huang et al. [34]. Compared with wavelet transform, EMD is more suitable to analyze nonlinear and non-stationary data because its basis functions are determined by the data itself, while wavelet transform need to select optimal wavelet basis. By EMD, a complicated signal is decomposed into a set of complete and almost orthogonal components IMFs, and a residue. However, one of major shortcomings of EMD is that it is prone to
Feature extraction
After being processed with EEMD, feature extraction method is the most critical step to identify the milling states. The chatter indicator should show the highest correlation to the change of milling condition. Two nonlinear dimensionless features are introduced here, combining the analysis in time domain and frequency domain, respectively.
The proposed chatter identification methodology
The vibration signal in milling process is composed of three parts: the periodic component due to the rotation of the cutter and intermittent milling of the tool, the chatter vibration component due to regenerative effect, and the stochastic perturbation component due to system noise, inhomogeneous material, etc. The key issue of chatter identification is to find out the occurrence of chatter component from the measured signal.
The flow chart of the proposed chatter identification scheme is
Experimental setup
Milling tests were performed on a CNC milling machine to verify the proposed methodology (Fig. 2). The workpiece material was a block of 7050 aluminum clamped on the worktable. The cutter used was a carbide end mill cutter with two flutes. The measurements were conducted with Cutpro-MalDAQ®. Accelerometers were mounted on the spindle housing to measure the vibration signals during milling process. Vibration signals were sampled with a data acquisition card and then transmitted to a PC which was
Results and discussions
The analysis of vibration signals measured in the milling process is carried out in this section.
In order to alleviate the interference of periodic components due to the rotation of the cutter and intermittent milling of the tool, a comb filter is used. Then, the EEMD method is applied to the filtered signal and sensitive IMFs are selected according to the relative energy ratio of each IMF. The two chatter indicators are calculated based on the sensitive IMFs.
Conclusion
In this paper, a new chatter identification method for the end milling process is presented. The vibration signals are decomposed with the EEMD method in a self-adaptive way, which avoids the interfering of operators. The sensitive IMFs that contain abundant chatter information can be selected according to the energy distribution of all IMFs. With the increase of chatter severity level, the frequency components present an accumulation phenomenon and eventually locating at near the system
Acknowledgments
The authors would like to acknowledge the support of Professor Yusuf Altintas from the Manufacturing Automation Laboratory (MAL), The University of British Columbia, for his support throughout this work. All the experiments of this paper were carried out in MAL. This work is jointly supported by the National Natural Science Foundation of China (No. 51421004 ) the National Science and Technology Major Project (2014ZX04001-191-01) and Fundamental Research Funds for the Central Universities.
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