Chatter identification in end milling process based on EEMD and nonlinear dimensionless indicators

Highlights

• An effective chatter identification method is presented for end milling process.

• The self-adaptive decomposition method EEMD is more suitable for chatter analysis.

• Two nonlinear dimensionless indicators are calculated for chatter identification.

• The indicators are independent of cutting parameters for chatter identification.

Abstract

Vibration analysis is widely used to reveal the fundamental cutting mechanics in machining condition monitoring. In this work, vibration signals generated in different chatter conditions as well as stable cutting are studied to understand chatter characteristics. Considering the nonlinear and non-stationary properties of chatter vibration in milling process, a self-adaptive analysis method named ensemble empirical mode decomposition (EEMD) is adopted to analyze vibration signals and two nonlinear indices are extracted as chatter indicators. Firstly, the vibration signal is preprocessed with a comb filter to eliminate the interference of rotation frequency, tooth passing frequency and their harmonics. Secondly, EEMD is applied to decompose the filtered signal into a set of intrinsic mode functions (IMFs). Sensitive IMFs containing rich chatter information are selected. With the development of chatter, an accumulation phenomenon appears in the spectrum of sensitive IMFs and chatter frequencies are modulated by the rotation frequency and tooth passing frequency. Finally, two nonlinear dimensionless indices within the range of [0, 1], i.e., C₀ complexity and power spectral entropy, are extracted from the sensitive IMFs in both time domain and frequency domain. The proposed method is verified with well-designed cutting tests. It is found that, the stochastic noise dominates in the sensitive IMFs of stable cutting and both the C₀ complexity value and power spectral entropy are the largest; with the increase of chatter severity level, the periodic chatter components dominate gradually and the proportion of stochastic noise decreases, and thus these two indicators decrease.

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.