011 on-line chatter detection using servo motor current signal in turning

SCIENCE CHINA Technological Sciences

© Science China Press and Springer-Verlag Berlin Heidelberg 2011 tech.scichina.com www.springerlink.com

*Corresponding author (email: [email protected], [email protected], [email protected])

• RESEARCH PAPER • December 2011 Vol.54 No.12: 3119–3129

doi: 10.1007/s11431-011-4595-6

On-line chatter detection using servo motor current signal in turning

LIU HongQi1*, CHEN QingHai1*, LI Bin1,2*, MAO XinYong1, MAO KuanMin2 & PENG FangYu1

1 National NC System Engineering Research Center, Huazhong University of Science &Technology, Wuhan 430074, China; 2 State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science &Technology,

Wuhan 430074, China

Received August 24, 2011; accepted September 16, 2011; published online November 5, 2011

Chatter often poses limiting factors on the achievable productivity and is very harmful to machining processes. In order to avoid effectively the harm of cutting chatter, a method of cutting state monitoring based on feed motor current signal is pro-posed for chatter identification before it has been fully developed. A new data analysis technique, the empirical mode decom-position (EMD), is used to decompose motor current signal into many intrinsic mode functions (IMF). Some IMF’s energy and kurtosis regularly change during the development of the chatter. These IMFs can reflect subtle mutations in current signal. Therefore, the energy index and kurtosis index are used for chatter detection based on those IMFs. Acceleration signal of tool as reference is used to compare with the results from current signal. A support vector machine (SVM) is designed for pattern classification based on the feature vector constituted by energy index and kurtosis index. The intelligent chatter detection sys-tem composed of the feature extraction and the SVM has an accuracy rate of above 95% for the identification of cutting state after being trained by experimental data. The results show that it is feasible to monitor and predict the emergence of chatter behavior in machining by using motor current signal.

chatter detection, current signal, empirical mode decomposition (EMD), support vector machine (SVM)

Citation: Liu H Q, Chen Q H, Li B, et al. On-line chatter detection using servo motor current signal in turning. Sci China Tech Sci, 2011, 54: 31193129, doi: 10.1007/s11431-011-4595-6

1 Introduction

Chatter is a self-excited vibration that occurs during ma-chining operations and becomes a common limitation to productivity and part quality. Chatter occurrence also has several negative effects, such as excessive noise, machine tool damage, disproportionate tool wear, damage of the tooling structure and the spindle bearing, and waste of ma-terials and energy. For these reasons, chatter avoidance is a topic of enormous interest for many researchers who have

focused on the solutions to the problem of chatter. A review of the literature regarding the chatter avoidance finds that there are two main types of strategies: using the lobbing effect and changing the system behavior. The first strategy aims to avoid chatter by situating the machining process in the stable zone of the stable lobes diagram (SLD) [1, 2], and the second strategy is to enlarge the stable zone of SLD by expanding the stability frontier or simply changing the sys-tem behavior [3, 4]. It is found that appropriate control strategy may be designed to avoid the emergence of cutting chatter by adopting controllable stiffness, which relies on

3120 Liu H Q, et al. Sci China Tech Sci December (2011) Vol.54 No.12

the on-line detection of cutting condition. Therefore, on-line chatter detection and identification are the base of the chat-ter avoidance. Combined with tool path optimization [5, 6] and tool positioning strategy [7, 8], chatter can be avoided, the surface quality and the processing efficiency can be im-proved effectively.

For chatter detection, the sensors mostly applied are dis-placement, acceleration, microphones, AE and plate dyna-mometers. In relation to the signal processing, several ana-lytical techniques are mainly applied to feature extraction, including time series modeling, spectral analysis [9] and time-frequency analysis. In addition, several smart pattern classifiers are introduced so far. Table 1 illustrates some researches which have focused on chatter detection. The table is organized to indicate the machining process, meas-ured physical quantities, sensors’ setup, signal processing techniques, chatter classification criteria and the reference.

According to Table 1 and lots of literature related to the chatter detection, these mostly used sensors are difficult to set up. Moreover, some sensors’ setup may affect the ma-chining operations, and they are expensive. Devillez et al. [10] detected tool vibration with eddy current sensors, but they must design a customized tool holder first, that is too inconvenient. Most of the chatter detection methods tabu-lated in Table 1 can only be used in laboratory, and be dif-ficult to use in practical production. Hence, in order that the on-line chatter detection technique can be applied to manu-facturing production, the selected physical quantities should be easily measured and be effectively used to detect chatter.

Nowadays, along with the servo system performance unceasing enhancement, the response speed and sensitivity improve continuously. So drive motor current can reflect the cutting state of machining processes. Many researches have been carried out on cutting force [11] tool-wear and

tool-breakage detection by using current signal, but this paper focuses on detecting chatter occurrence during ma-chining operations by adopting drive motor current. The advantage of chatter detection based on motor current is that it is easy to acquire current signal, the sensors are cheap and convenient to set up, and it can avoid the interference from the cutting environment. So on-line chatter detection based on current signal is conducive to extent of spreading and application of this technique. Soliman and Ismail [15] used ratio of the second moments of the high- and low-frequency components of the spindle current to detect chatter in mill-ing. This method might work well for low spindle speeds. However, because spindle of miller has small inertia, it is mainly suitable for milling.

Because spindle of the heavy duty NC vertical lathe has large inertia, spindle motor current is insensitive to the change of cutting state. However, the feed motor is smart and sensitive to the change of cutting force and cutting state. Accordingly, we can choose the feed motor current signal to analyze and detect chatter.

This paper proposes a novel method for chatter identifi-cation in the turning process. Feed motor current signal is adopted for on-line detection. The feature vector of current signal used for chatter identification is constructed on the basis of empirical mode decomposition (EMD). In addition, acceleration signal of tool is taken as reference and used to compare with the results from current signal. The pattern classification results in terms of current signal are compared with acceleration signal. Subsequently, a support vector machine is designed for pattern classification. After super-vised learning of support vector machine (SVM), an excel-lent performance is achieved for the chatter identification. Figure 1 shows the structure diagram of chatter detection system based on current signal.

Table 1 Summary of chatter detection research

Process Physical quantity Sensor Signal processing Chatter classification criteria Ref.

Turning tool vibrations eddy current sensors spectral analysis of tool micro-movements

number of excited frequencies increases

[10]

Turning cutting forces dynamometer mounted on the slides

CER of the cutting force signals define a threshold of CER, CER below it

[12]

Grinding grinding force AE force sensor under the tail stock, AE sensor on the spindle

entropy and NCIR of force signal and AE’s RMS

define thresholds of NCIR and entropy, high NCIR and low entropy

[13]

Turning tool vibrations Accelerometer mounted on the tailstock

ST of acceleration signal damping index in a narrow band drastically reduced

[14]

Milling spindle current current sensors R-value of the spindle current signal

define a threshold of R-value, R-value above it

[15]

Milling spindle vibrations, cutting forces

accelerometers mounted on the machine head, axial force sensor

wavelet decomposition and calculation of statistical parameters

chatter classification by using a neural network and fuzzy logic

[16]

Turning cutting forces dynamometer under the tool turret PSD of cutting force define thresholds, larger ratio of area of PSD

[17]

Milling tool vibrations accelerometer near tool holder DWT, WTMM chatter index based on WTMM exceeds a threshold

[18]

Boring tool vibrations accelerometer at free end of boring bar

WT of acceleration signal chatter classification based on SVM [19]

Turning sound microphone placed on the compound PE of the audio signals a sharp drop in PE value [20]

CER, coarse-grained entropy rate; NCIR, normalized coarse-grained information rate; ST, s-transform; PSD, power spectral density; DWT, discrete wavelet transform; WTMM, wavelet transform modulus maxima; WT, wavelet transform; PE, permutation entropy.

Liu H Q, et al. Sci China Tech Sci December (2011) Vol.54 No.12 3121

Figure 1 Structure diagram of chatter detection system.

2 Feature extraction based on empirical mode decomposition

2.1 Empirical mode decomposition (EMD)

The EMD method is proposed by Huang et al. [21] as a new signal decomposition method for nonlinear and nonstation-ary signal. It provides an alternative to traditional time- frequency or time-scale analytical methods, such as the short-time Fourier transform and wavelet decomposition. The EMD decomposes a signal into a collection of oscilla-tory modes, called intrinsic mode functions (IMF), which represent fast to slow oscillations in the signal. Each IMF can be viewed as a subband of a signal. Thus, the EMD can be viewed as a subband signal decomposition. Traditional signal analytical methods, such as Fourier and wavelet- based methods, require some predefined basis functions to represent a signal. The EMD relies on a priori known basis, and it depends only on the data itself and is completely un-supervised. Compared with traditional analysis methods, the EMD is intuitive, direct, posterior and adaptive. Due to these special properties, the EMD has been used to address many science and engineering problems [22, 23].

The algorithm to create IMFs is established with the definition of local maxima and minima of the time series of the signal x(t). The local maxima xmax(t) and minima xmin(t) are connected by a cubic spline line to produce respectively upper envelope u(t) and lower envelope l(t). The upper and lower envelopes should meet the following condition:

( ) ( ) ( ).l t x t u t

Here, mean is denoted as m1(t) and is given by

1

( ) ( )( ) .

2m

u t l tt

(1)

The difference between the signals x(t) and m1(t) is the first component, h1(t), i.e.

1 1( ) ( ) ( ).h t x t m t (2)

Ideally, if h1(t) is an IMF, the following definitions must be fulfilled [21, 24]:

(1) In the whole data set, the number of extrema and the

number of zero-crossing must either equal or differ at most by one.

(2) At any point, the mean value of the envelope defined by local maxima and the envelope defined by the local minima is zero.

If h1(t) is not an IMF, then h1(t) is treated as the original signal and repeats the sifting process up to k times, as it is required to reduce the extracted signal to an IMF. Then, hk(t) becomes an IMF, that is

1( ) .k k kh t h m (3)

Then, it is designated as 1 ( ),kc h t the first IMF compo-

nent from the original signal x(t). Some stopping criteria are used to terminate the sifting process. A commonly used criterion is the standard deviation S:

2

1

21 1

( ) ( ),

( )

Tk k

t k

Sh t h t

h t

(4)

where T is the total length of the signal. A typical value for S can be smaller than 0.3.

Separating c1 from x(t), we could get

1 1( ) ,r x t c (5)

where r1 is viewed as the original data, and repeating the above processes, the second IMF component c2 of x(t) could be got. Repeating the process as described above for n times, n-IMFs of signal x(t) could be got. Then,

2 1 2

1

.

n n n

r r c

r r c

(6)

The whole procedure terminates when the residue rn is either a constant, and monotonic slope, or a function with only one extremum. Combining eqs. (5) and (6) yields the EMD of the original signal,

1

( ) .n

j nj

x t c r

(7)

The main characteristic of the EMD method is that it can process nonlinear and nonstationary signal smoothly, and retain data characteristics during decomposition. Conse-quently, the EMD method is used to decompose motor cur-rent signal into a series of different feature scale signals, and get the essential message about cutting state.

2.2 Energy index—energy of IMF

Chatter occurrence during machining operations can lead to the change of cutting forces, and motor current of the CNC can reflect this change brought by chatter. In the proposed method for chatter detection in turning, feed motor current


signal is decomposed into a series of different features scale signals, the variations of IMF’s energy represent the cutting state in machining processes. So we can choose the energy of these IMFs which are sensitive to chatter as the feature values. Feature extraction based on EMD consists of the following main steps:

(1) Sampling current signals by a frequency of 10240 Hz, collecting a segment of data of 1 s for processing, and slid-ing data length by 0.1 s.

(2) Calculation of the root mean square (RMS) of the sampled feed motor current signal is made for converting the AC current to the equivalent DC current and the RMS of feed motor current signal can be calculated by

2 2 2

RMS U V W

1[ ]

3.I I I I (8)

(3) Decomposing the sampled signal into a set of mono- component signals, IMFs, as described in Section 2.1.

(4) Choosing the IMFs which are sensitive to chatter (signal amplitude which is obviously different in chatter is the most crucial).

(5) Calculating the energy of the selected IMFs by

2

( ) d .i iE c t t

(9)

(6) Summing the energy calculated in eq. (9) as the fea-ture value by

.iE E (10)

2.3 Kurtosis index—kurtosis of IMF

Kurtosis is a dimensionless numerical statistic, it can be used to reflect the distribution characteristics of the signal. When there are instantaneous mutations in signals, it will result in higher kurtosis value. Utilizing this characteristic, kurtosis index is usually used for detecting the mutations or transient information in signals. Chatter occurrence will lead to the mutations of drive motor current, and kurtosis index can be used to extract these instantaneous mutations.

Kurtosis coefficient K is a normalized fourth order center distance, and can be represented as

4

4

( ) ( )d,

x t x p x xK

(11)

where x(t) is the instantaneous amplitude of the signal, x is the average value, p(x) is the probability density, and is the standard deviation.

For the discrete signal data, kurtosis coefficient K is:

4

1

1,

Ni

i t

Kx x

N

(12)

where xi is the instantaneous amplitude of the signal, x is

the average value, N is the total length of the signal, and t is the standard deviation.

The kurtosis index K of the motor current signal can be calculated through the same steps described in Section 2.2.

3 Support vector machine

SVM is an effective machine learning method for classifi-cation problems, especially for small sample of training vectors, and eventually results in better generalization per-formance than most traditional methods [25]. SVM maps input vectors into a higher dimensional feature space and one can construct an optimal separating hyperplane in this space. This basically involves solving a quadratic program-ming problem, while gradient-based training methods for neural network architectures on the other hand suffer from the existence of many local minima. A brief review of some basic work on SVM for binary classification problem is given herein. For all the further details we can refer to Vap-nik’s book [26].

First, we review the simplest case, i.e. the linearly separable case. Given a training set of N data points 1{ , } ,N

i i iy x

where nix R is the ith input vector and { 1, 1}iy is

the ith output pattern. There exists a separating hyperplane, the function of which is

0,x b (13)

where nR is a normal vector, the bias b is a scale. Two

parallel hyperplanes can be represented as

1, if 1;

1, if 1,i

i

x b y

x b y

(14)

which is equivalent to

( ) 1, 1, 2, , .i iy x b i N (15)

SVM tries to maximize the margin between two classes, where the margin width between the two parallel hyper-planes equals 2 . Therefore, in a linearly separable case,

one can find the optimal hyperplane by solving the follow-ing quadratic optimization problem:

21

Min , s.t. ( ) 1.2 i iy x b (16)

By introducing Lagrange multipliers ( 1,2, , )i i N

for the constraint, the primal problem becomes a task of finding the saddle point of Lagrange. Thus, the dual problem becomes

1 ,

1

1Max ( ) ( ),

2

s.t. 0, 0.

n n

i i j i j i ji i j

n

i i ii

L y y x x

y

(17)


By applying Karush-Kukn-Tucker (KKT) conditions, the following relationship holds:

[ ( ) 1] 0.i i iy x b (18)

If i>0, the corresponding data points are called support vectors (SVs). Hence, the optimal solution for the normal vector is given by

*

1

M

i i ii

y x

(19)

where M is the number of SVs. By choosing any SVs ( , ),k kx y one can obtain * * .k kb y x After * *( , )b is

determined, the discrimination function can be given by

*

1

( ) sgn ( )M

i i ii

f x y x x b

(20)

where sgn(.) is the sign function. In the linearly non-separable case, the support vector

method approach aims at constructing a classifier of the form:

*

1

( ) sgn ( ) ,N

i i ii

f x y x x b

(21)

where ( , ) is the kernel function. SVM can map input

vector nix R into a higher dimensional feature space,

and can thus solve the linearly non-separable case based on the kernel function. For ( , ) , typically one can have the

following choices:

Linear kernel ( , ) ;i j i jx y x x

(22a)

Polynomial kernel of degree g ( , ) ( ) , 0;g

i j i jx y x x r (22b)

Radial basis function

2

( , ) exp{ }, 0;i j i jx y x x (22c)

Sigmoid kernel

( , ) tanh( ), 0;i j i jx y x x r (22d)

where r, and g are kernel parameters. Unlike most of the traditional methods which implement

the empirical risk minimization principle, SVM implements the structural risk minimization principle, which can even-tually result in better generalization performance. Therefore, in this work, a model of SVM classifier to recognize chatter based on feature vector extracted from motor current signal is proposed.

4 Experimental setup for chatter detection

The schematic diagram of the experimental setup used in

our study is depicted in Figure 2. The experiments are per-formed on a NC Vertical Lathe (VL-850HR+P, Yu Shine Precision Machine Co Ltd, Taiwan, China) with AC per-manent magnet synchronous motors. Based on a tool bar with a diameter of 32 mm and a length diameter ratio of 6, chatter easily emerges due to the low stiffness of the tool bar. In order to detect chatter, three current sensors (CSNF161, Honey well, USA) are used to measure the three-phases current of feed motor: IU, IV, IW. A piezoelec- tric acceleration sensor (356A15, PCB Piezotronics, USA) is placed at the free end of the tool bar to measure the vibra-tion of tool. The material of workpiece is aluminum alloy, and the shape of workpiece is round plate with major di-ameter (540 mm), inner diameter (150 mm), and thickness (25 mm). The clamping of workpiece and setup of accelera-tion sensor are shown in Figure 3. A high speed signal ac-quisition system (LMS Test. Lab, Signature Testing func-tion module) is used to collect acceleration signal and cur-rent signal synchronously. So it is favorable for comparative analysis of acceleration signal and current signal.

A good chatter detection system must be adapted to the variations of the cutting parameters. To evaluate the per-formance of the proposed method, a series of experiments

Figure 2 Schematic diagram of the experimental setup.

Figure 3 Installation of the workpiece and sensor.


have been conducted under different cutting conditions. Table 2 lists the cutting conditions of this work.

5 Experimental results and discussion

5.1 Analysis of feed motor current signal

Figure 4 displays the feed motor current signals and tool vi-bration signals collected at a linear velocity of 150 m min1. The feed speed is 0.1 mm r1 and the depth of cut is 0.5 mm. It can be seen that the amplitude of acceleration signals in-creases sharply during the period of unstable cutting. Meanwhile, the feed motor current signals are seriously distorted. The changes in the feed motor current signature may occur due to chatter. On the purpose of effective rec-ognition of chatter based on current signals, these changes must be extracted. Figure 5 shows the chatter marks and their distribution in workpiece. It can be seen that chatter marks mainly appear in three areas of the workpiece surface

Table 2 Experimental condition

Tool Kentanium; Kr (negative rake)= 95°

Tool bar L (length)=200 mm; dm (diameter)=32 mm

Cutting condition linear velocity 100, 120, 150, 200 m min1, feed rate 0.1, 0.2, 0.3 mm r1, depth of cut 0.1, 0.2, 0.3, 0.4, 0.5 mm

Turning method constant linear velocity and variable spindle speed—without coolant

where stiffness is smaller than other local. And among them, the regional one is badly damaged. From the distribution of chatter marks, we can know that it is coincident with tool acceleration signals during the period of unstable cutting.

The root mean square (RMS) of feed motor signals be-fore and after chatter is shown in Figure 6. The figure shows that during unstable cutting, RMS of the feed motor current signals fluctuates as that of tool vibration shown in Figure 4. And RMS of the feed motor current signals during the steady-state cutting is stable as tool vibration signals during the same period.

5.2 Chatter detection based on current signal

To test the performance of the new detection method, a lot of real machining signals are analyzed. Figure 7 shows 14 components of the IMFs obtained by using the EMD method for feed motor current signals during steady-state cutting (Figure 7(a)) and in the case of chatter (Figure 7(b)). The components are listed from high to low frequency. The last one (res.) is the residue signal and it is a monotonic function and represents the central tendency of the signal.

It can be seen that the amplitudes of IMFs vary from one to another. They demonstrate that lower order IMFs capture fast oscillation modes while higher order IMFs typically represent slow oscillation modes. Lower order IMFs (e.g. c1–c4) contain most of the noise, and they can be easily separated from the data. The higher order IMFs (e.g. c13–c14) have no physical sense and can be removed from

Figure 4 Feed-motor current and tool acceleration signal. (a) Steady-state cut; (b) unsteady-state cut.


Figure 5 Chatter marks and their distribution in workpiece.

the analysis, because their amplitudes are much smaller than other IMFs. Obviously, the first 7 modes are almost similar in the two cutting states and thus they may represent the information about the background signal. From c8 to c12, there are significant differences. These modes fluctuate violently and have higher amplitudes during the period of

Figure 6 RMS of feed-motor current signal for steady-state cut (a) and chatter (b).

Figure 7 Decomposition by EMD of the feed-motor current signal (5–10 s) shown in Figure 6 for steady-state cut (a) and chatter (b).


chatter. So these IMFs contain the main effective informa-tion which is sensitive to the detection of chatter. In order to see the differences between the two cases clearly, Figure 8 shows the instantaneous amplitudes of c9 components. However, the order of the most informative IMFs depends on the length of the data for analysis and the cutting condi-tions. To select these IMFs automatically, different length feed motor current signals under different cutting conditions are analyzed thoroughly. It can be found that if the length of the data for analysis is a constant value, the order of the informative IMFs is in a certain range. The most informa-tive IMFs that indicate cutting state can be selected auto-matically by removing the residual and considering only the components in this range. So the signal to disturbance ratio can be greatly improved.

In order to calculate the energy and kurtosis of the in-formative IMFs, we collect a segment of 1s data for proc-essing with EMD method, and to slide data length by 0.1s. Based on analysis of large quantities data of 1s, the most informative IMFs in the range of c6–c10 are found. Energy index E and kurtosis index K of these informative IMFs can be calculated through the method proposed in Sections 2.2 and 2.3. Figure 9 shows the energy index E and kurtosis index K of feed motor current signal comparing with the standard deviation D of acceleration signal. The current data and acceleration data come from the cutting conditions: linear velocity is 100 m min1, feed rate is 0.2 mm r1, depth of cut is 0.5 mm. It can be seen clearly that chatter occurred at about the 3rd second from the acceleration signal and its standard deviation D. When chatter occurs, the energy index E and kurtosis index K of current signal change abruptly. During the period of steady-state cut, the energy index E and kurtosis index K keep smooth and steady, and at a rela-tively low level. But when chatter occurs, they increase sharply, and become unsteady and variable. So the energy and kurtosis of these informative IMFs can distinguish

Figure 8 Instantaneous amplitudes of c9 components.

cutting state clearly, and the energy index E and kurtosis index K can be used to classify chatter. In order to prove the reliability of these indexes, a lot of real machining signals from different cutting conditions are analyzed. Figure 10 shows the results from other cutting conditions: linear ve-locity is 150 m min1, feed rate is 0.1 mm r1, depth of cut is 0.5 mm. In this analysis the energy index E and kurtosis index K are found to reflect the change of cutting state in time and effectively.

Based on the EMD method, the energy index E and kurtosis index K of feed motor current can construct a feature

Figure 9 (a) Acceleration signal; (b) energy index of current signal and standard deviation of acceleration signal; (c) kurtosis index of current signal and standard deviation of acceleration signal. (Linear velocity 100 m min1, feed rate 0.2 mm r1, depth of cut 0.5 mm).

Figure 10 (a) Acceleration signal; (b) energy index of current signal and standard deviation of acceleration signal; (c) kurtosis index of current signal and standard deviation of acceleration signal. (Linear velocity 150 m min1, feed rate 0.1 mm r1, depth of cut 0.5 mm).


vector [E K] for chatter prediction. Although this method is not based on dynamical model, this vector has a compre-hensive response of the development in time domain and energy spectrum. So it is very applicable to the chatter de-tection and recognition.

6 Chatter recognition based on SVM

The main target of pattern classification is to identify the category of current signal based on the feature vector [E K] by SVM. In this way, we can detect the cutting state effec-tively. A brief review of some basic work on SVM for bi-nary classification problem is given in Section 3. In order to solve the linearly non-separable problem, kernel function was introduced. The idea of the kernel function is to enable operations to be performed in the potentially high dimen-sional feature space rather than in the input space. Hence the inner product does not need to be evaluated in the fea-ture space. This provides a way of addressing the curse of dimensionality. In order to obtain a good classification re-sult, choice of kernel function is also a very important seg-ment. In general, radial basis function (RBF) is a first rea-sonable choice. The RBF kernel nonlinearly maps samples into a higher dimensional space. Unlike the linear kernel, it can handle the case when the relation between class labels and attributes is nonlinear, and the RBF kernel has less nu-merical difficulties [27]. So a RBF kernel was selected for classification. To classify the two patterns, a SVM was con-structed using a MATLAB toolbox—LIBSVM developed by Hsu and Lin [28], a simple and effective support vector machines tool for classification, regression and distribution estimation. For parameter selection, LIBSVM provides a simple tool to check a grid of parameters. Moreover, for multi- classifica- tion, under a given parameter vector (C, ), LIBSVM uses the one-against-one method to obtain the cross validation (CV) accuracy. The parameter selection suggests the same (C, ) for all k(k1)/2 decision functions. LIBSVM is simple, effective, and its faster computational time is a key requirement for on-line chatter identification.

According to tool vibration signals, the states in machin-ing process can be classified into two categories: stable state (Pattern 1) and chatter state (Pattern +1). The feed motor current data are chosen to refer to the tool vibration signals according to the following rules: when the vibration signals have a long-term and low-amplitude smooth cutting, it is considered to be in Pattern 1; when the vibration signals have prodigious amplitude or the rhythm-vibration phe-nomenon occurs, it is considered to be in Pattern +1.

Referring to the tool vibration signals and the rules men-tioned above, 120 section feed motor current signals of two categories were acquired from machining experiments un-der different linear velocities, cutting depths and feed rates. Each pattern had 60 signals. The energy index E and kurto-sis index K for each signal were calculated with EMD

method. The distribution of feature vector [E K] of each pattern is shown in Figure 11. 40 signals of each pattern were taken out from the 120 signals on the purpose of training, and the remaining 20 signals of each pattern were used for test. The training of the SVM was performed in Matlab. The efficiency of the chatter recognition model after training was tested by the input of the 80 training sig-nals and the 40 test signals respectively.

In order to prove the reliability and applicability of the chatter recognition model, experiments were carried out by adopting the method of changing the cutting conditions, such as fixture, workpiece and cutting parameters. 132 sec-tion feed motor current signals were acquired from these experiments to test and verify the chatter recognition model. A total of 6 groups cutting parameters, each group cutting parameter has 22 current signals. Figure 12 shows the dis-tribution of all these feature vectors [E K] of each pattern. Parts of the results are listed in Table 3. It demonstrates that

Figure 11 Distribution of feature vector [E K] of each pattern for training and testing the chatter recognition model.

Figure 12 Distribution of feature vector [E K] of each pattern from new experiments for verifying the chatter recognition model.


Table 3 Pattern classification results of the chatter recognition model

Input No.

E K Output Target Result

Linear velocity (m min1)

Feed rate (mm r1)

Cutting depth (mm)

1 32.7135 2.8227 1 1 correct 130 0.3 0.8

2 28.9705 2.8985 1 1 correct 130 0.3 0.8

3 26.5276 3.2352 1 1 correct 130 0.3 0.8

4 26.2586 2.8605 1 1 correct 130 0.3 0.8

5 290.629 3.1195 +1 +1 correct 130 0.3 0.8

6 284.968 4.1060 +1 +1 correct 130 0.3 0.8

7 234.683 2.9498 +1 +1 correct 130 0.3 0.8

8 380.846 3.1630 +1 +1 correct 130 0.3 0.8

9 433.817 4.0686 +1 +1 correct 130 0.3 0.8

10 20.8446 3.1821 1 1 correct 160 0.1 0.5

11 26.5663 2.9206 1 1 correct 160 0.1 0.5

12 29.0302 3.1026 1 1 correct 160 0.1 0.5

13 18.5127 2.9643 1 1 correct 160 0.1 0.5

14 38.8059 4.0185 +1 +1 correct 160 0.1 0.5

15 53.0238 3.7320 +1 +1 correct 160 0.1 0.5

16 79.1480 4.7464 +1 +1 correct 160 0.1 0.5

17 114.451 5.0388 +1 +1 correct 160 0.1 0.5

18 51.3077 4.2334 +1 +1 correct 160 0.1 0.5

19 22.6092 2.7947 1 1 correct 160 0.2 0.4

20 23.3091 2.8803 1 1 correct 160 0.2 0.4

21 27.4309 2.6593 1 1 correct 160 0.2 0.4

22 24.5725 2.9635 1 1 correct 160 0.2 0.4

23 18.2346 2.5681 1 1 correct 160 0.2 0.4

24 92.7392 3.6702 +1 +1 correct 160 0.2 0.4

25 197.955 3.3718 +1 +1 correct 160 0.2 0.4

26 236.297 3.7305 +1 +1 correct 160 0.2 0.4

27 255.160 4.2908 +1 +1 correct 160 0.2 0.4

28 218.906 4.7624 +1 +1 correct 160 0.2 0.4

29 20.7560 3.0038 1 1 correct 160 0.3 0.2

30 19.1263 2.9321 1 1 correct 160 0.3 0.2

31 16.5012 2.9882 1 1 correct 160 0.3 0.2

32 17.8797 2.9115 1 1 correct 160 0.3 0.2

33 15.5732 3.2661 1 1 correct 160 0.3 0.2

34 46.5545 3.1003 +1 +1 correct 160 0.3 0.2 35 63.0903 3.3704 +1 +1 correct 160 0.3 0.2 36 43.2717 4.2037 +1 +1 correct 160 0.3 0.2 37 49.5488 3.0752 +1 +1 correct 160 0.3 0.2 38 42.4244 3.0221 +1 +1 correct 160 0.3 0.2 39 24.4285 3.0627 1 1 correct 190 0.3 0.2 40 33.7392 2.9987 +1 1 in correct 190 0.3 0.2 41 24.6545 2.9719 1 1 correct 190 0.3 0.2 42 31.4310 3.4046 1 1 correct 190 0.3 0.2 43 23.9407 3.3470 1 1 correct 190 0.3 0.2 44 54.9162 3.4730 +1 +1 correct 190 0.3 0.2 45 51.4100 3.6469 +1 +1 correct 190 0.3 0.2 46 42.2602 3.5756 +1 +1 correct 190 0.3 0.2 47 46.6221 3.3755 +1 +1 correct 190 0.3 0.2 48 45.9620 4.0435 +1 +1 correct 190 0.3 0.2 49 25.9378 2.5628 1 1 correct 220 0.3 0.2 50 29.9697 2.9401 1 1 correct 220 0.3 0.2 51 22.2719 2.9121 1 1 correct 220 0.3 0.2 52 23.1481 3.1567 1 1 correct 220 0.3 0.2 53 34.0250 3.1234 +1 1 incorrect 220 0.3 0.2 54 246.890 3.7628 +1 +1 correct 220 0.3 0.2 55 210.485 5.0534 +1 +1 correct 220 0.3 0.2 56 256.991 7.0680 +1 +1 correct 220 0.3 0.2 57 293.460 5.7599 +1 +1 correct 220 0.3 0.2 58 229.780 9.0551 +1 +1 correct 220 0.3 0.2


most samples have been recognized correctly with an accu-racy rate of above 95%. It can be seen that chatter recogni-tion model based on the EMD method and SVM has an ex-cellent performance for chatter premonition identification, which is robust for different cutting conditions.

7 Conclusion and future work

In this paper, the application of energy index and kurtosis index for the detection of onset of chatter in turning using feed motor current signal was verified. Moreover, an intel-ligent chatter recognition system based on EMD and SVM was investigated. Experiments were conducted under many different cutting conditions. A feature vector [E K] was constituted by the energy index E and kurtosis index K which were extracted from feed motor current signal based on the EMD method. This vector can effectively reflect the change of cutting state in time, and the classification results by LIBSVM indicate that it is suitable for chatter premoni-tion recognition. The system with combination of the EMD’s feature extraction capability and the SVMs pattern classification capability has an accuracy rate of above 95% for cutting states recognition. Additionally, energy and kur-tosis analysis of feed motor current signal is a fairly low- cost, non-contact, and non-destructive technique which en-hances its suitability for on-line detection of chatter without disturbing the machining process. For these advantages, this system for chatter detection can be applied to real-time turning process with the help of suitable chatter suppression methods and control mechanism.

For future work, although the feature value based on EMD of feed motor current signal mentioned above has a good performance, type and parameters of servo system may affect the detection results. It is still a challenge of how to ascertain these effects and eliminate them. Therefore, it is suggested that the following research is to investigate ap-plication of this method for different types of servo system and find out methods to eliminate effects. In addition, the optimum feature vector will be another interesting work in future.

This work was supported by the Major State Basic Research Develop-ment of China (Grant No. 2011CB706803), National Natural Science Foundation of China (Grant No. 50875098), and Important National Science & Technology Specific Projects of China (Grant No. 2009ZX04014-024).

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011 on-line chatter detection using servo motor current signal in turning

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