Scholarly article on topic 'Fuzzy Clustering and Visualization Analysis of Tool Wear Status Recognition'

Fuzzy Clustering and Visualization Analysis of Tool Wear Status Recognition Academic research paper on "Materials engineering"

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{"Tool Wear Status Recognition" / "Fuzzy Clustering" / "Visualization of Clustering" / "Frequency Band Energy Analysis"}

Abstract of research paper on Materials engineering, author of scientific article — Pan Fu, Weilin Li, Liang Guo

Abstract One of the biggest problems in manufacturing is the failure of machine tools which due to loss of surface material in cutting operations. Therefore, an effective diagnosis mechanism is necessary for the tool condition monitoring so that production loss and downtime can be avoided. For this, signals acquired from vibration and force sensors were processed to monitor the status of the tool wear. This paper explores the use of Frequency Band Energy (FBE) analysis and Fuzzy Clustering (FC) techniques for tool wear status recognition in metal cutting. In the first stage of the proposed scheme, FBE based on wavelet packets decomposition is performed on cutting vibration and force signals measured on the CNC machine tools. The different stages of tool wear can enhance or inhibit the effect of different frequency components. It made the extracted features sensitive to tool wear. The recognition method for tool wear status was studied through Fuzzy C-means clustering system. In order to examine the performance of clustering results, Visualization of clustering is mapped by principal component analysis (PCA). Experimental results have shown that this approach is a superior and effective method for tool wear status recognition.

Academic research paper on topic "Fuzzy Clustering and Visualization Analysis of Tool Wear Status Recognition"

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Procedía Engineering

ELSEVIER

Procedía Engineering23(2011) 479 - 486

www.elsevier.com/locate/procedia

2311 International Conference or Power Electronics aed PegcEddrceg Application

(PPPA 2211)

Fuzzy Clustering and Visualization Analysis of Tool Wear

Status Recognition

One of the bioodst problems in maeufacturieo is the failure of machine tools which due to loss of surface material in cutting operations. Therefore, an effective diagnosis mechanism is necessary for the tool condition monitoring so that production loss and downtime can be avoided. For this, signals acquired from vibration and force sensors were processed to monitor the status of the tool wear. This paper explores the use of Frequency Band Energy (FBP) analysis and Fuzzy Clustering (FC) techniques for tool wear status recognition in metal cutting. Ie the first stage of the proposed scheme, FBP based or wavelet packets decomposition is performed or cutting vibration aed force signals measured or the CNC machine tools. The different stages of tool wear car enhance or inhibit the effect of different frequency components. It made the extracted features sensitive to tool wear. The recognition method for tool wear status was studied through Fuzzy C-meaes clustering system. Ie order to examine the performance of clustering results, Visualization of clustering is mapped by principal component analysis (PCA). Pxperimeetal results have showe that this approach is a superior aed effective method for tool wear status recognition.

© 2311 Published by Plsevier Ltd. Selection aed/or peer-review under responsibility of [rame organizer]

Keywords: Tool Wear Status Recognition, Fuzzy Clustering, Visualization of Clustering, Frequency Bard Peergy Analysis.

1. Introduction

Monitoring of the tool wear status is very crucial to assure the reliability aed safety of the unmanned manufacturing systems employing cutting processes. Cutting tool wear affects the quality, efficiency aed production safety directly. How timely aed efficiently to monitor tool wear has become ae important problem which reeds to be solved.

* Corresponding author. Tel.: +86-13678138591; fax: +86-87631164 E-mail address: hiweilie@gmail.com.

Par Fua, Weilie Lib, Liaeg Guo,a*

a,b Mechanical Engineering Faculty, Southwest Jiaotong University, Chengdu, China

Abstract

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.2534

A considerable amount of research has been carried out before for the development of effective tool wear monitoring techniques. Sensors and sensor systems for these techniques can be categorized into two main groups: direct and indirect methods. Direct methods require direct measurements from the tool, while the indirect methods utilize cutting parameters such as force, vibration, acoustic emission and power measured during the cutting process [1]. Direct measurement has a high degree of accuracy. However, many direct methods can only be used as laboratory techniques. This is largely due to the practical limitations caused by access problems during machining, illumination and the use of cutting fluid. Indirect methods are also less complex and more suitable for practical applications and online monitoring [2]. In this paper, the cutting vibration and force were measured.

Cutting force and vibration signals can be changed by other cutting conditions, such as the hardness of material, cutting inequality, and the length of the workpiece. Therefore, the actual cutting signals are affected by many cutting factors. Using the general frequency analysis is very difficult to extract the tool wear information [3], [4]. It is well known that the energy of fault signals has great difference from the normal signals in certain frequency bands. It can increase or reduce. Therefore, the signal energy in these bands contains a wealth of fault information. The changing of one or a few FBE can represent some kinds of fault status. This paper decomposes these signals in different frequency bands by wavelet packet analysis, and verifies its effectiveness.

The cutting operations are a gradual process from normal to abnormal, which has shown ambiguous in many cases. Fuzzy mathematics just provides a new way to solve the problems of fuzziness. Fuzzy clustering analysis based on fuzzy mathematics can categorize and identify the fuzzy state samples by determining the affinities between those samples [5], [6]. Compared with artificial neural networks, it can form the actual general (inductive) system from a large quantity of objective information. This system does not rely on expert experience and other subjective evaluation. Therefore, it can improve the efficiency of pattern recognition. We can resolve the ambiguity problem of tool wear by FCM (Fuzzy C-means) clustering algorithm.

It is impossible to map the high-dimensional data on plane X-Y. The clustering space of tool wear features is a high-dimensional space. The clustering result can be shown in the classification-matrix and centers matrix, which can be mapped. This paper researched the visualization of multidimensional classification by principal component analysis (PCA) which can project the n-dimensional clustering into 2-dimension and 3-dimension.

2. Theory of Wavelet Packets Transform and FBE Features

2.2. Wpvalat Ppakats Tepasfoem.

In the multi-resolution analyzing process, time-frequency windows with different scales have different shapes. When the scale is small, the frequency resolution is low. But when the scale is big, the time resolution becomes low. Wavelet packets method is a finer orthogonal method based on multi-resolution processes. It can choose frequency band flexibly according to characters of error signals to determine signal resolution for different frequency bands.

When ju0 (x) = ((x), /U1 (x) = y/(x), there is a double scaling relation between the scaling function ((x) and the wavelet function y/(x) [7]:

M2 n (x )=£h (k )Vn (2 x " k )

M2 n+1 (x )= I g (k )Mn (2 x " k )

k = -»

The defined Mn (x), n e z is called orthogonal wavelet packet of orthogonal scaling function m0 (x) = (p(x).

2.2. Froquoncy Band Energy Foaturo.

Applying wavelet packets analyzing technique, the signal can be orthogonally decomposed onto independent frequency bands and onto arbitrarily fine frequency bands in none-redundant and none-oversight way. Energy statistics on these frequency bands can form feature vectors. Analyzing changes of energy ratios on corresponding frequency bands, cutting tool wear states can be effectively reflected.

The applied wavelet packets decomposition is an orthogonal decomposition, and the following relation exists [8]:

2k-1 t > \ 2k-1 , . 2k-1 , . En (x(( ))= IX fem )= IX ((2k+m )= IX ((k (i)) (2)

m=0 m=0 m=0

Here, En (°) represents signal energy. In the wavelet packets decomposition on j level resolution, xk,m (i) represents discrete signal of on x2k+m sub-space.

Assuming the length of original signal is N, the data length of the discrete signal xk,m (i) in decomposition frequency band decreases to 2-k N . Its energy can be expressed as:

2-kN -1 1=1^ v"

a- (xk m ))=i-kjv^T I ( ^ )

Here, k is the decomposition number, m = 0,1,2, •••,2 , is the sequence number decomposition frequency.

3. Theory of Fuzzy C-means Clustering Algorithm

Fuzzy clustering analysis allows a data vector to be a member of many clusters with different degrees of membership at the same time.. This paper focuses on the fuzzy c-means algorithm which uses cluster centers and Euclidean distance function [9], [10].

First of all, in this method, a number of cluster centers are selected randomly and the fuzzy membership to certain cluster center is assigned for all the dates. And then the cluster center is revised constantly by iterative methods. In the process of iterative, the weighted sums of minimizing distance between all the points to each cluster center and the membership values is used as the optimization objective. Iterative process is end when reaching the maximum iteration number or the decrease degree of the objective function value in two iterations is less than the given minimum increment.

On the mathematical level, fuzzy C-means clustering is to find the fuzzy dividing matrix U = [u ik]c x n ^at makes clustering objective function J minimum and the clustering center P.

Objective function J is calculated as [11]:

Jm (U, P) = Z Z (Mik)m(dikr (4)

2k = 1=1

Where, (d[k) = \xk - Pi is the distance between the two vectors xk and p^ , xk is the k th samples of data, pi is the i th clustering prototype, i = 1, 2,..., c; k = 1, 2,..., n, m e (l, ro)is weighting exponent, the objective function J is the square sum of the weighted distance between a variety of data and the corresponding cluster center.

4. Visualization of Clustering

In order to examine the performance of the proposed clustering methods about, the visualization of multidimensional classification must be researched. Cause of the too many data points there is no use to show the partition matrixes in tables, so the results of the n-dimensional clustering was projected into 2-dimension, and the 2-D results were plotted. This paper focused on the Principal Component Analysis mapping method for the visualization of the clustering results.

PCA involves a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables called principal components. The covariance matrix of the data set (also called the"data dispersion matrix") is defined as follows [12]:

F=N (- xk )xk- v )T (5)

This mapping uses only the first few q nonzero eigenvalues and the corresponding eigenvectors of the Fi = UiA{Uf covariance matrix, decomposed to the Ai matrix that includes the eigenvalues of Fi in its diagonal in decreasing order, U i matrix includes the eigenvectors corresponding to the eigenvalues in its columns. The vector yi k = WiT (xk) is a q-dimensional reduced representation of the observed vector xk , where the Wi weight matrix contains the q principal orthonormal axes in its

column Wt = Ut q A2 q .

5. Tool Wear Monitoring Experimental Platform

Experiments are carried out on the CK6143 machining center. The tool wear monitoring system is composed of an accelerometer, data-acquisition devices and a micro-computer. Fig.1 is the picture of sensors installation. Fig.2 is the picture of worn cutting tool.

Figurel. Picture of sensors installation

Figure 2. Picture of worn cutting tool

The experimental material is 45 steel. The cutter material is YT15. The cutting form is symmetrically milling and the cooling fluid wasn't used. The tool wear are 0.0mm(new), 0.08mm ~ 0.1mm(mild wear), 0.15mm ~ 0.17mm(moderate wear), and 0.25mm ~ 0.27mm(severe wear). The sampling frequency is 100 kHz. The length of sampled data is 100000. The experiments were performed at three working conditions. Their cutting velocity, cutting feed and depth respectively are as follows: (500r/min, 0.5mm/r, 0.5mm), (1000r/min, 0.5mm/r, 1mm), and (1500r/min, 0.8mm/r, 1.5mm).

6. Band Energy Feature Extraction of Tool Wear Status

By analyzing the power spectrum of vibration signals, chose 6-layer wavelet packet to decompose the vibration signals. Calculate the energy features for the 64-band obtained by 6-layer wavelet packet decomposition. Take the vibration signal of Z direction as an example; get the front 16 normalized energy features of each wear state. The data are listed in Table 1, which have two samples in each state.

By analyzing the power spectrum of cutting force signal, it can be shown that the sensitive frequency band for tool wear is below 1000 Hz. Based on characters of some common wavelet basis, db4 wavelet is adopted and the decomposition layers are 4 in the wavelet analysis process. The method of FBE based on wavelet packets is applied to extract features.

Table 1. FBE features of Z direction vibration signal

Band No FBE Features

No. New (0.08~0.1)mm (0.15~0.17)mm

1 0.0146 0.0137 0.0144 0.0133 0.1144 0.1219

2 0.0923 0.0891 0.1028 0.1101 0.1142 0.1331

3 0.1440 0.1360 0.1686 0.1624 0.0036 0.0037

4 0.0814 0.0832 0.0984 0.0930 0.0240 0.0227

4 0.1427 0.1480 0.1638 0.1668 0.28213 0.3048

6 0.0919 0.1142 0.1264 0.1188 0.1128 0.1181

7 0.1196 0.1040 0.1111 0.1103 0.1704 0.1448

8 0.0603 0.0819 0.0931 0.0868 0.3131 0.2904

9 0.0043 0.0043 0.0044 0.0039 0.4930 0.4077

10 0.0336 0.0346 0.0249 0.0249 0.6468 0.6400

11 0.2222 0.2463 0.2694 0.2411 0.1144 0.1219

12 0.1488 0.1494 0.1234 0.1298 0.1142 0.1331

13 0.1414 0.1808 0.1779 0.1924 0.0036 0.0037

14 0.2647 0.2440 0.3161 0.3003 0.0240 0.0227

14 0.4474 0.4419 0.4690 0.4897 0.2821 0.3048

16 0.7313 0.7264 0.6661 0.6633 0.1128 0.1181

7. Clustering and Visualization Analysis of Experimental Data

In the experiment, collect several groups of data under each working condition to ensure the sufficient and reliability of data. Taking first condition for example, the cluster identification process is as follows:

First of all, form a matrix X for being clustered according to FBE features and set s = 10-4 as the error of objective function. Set c = 4 as the classification number because there are three conditions in

this paper. By FCM algorithm, we can obtain the classification-matrix U by iteration. The data are listed in Table 2. There are three samples in each status, so U is a 4 x 12 matrix.

Table 2. The classification-matrix U

Classification-Matrix U

0.118 0.057 0.172 0.783 0.797 0.664 0.188 0.123 0.109 0.064 0.04 0.04

0.731 0.866 0.666 0.052 0.05 0.081 0.032 0.05 0.028 0.052 0.025 0.034

0.069 0.037 0.065 0.039 0.033 0.062 0.063 0.162 0.055 0.787 0.842 0.848

0.082 0.039 0.097 0.126 0.12 0.193 0.717 0.666 0.808 0.097 0.093 0.078

From the classification-matrix, the 1th ,2th,3th row of X are one class ,4th,5th,6th row of X are one class,7th,8th,9th row of X are one class, 10th, 11th, 12th row of X are one class, which coinciding with the actual results ,and the clustering results are correct. At the same time, the cluster centers matrix can be obtained. Considering the length of the paper, the cluster centers matrix isn't be list in this paper.

According to the PCA algorithm before, project the high-dimensional tool wear features into 2-dimension and 3-dimension, and the visualization result of this multidimensional classification is showed

Figure 3. 2-D and 3-D visualization of known samples clustering result

The cluster center obtained can be a standard mode for judging tool wear status. The closeness degree of the new samples to the standard mode can be got, and then determine its class according to the result of closeness degree. Or put the samples into matrix X directly, and make FCM calculation again. Finally, we can get the ownership of the testing sample according to the classification-matrix obtained.

Making the same signal acquisition and processing for severe wear status in the same conditions and get a new sample U1, part contents are as follows:

U1=[0.0096 0.0711 0.1522 0.0982 0.01292 0.1311 0.1264 0.1650 0.0033 ....]

After calculating the closeness degree, what we can get the distance between U1 and cluster centers are: 1.9282, 2.4168, 0.4495, 1.2654, the sample is closest to the third row of cluster centers. So the sample is severe wear, which coinciding with the actual condition.

8. Conclusions

In view of the modulation and ambiguous feature of vibration and force signals of cutting tool, this paper presents a method for tool wear status recognize based on FBE and fuzzy C-means clustering. Firstly, make wavelet packet demodulation for signals and extract FBE features effectively. Finally, make the fuzzy C-means clustering for these features as a classifier, and determine wear status for cutting tool. In order to examine the performance of clustering results, make a 2-D mapping for the higher-dimensional clustering space based on PCA.

The experiment result shows that, FBE based on wavelet packet demodulation is effective for feature extraction in the status recognize of cutting tool. Make it possible for recognizing early stage tool wear. Fuzzy clustering method efficiently identified the wear statuses which include mild wear, moderate wear and severe wear. Also, it is unlike neural networks which need a large number of samples to learn, thus reducing the diagnosis time greatly and can be used for real-time diagnosis. Its PCA mapping is completed to display the real clustering status visually. It is of universal applicability and transplantability and provides a new method for tool wear status recognize.

Acknowledgements

This paper is supported by the Fundamental Research Funds for the Central Universities , SWJTU09ZT06 -- Research of Key Techniques of Digital Designing and Manufacturing of Mechanical Equipments.

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