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International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), International Journal of Production Technology ISSNManagement (IJPTM), ISSN 0976 – 6383(Print) IJPTM and 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME ISSN 0976 – 6391(Online) Volume 1 Number 1, January- February (2011), pp. 56-64 ©IAEME © IAEME, http://www.iaeme.com/ijptm.html DETECTION OF CHATTER IN TURNING USING RECURRENCE PLOT ANALYSIS OF INPUT CURRENT, VIBRATION OF TOOL AND SPECKLE IMAGE OF MACHINED SURFACE Jacob Elias Narayanan Namboothiri V.N Division of Mechanical Engineering, School of Engineering, Cochin University of Science and Technology, Cochin, Kerala-682022, India Rajesh V.G Model Engineering College, Thrikkakkara, Cochin, Kerala – 682022, India ABSTRACT Metal cutting is complex nonlinear dynamical process. Cutting signals from turning operation exhibit a low dimensional chaos. When the depth of cut increases, with all other cutting parameters remaining constant, creation of chatter occurs. A recurrence plot based methodology is used to find the point of transition from normal cutting to chatter cutting. In this method two signals, one input signal (current) and one output signal (tool vibration) are recorded simultaneously at a constant sampling rate. A time series is generated from the recorded values and recurrence plot is prepared for the input signal and the output signal. This recurrence plot can be quantified using Recurrence Quantification analysis (RQA). Variations in the roughness of machined surface created by virtue of chatter, manifests as changes in the statistical properties of speckle images of the surface when examined frame by frame along the axis of the machined part. A significant parameter of such images, the frame wise average intensity value is extracted separately and arranged in sequence for constructing the time series. Since this time series is found to be non-stationary in nature, the nonlinear time series analysis methodology of RQA is used for analyzing the time series. The result obtained is compared to that of recurrence plot methodology. The experiment is repeated with different work piece materials. The present study ascertains that this methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the work piece material and the type of signal. Keywords: Cutting signals, Recurrence Plot, Speckle image, Time Series Analysis 56 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME 1. INTRODUCTION Machining vibrations, also called chatter, correspond to the relative movement between the work piece and the cutting tool. The vibrations result in waves on the machined surface. This affects typical machining processes, such as turning, milling and drilling, and atypical machining processes, such as grinding. Chatter results in poor surface quality, unacceptable inaccuracy excessive noise, tool wear, machine tool damage, reduced metal removal rate waste of materials and waste of energy. A new method called recurrence plots (RP), based on nonlinear data analysis has become popular in the last decade. It is relevant for short, noisy and non-stationary data. These features are indeed the crucial advantage of RPs. As deduction of information by visually examining the RPs is more subjective, it was then developed into recurrence quantification analysis (RQA). Here the number and duration of recurrences of a dynamic system presented by its phase space trajectory are quantified. The Features extracted from the RPs by RQA, contain information about the system. These features are called the RQA variables and it can be used for characterizing a dynamic system. In the present work, the RQA methodology has been used in the analysis of an input signal (current) and an output signal (vibration) for machining mild steel. The signals are captured in a lathe under specified conditions of chatter, and investigated the sensitivity of the extracted RQA variables to the transition from chatter free to chatter cutting that had taken place during the process. It has been reported by Jacob et. al [1] that by carrying out RQA analysis on the input signal, the point at which the onset of chattering began could be determined. The abrupt changes that are seen in various RQA variable values are suggestive of the onset of chatter. In this paper the possibility of doing the same with an output signal and comparing it with the input signal is explored. 2. MATERIALS AND METHODS 2.1 Experimental Setup An MS rod of 30 mm diameter is used as the test specimen in the present study. This is converted into conical work piece with small end diameter of 20 mm and the larger end diameter of 30 mm which has 150 mm axial length. The cutting has been carried out in a heavy duty lathe of PSG make. The work involves reducing the tapering section into a rod of 20 mm uniform diameter in a single pass of the cutting tool. A CNMG 120408PM cutting tool with standard tool holder is used for this purpose. A feed rate of 0.1mm/rev. at 360 rpm are set as the fixed cutting parameters whereas the depth of cut steadily increases along the axis of the specimen at a constant rate owing to the geometry of the section; the depth of cut varying from 0 mm to the maximum of 10 mm at the 150 mm axial distance from the smaller end (Figure 1). 57 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME Figure 1 Test specimen With the continuous increase in depth of cut a progressive reduction in surface finish is expected due to increase in chip thickness. Keeping the spindle speed and feed rate constant the chatter is to begin at some increased depth of cut or chip thickness. When the chatter has begun, a drastic reduction in surface finish must result due to non-uniform chip thickness. During the experiments two sensors are used. One is a lathe drive motor current sensor and the other is an accelerometer for picking tool vibrations. The sensor measurements are made simultaneously. The data acquisition system for drive motor current uses a 3 phase line current sensor to measure the current drawn by the lathe drive motor. The sensor consists of a current transformer (CT) having an output range of ±5 volts. The analog voltage signal from the output of the CT is sent to DAC NI PCI 6221 through NI SHC68-68-EPM and SCB 68 for converting it to the digital domain. The sampling rate is fixed at 500Hz which guaranteed that the whole frequency domain contained in the signal is covered. The digitized data is recorded in the PC hard drive using NI LabVIEW. Figure 3 shows the set up for current measurement. Using this setup a time series of the input current is obtained. Figure 2 Experimental set up used for Figure 3 Experimental set up used for drive motor current recording speckle image recording 58 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME An ADXL-150 accelerometer sensor is used to pick up the vibration of the cutting tool. It is placed on the tool holder near its tail end to measure vibration in the feed direction. The resulting output voltage signal, due to vibration, is amplified and passed through a low pass filter having a cut-off frequency of 1 kHz. Here the sampling rate is fixed at 10 kHz. The data acquisition system for vibration signals used a different channel of the same DAC NI PCI 6221 and similarly other peripherals along with NI LabVIEW. Another time series with vibration is obtained from this. The variations in the surface finish are recorded in speckle images captured in sequence from point to point along the axis of the rod. Speckle photographs of the machined surface are taken using Helium -Neon laser with a maximum of 10mW power out at 633nm. A spatial filter lens of 10mm focal length and 25µ pinhole size were used in conjunction with it. The spatial filter output was collimated using an objective lens of 5cm focal length. The laser beam after filtering and collimation fall over the machined surface at an angle of 45 degrees. The incident light which scatters off the surface has been focused using a lens of focal length 10cm and the resulting subjective speckle pattern was recorded. A Sony make Charge Coupled Device (CCD) array of VGA type, 1/3 inch, with 8bit mono recording and with 7 micrometer pixel size is used in the recording. The exposure and the gain of the CCD were adjusted to ensure that the recorded intensity lies well below the saturation value. For obtaining the maximum contrast speckle pattern the position of the focusing lens and CCD array was adjusted. The light distribution on the CCD was viewed through an IBM compatible computer. Keeping the laser source position fixed, the machined sample was moved horizontally along its axial direction in short steps with pauses in between using a micro-translator. The test specimen axis and the line of the laser beam were designed to be contained in the same horizontal plane so that effects due to the surface curvature are minimized. The test specimen movement and the capturing of the speckle images are synchronized using Motion Control and NI Vision Development Module software through PCI 6221 DAQ Card. The speckle images of 480 x 640 sizes with 0 to 255 gray levels recorded at a rate of one for each pause of micro translator. They were stored in a personal computer hard disk for later processing. The speckle images of the surface were taken for the entire axial length. The experimental set up used for speckle image recording is shown in Figure 3. 2.2 Time series construction The recorded speckle patterns have been statistically analyzed to obtain some significant parameter, which would vary with the surface roughness. It has been already established that the parameters contrast ratio and surface roughness has an inverse relation between them. [3] In the present study, the mean gray level value of the histogram of the speckle is taken into consideration as it denotes the intensity of the speckle. The mean grey level of the histogram is defined as ∑ 255 i =0 i f yi µ= (1) ∑ 255 i =0 fi Where f i is the number of pixels having yi gray levels 59 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME The mean gray level values of all the speckle images have been calculated and arranged as per the order of capturing to get a spatial time series for offline analysis. The so obtained time series is further analyzed for recurrence and subsequent quantification. In this following section, the approach used in the study has been described which is based on phase-space reconstruction, the recurrence plot, and the recurrence- quantification analysis. 2.3 Phase space reconstruction Delay coordinate reconstruction is the standard first step in most non-linear time series analysis algorithms and proceeds by forming the multidimensional state space trajectory of the signal. Takens [4] proved a theorem that is the firm basis of the methodology of delays. Since only one variable is considered at a time, the delay coordinate approach is used in the present analysis. Given a time series x(1), x(2), x(3),..........x(N) one can define points X (i) in an m -dimensional state space as X (i) = [ x(i), x(i +τ ), x(i + 2τ ),.......x(i + (m −1)τ )] (2) for i = 1, 2,3,...., N − (m − 1)τ where i are time indices, τ, a time lag and m represents the embedding dimension. Time evolution of X (i) denotes a trajectory of the system, and the space, which this trajectory evolves in, is called the phase space. The parameter τ plays an important role in proper reconstruction of phase space and had been carefully chosen. After the transients were over, the evolution of the trajectory of the system settled typically near a subset of an m-dimensional space and is named as an attractor [5]. 2.4 Selecting the minimum embedding dimension The purpose of the time-delay embedding was to unfold the trajectory in a sufficiently large state space. If the embedding dimension had been too low, some neighbor points might be close to each other due to the projection from some higher dimension down to their lower dimension. Whereas, a too high an embedding dimension could lead to excessive computation during evaluation of parameters. As Franca and Savi [6] indicates, the method of false nearest neighbors is insensitive to noise; it is utilized here for the determination of the embedding dimension. By checking the neighborhood of points embedded in projection manifolds of increasing dimension, the algorithm eliminates 'false neighbors'. This indicates that points apparently lying close together due to projection have been separated in higher embedding dimensions [7]. A natural criterion for catching embedding errors appears to be the increase in distance between two neighbored points is large when going from dimension m to m+1. This criterion has been stated by designating as a false nearest neighbor any neighbor for which the following is valid. 60 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME 1/ 2 Rm+1 (i, r) − Rm (i, r) 2 2 x(i + mτ ) − x(ir + mτ ) 2 = > Rtol (3) Rm (i, r) Rm (i, r) Here i and ir are the times corresponding to the neighbor and the reference point, respectively. Rm denotes the distance in phase space with embedding dimension m and Rtol is the tolerance threshold. 2.5 Selecting the time lag For choosing the time lag, τ, in the present study, the non linear correlation function of average mutual information is used, which, again as Franca and Savi [8] indicates, has no noise sensitivity. Fraser et. al [9] have established that delay corresponds to the first local minimum of the average mutual information function I (τ ) which has been defined as follows. P(x(i), x(i +τ )) I (τ ) = ∑P(x(i), x(i +τ ))log 2 P(x(i))P(x(i +τ )) (4) where P( x(i)) , is the probability of the measure x(i) , P( x(i + τ )) is the probability of the measure x(i + τ ) and P( x(i), x(i + τ )) is the joint probability of the measure of x(i) and x (i + τ ) . Plotting I (τ ) versus τ makes it possible to identify the best value for the time delay, this is related to the first local minimum The time lag value is located at the first local minimum of the average mutual information function and it is selected as 7. The embedding dimension is selected by false nearest neighbors algorithm to be 6. 3. PROCEDURE 3.1 Analysis based on Recurrence Plots A recurrence plot is a way to visually investigate the multi dimensional phase space trajectory through a two-dimensional representation. Recurrence of states of the system, in the meaning that states are arbitrarily close after some time, is a well-known property of deterministic dynamical systems and is typical for nonlinear or chaotic systems. An RP has been derived from the distance plot, which is a symmetric NxN matrix where a point (i, j ) represents some distance between coordinates X (i ) and X ( j ) on the phase space trajectory. Thresholding the distance plot at a certain cut-off value transforms it into an RP which shows all the recurrent points as black spots. In the present analysis recurrence plots are constructed applying L2 norm in distance calculations. The threshold ε has been chosen by analyzing the measure of recurrence point density [10] as percentage of maximum distance. For the time series under study the calculated value of ε is 41. 61 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME 3.2 Recurrence Quantification Analysis The RQA is a tool based on the statistical description of the parallel lines distribution among the RP [11]. Measures of complexity are defined using the recurrence point density and diagonal line structures in the recurrence plot. These measures provide a qualitative description of the dynamics underlying the time series that is studied. In the original definition Eckman et al [12] used a fixed number of neighbours for determining recurrences. In the present analysis we use a fixed value for the threshold ε due to which the RP is symmetric across the central diagonal, called the line of identity (LOI). Attention has been focused on the diagonal and vertical structures in the RP since from those stem the recurrence variables or quantifications. As the recurrence plot is symmetrical across the central diagonal, all quantitative feature extractions take place within the upper triangle in the RP [10], excluding the long diagonal, which provides no unique information and lower triangle, and gives only redundant information. Eight statistical values could be derived from an RP using RQA. These are: (1) Percent recurrence (2) Percent determinism (3) Linemax (4) Entropy (5) Trend (6) Percent Laminarity (7) Vmax and (8) Traptime 4. RESULTS AND DISCUSSIONS Turning of the designed conical workpiece can produce chatter and chatter free cutting. Upto certain length the cutting is chatter free and beyond this point onset of chatter occurs. By checking the machined workpiece under a profilometer this can be ascertained from the poor surface finish. The constructed time series obtained from the sequential speckle images (Figure 4) taken over the entire axial length of the test specimen therefore contains this information about chatter-onset and the subsequent chatter-cutting. Using this time series of mean gray level value of the histogram of the speckle, a recurrence plot is constructed with the above chosen parameters for phase-space reconstruction and the threshold radius (Figure 5). The RP axes are in time units. While plotting, a colour scheme is selected to represent different recurrence points that are lying at different radius within the threshold. As it could be seen there is a transition taking place at some point of time, which in our case is a spatial point along the axial length of test specimen. This point could be taken as the location where onset of chatter takes place. A recurrence plot is plotted for the input parameter (current) and output parameter (vibration) from the time series obtained from the current transformer and the accelerometer. 62 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME Figure 4 Time series chart from mean gray level value Figure 5 Recurrence Plot 5. CONCLUSION In the present investigation, recurrence plot prepared for the the input parameter (current) and output parameter (vibration) are compared with the recurrence plot prepared from the speckle images. By carrying out RQA analysis the point at which the onset of chattering began could be determined. The abrupt changes that are seen in various RQA variable values from Epoch No. 60 are suggestive of the onset of chatter. It has been found all except the two RQA variables; Traptime and Laminarity exhibits this trend by producing a sudden change in their values. Hence it can be concluded that any one signal can faithfully reproduce the onset of chatter. The present work is an offline analysis of the sample. It is possible to extent this technique for online detection of chatter. Compared to the conventional chatter detection methods, this method is inexpensive and is a non- contact and non-destructive technique. 63 International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391(Online) Volume 1, Number 1, January - February (2011), © IAEME REFERENCE 1. Jacob Elias, V. G. Rajesh, V. N. 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