Chatter Identification of Vibration Signals and Surface Roughness using Wavelet Transform and I-kazTM Methods

The paper describes the method to identify chatter in low-cutting-speed operations. It is based on vibration and surface roughness measurements. Tool chatter is the self-excited relative motion between the cutting tool and work piece. Tool chatter leads to poor surface quality and tool wear. The LMS Scadas testing system and accelerometer were used to measure the vibration signals during the turning operation, and Marsuft Psi was used to measure the surface roughness. When various cutting parameter combinations, such as cutting speed, feed rate, and depth of cut, were employed throughout the machining process, chatter and vibrating phenomena occurred. After the recorded signals were analyzed using the wavelet transform (WT), a chatter index (CI) was produced to determine how severe the chatter was. According to the results analysis, the experimental study demonstrated the close relationship between the surface roughness values and the chatter index when evaluating chatter identification.


Introduction
Both the components of the machine structure and the characteristics of the machining operations influence the stability of the machining process.The machining system's structure and operations impact the included component, tool, and machine, all of which are exposed to machining dynamic loads during the machining process.Machine cutting tool dynamics play a crucial role in establishing the cutting process stability.Chatter results in a poor surface finish, a shorter tool life, and decreased productivity are the outcomes of chatter.Despite extensive research, chatter stability in metal cutting remains a challenge due to the need to consider cutting parameters such as feed rate, depth of cut and cutting speed.The predominant techniques used for identifying chatter in manufacturing processes include the extraction of certain characteristics from acoustic, vibrational, or force signals.These extracted features are then compared to specified markers of chatter or surface roughness values [1].
Kumar and Singh proposed chatter index using wavelet denoising and statistical approach.They mentioned, CI illustrates the importance of a certain set of characteristics in creating chatter during a turning operation.The greater the value of CI, the greater the resulting chatter [2].Chatter is related to surface roughness, and multiple researchers have sought to enhance surface roughness using various ways.Chatter signals were denoised using the WT approach, and a new metric known as the chatter index (CI) was calculated.Furthermore, in order to forecast chatter, ANN and RSM models were built that took into account three cutting parameters: feed rate, depth of cut and spindle speed.Finally, statistical and regression analyses were performed to determine the statistical significance of the suggested models [3].Nuawi proposed an integrated kurtosis-based algorithm for Z-filter (I-kaz TM ) approach for estimating the degree of data centroid scattering in dynamic signal analysis.They investigated dynamic fluctuations in machining processes using statistical metrics such as average, variance, root mean square, and kurtosis [4] [5].Most researchers choose force and vibration signals because they give detailed insight into the machining tool dynamics of the cutting process and are particularly valuable in monitoring the state of the cutting operations [6].Additionally, the wavelet transform (WT) technique emerged as a solution to specific limitations in the aforementioned methods.When comparing short-time Fourier transforms (STFT), Fourier transforms (FT) and WT exhibits several advantages, including the capability to conduct local analyses, accommodate both stationary and non-stationary signals, and deliver time-frequency analyses in an efficient manner [7][8] [12].The current study employs WT to denoise the unprocessed conversation signal with the intention of removing any ambient noise that may be present in the signal.The goal of this paper was to determine if there were a relationship between cutting tool vibrations, chatter conditions and surface roughness characteristics.Machining is the most common production method, offering superior dimensional control and surface polish.Turning is a common method for cutting cylindrical components.The roughness of the machined surface affects assembly, fatigue strength, aesthetics, and optical qualities.Surface finish prediction and enhancement of machined components remain a research focus [9].

Method and Material
The workpiece used in this investigation was a cylindrical rod composed of S45C medium carbon steel, with a 59 HRB hardness.The workpiece had dimensions of 250 mm in length and 75 mm in diameter.The workpiece has the following nominal material composition: P = 0.03%, S = 0.035%, Mg = 0.6%-0.9%,Si = 0.15%-0.35%,and C = 0.42%-0.48%.Figure 1 illustrates the experimental procedure, which included using a CNC turning machine (Mazak 200MY).Figure 1(a) shows that the workpiece was positioned on the tailstock.The cutting tool manufacturer specified the parameter ranges for a CVDcoated carbide insert used AC2000 (CNMG120404N-G) with a carbide tool holder (ECLNR-2020K12) for dry cutting turning operations.Next, establish the connection between tool holder and insert with the machine tool drive.Proceed to install on the CNC machine.During the turning process, LMS Test.Lab was used to measure the vibration signals and a portable LMS Scadas which has four channels, a bandwidth of 2048 Hz, 163384 spectral lines, and a precision of 0.125 Hz with an accelerometer (triaxial) and an accelerometer (single-axial) on the tool holder.
Figure 1(b) illustrates how the vibration was measured.The instrument holder is shown in Figure 1(b) with an accelerometer (tri-axial) of the type 3263M8 Dytran.The sensitivities of the accelerometer are as follows: 99.62 mV/g, 100.07 mV/g and 100.55 mV/g for Z, Y and X axes respectively.An accelerometer (single-axial) of the type 3145A Dytran with a 101.3 mV/g sensitivity was used as a reference for the tangential or cutting direction of the signals.A portable PS2 MarSurf Psi gauge is applied to measure the machined workpiece surface roughness as shown in Figure 1(d), which contains an illustration of this process.A total of three cutting parameter ranges are included in the experimental design.These ranges are as follows: 50-250 m/min for cutting speed, 0.1 mm/rev for feed rate, and 0.5-1.0mm for depth of cut.
The objective of this paper was to determine whether or not the parameters for cutting had an effect on the signal of vibration responses in the tangential (Y), axial (X), and radial (Z) directions, as well as the surface roughness arithmetic mean (Ra) values that were collected during the testing process.Last but not least, as can be seen in figure 1(c), vibration signals for feed, cutting and thrust forces were recorded all the way through the cutting operation, and surface roughness was assessed thereafter.The vibration signals gathered from the time response data recorded by the DAQ of the LMS Scada equipment after converting it to text format.Figure 2 shows the vibration signals that indicate the cutting directions.At three different points on the workpiece round surface, measurements of surface roughness were taken.The surface roughness value was obtained by the average of the measured values.In order to do signal statistical analysis, each and every piece of data was processed and analyzed using MATLAB.

Signal processing using I-kaz TM method
The approach for signal processing is known as the I-kaz TM technique is employed for the representation and analysis of acoustic, vibrational, and force signals.The statistical principle of kurtosis, denoted as K, represents the signal values with fourth-order statistical moment.The spikiness of the unprocessed data [4] exhibits significant sensitivity.By using the Z-notch filter, this technique removes noise from the observed machining signal data [6] [11] in a dependable and efficient manner.The signal decomposition procedure employed the second-order Daubechies approach, wherein the fmax values for low frequency (Lf), high frequency (Hf), and very high frequency (Vf) varied from 0 to 0.25, 0.25 to 0.50, and exceeding 0.50, respectively.The sampling frequency, fs, of the unprocessed signal data determines the maximal frequency span, fmax.The fmax is equal to fs/2.56 Nyquist number 2.56.
The points at a particular moment in time (xi) to be used to obtain the mean value (u), the variance (σ 2 ) and the magnitude deviation (xi -u).After applying the I-kaz method to disperse the variance of data distributions from the Lf, Hf, and Vf frequency bands for the x, y, and z axes, respectively, a 3D graph can be created.
where    quantity of data points is N.Then, the total root mean square (RMS) variance in equations (1 to 3) may be stated as the I-kaz coefficient and impacts the RMS variance. ∞ then be written as: Equation ( 4) simplifies the I-kaz coefficient calculation.Equation ( 5) uses for each signal data point by multiplying the standard deviation (s) and root mean square (RMS) values.In this case, there are n data points.  ,   and   show the kurtosis of the signal, and   2 ,   2 and   2 show the standard deviations in the Lf, Hf, and Vf bands, respectively.Equation ( 1) can be used to make a threedimensional graph of the scattering of statistical signal analysis using the I-kaz method, which can be seen in figure 3. Meanwhile equation ( 6) is used to figure out the signals' I-kaz coefficient.For data processing, MATLAB was put in place.

Chatter Index (CI)
By using the wavelet transform denoised signals, an alternative metric known as the chatter index (CI) has been developed to measure the intensity of chatter.The amount of chatter that results increases with the chatter index's value.The relationship that is supplied is used to calculate the chatter index [3] [10].
Where CI is chatter index, n is the length of signal and µ is the mean from the wavelet transform with denoise signal obtained using Wavelet Signal Denoiser App by MATLAB.

Wavelet Transform Signals
The wavelet transform signals have been obtained as shown in figure 4. The wavelet parameters have been used wavelet db2, denoising method was universal threshold, level 4, threshold rule soft and noise estimate was level independent.Figure 5 and 6 show the wavelets localise data characteristics to multiple scales, preserving significant signal while reducing noise.Wavelet thresholding and denoising use the wavelet transform to represent numerous real-world signals sparsely.This implies the wavelet transform concentrates signal and picture characteristics in a few large-magnitude components.Small wavelet coefficients are noise and may be "shrink" or removed without impacting signal quality.The data is reconstructed using the inverse wavelet transform after coefficient thresholding.Figure 7 shows the amplitudes that are found in the matching FFT for a wavelet denoised signal that is significant.

Results and discussion
As shown in table 1, five tests were carried out, where cutting speed (Vc), feed rate (f), depth of cut (d), vibration I-kaz coefficients (z ∞ ), surface finish (Ra) and chatter index (CI) based on machining of the vibration signals.As indicated in table 1, test runs 3, 4 and 5 had lower I-kaz coefficient, surface roughness and chatter index values than test runs 1 and 2. Meanwhile test runs 1 and 2 had chatter severities with surface roughness values 6.203 µm and 1.832 µm respectively.The relationship between surface roughness, chatter index values, and I-kaz coefficients for each experimental run is shown in figure 8.These relationships suggested that there is a very significant correlation between the cutting conditions.The observed signal with limited energy is processed through a low-pass and high-pass filter in the wavelet decomposition approach.A high-pass filter will provide a detailed coefficient, while a low-pass filter will produce an approximate coefficient, figure 5 and 6 show the signal decomposition process.The findings show that the I-kaz coefficient (Z ∞ ) and chatter index relationship reduces when the surface roughness measurement lowers as shown in figure 8.When compared to the chatter index, Z ∞ shows a more significant impact on surface roughness.The value of regenerative vibration stability may be summarized.This emphasizes the importance of the Z ∞ impact, which may enhance or reduce chatter stability (CI); higher I-kaz coefficients frequently result in chatter instability.More research is needed to understand how the sequence affects Z ∞ and chatter stability in machining operations.

Conclusion
I-kaz TM has been demonstrated to be an effective method for assessing the chatter stability of vibration signals and monitoring surface roughness throughout the turning process.When it comes to the I-kaz coefficient (Z ∞ ), surface roughness (Ra), and chatter index (CI), it is considered that there is a significant relationship between these three variables.In addition, the findings illustrate the relevance of the I-kaz coefficient in the investigation of chatter vibration.

Figure 7 .
Figure 7. Vibration signals and FFT of CWT signal.Figure 8. Cutting conditions for each run.

Figure 8 .
Figure 7. Vibration signals and FFT of CWT signal.Figure 8. Cutting conditions for each run.