A model of milling process based on Morlet wavelets decomposition of vibroacoustic signals

Abstract

The paper considers the problem of online monitoring the condition of cutting tools to avoid its unexpected failure. To approach this problem we proposed a model of milling process based on Morlet decomposition of vibroacoustic signals. In addition, using the wavelets scalogram, we imposed a new condition that helps to improve early wear detection of the cutting tool. The findings of this research reveal the advantages of the proposed model compared to the previously reported models that rely on Haar wavelets and Short-time Fourier transform. The increasing demands for the characteristics of modern gas turbine engines make it necessary to improve the accuracy and reliability of their manufacture. This improvement permits to increase the durability of critically important components such as rotating turbine discs. The processing characteristics sharply deteriorate at high mechanical strength at high temperatures as well as low thermal conductivity of Ti / Ni-based alloys [1-5]. Cutting off parts from nickel-base heat-resistant alloys (for example, Inconel 718, Udimed 720) leads to both a rapid wear of the cutting tool and tool surface [1, 11-16], which can be generally called surface anomalies. These surface anomalies are the result of the bad processing characteristics of nickel-base alloys and the trend of rapid tool wear at cutting regardless of the types of machining operations [11, 12, 14-22]. Aircraft engine manufacturers are developing a monitoring system to detect anomalies in the processing and to react against it [34]. The procedure behind most monitoring systems consists of the following steps. First, it is a need to measure parameters second, these parameters need to be analyzed by means of specific methods such as wavelet decomposition, Shot-time Fourier transform (STFT) and etc. One of the efficient methods of spectral analysis is the wavelet transformation (decomposition), the advantage of which is the possibility to analyze non-stationary signals. The wavelets frequently used in practice are described in [8, 34, 37]. The main purpose of this study is to develop a model of milling process based on Morlet decomposition of vibroacoustic signals and, thus, to propose tool wear condition. This condition is of use in solving the problem of identifying both nonstationary modes and early tool wear.

Keywords

• milling process
• acoustic emission
• wear detection
• Morlet wavelet decomposition

1. Introduction

2. Problem statement

 2 

Mathematical Modeling / A.I. Khaymovich, S.А. Prokhorov, А.А. Stolbova, А.I. Kondratyev As a result, power spectral density is defined by wt,   1 g  e j 1  af   / 2 f *   / 2d d . ( 5 ) 4a  1 a

Formant analysis [33] is used to analyze a vibroacoustic signals because these signals have multi-frequency components connected with different anomalies while cutting [35, 6].

The efficiency of time-frequency methods is presented in Fig. 1 [7].

The informative parameter characterizing the cutting tool (CT) wear is the dispersion of the detail coefficients of the Haar wavelet decomposition of AE signal. This parameter is insensitive to changes in processing modes [31]. The minimum duration of the analyzed sample is 0.1 s. Wear identification of cutting tool is carried out according to the energy value of the j-th detail factors. For Haar wavelet decomposition, it is advisable to take 3 <j <6. The forecast of CT wear in real time is in correction of the base model estimation from the results of current measurements of the AE signal parameters by an additive component obtained on the basis of extrapolation of the residual function. The study [35] proposes the adaptation of the suggested method for molding conditions by automatic window selection of a fragment of the AE signal which falls on the cutter tooth.

The main drawback of the Haar wavelet is the asymmetric and non-smooth, consequently, an infinite alternation of "petals" arises in the frequency domain due to sharp boundaries in the time domain. The complex Morlet wavelet does not suffer from these drawbacks.

3. A model of milling process based on Morlet wavelets decomposition of vibroacoustic signals

Wavelet transformation coefficients can be defined as [10, 36, 37]: W a, b  1  f t   t  b dt ,

a   a  where f t  is a random process,  t  is a chosen wavelet, a  0 is a scale parameter, b  0 is a shift parameter.

Morlet wavelet is given by

 t 2   t   exp  jk texp    ,

 2  where j is the imaginary unit, parameter k  2 [37] controls the time-frequency resolution.

The graphical results of wavelet transformation can be calculated by wi, j  W ai , b j  ,

2 where i  0, , N a  1 , j  0,

, N b  1 , N a is a counting scale, N b is a counting shift.

The scalogramms are obtained from ( 9 ) as

1 Nb 1 yi  N b j0 wi, j ,

We propose to use the equation ( 11 ) to calculate area under curve of scalogramms:

Mathematical Modeling / A.I. Khaymovich, S.А. Prokhorov, А.А. Stolbova, А.I. Kondratyev s    y0  y N 1   yi  , ( 11 )

N 2   2 i1  where  is a frequency of quantization interval, y is a scalogramm, N is a counting rate of scalogramms.

We use a new identification criterion ( 12 ) to analyze processing parameters. This criterion is a cross-factor CF of the spectral energy density in the frequency bands  max    of every local maximum of scalogramms. We built the scalogramms in the frequency intervals   .

CFmax 

 wi, j d   max  m ax  wi, j d 

.

To identify wear the following equations were considered:

t  kmax  CFmaxt0  ,

CFmax d where t 0 is the time of tool work without wear out, t d is the time of tool work with wear out.

In accordance with equations ( 11-13 ), the calculation of the wear identification coefficient can be made by: kmax  ss tt0d  ssmmaaxxttd0  . ( 14 )

4. Results

4.1. Experiments design

The phenomena explained by the dislocation theory, of deformation distortions of the crystal lattice, friction, the formation and extension of cracks, phase transformations leads to AE. In metal cutting, the processes arised at an interaction between the part and tool are the most important sources of AE [23].

We register acoustic emission and power cutting of milling by the lateral and end surfaces of the milling tool. The main system element for measuring power cutting is the piezo-multicomponent dynamometer Kistler – Type 9257B (Switzerland) This dynamometer was installed at the base of the machining center Micron UCP 800. We use the LTR22 analog to frequency converter to record vibroacoustic signals with the microphone sensor (OCTAFON-110).

The connection scheme of the experimental setup for data collection is shown in Fig. 3. ( 12 ) ( 13 )

Mathematical Modeling / A.I. Khaymovich, S.А. Prokhorov, А.А. Stolbova, А.I. Kondratyev

The machining process with variable allowance was simulated to analyze the influence of the cutting depth on the acoustic emission parameters and the stability of the wear identification technique. The processed sample of steel 45 was a blank part with a stepwise increase in allowance during milling (Fig. 4). A special groove on the surface of the blank part is designed to simulate intermittent cutting.

The cutting conditions for the experiments are given in Table 1.

4.2. Experiment results

f)

Fig.5. Wavelet spectrum of analyzed signals.

Mathematical Modeling / A.I. Khaymovich, S.А. Prokhorov, А.А. Stolbova, А.I. Kondratyev

We use six different AE signals to analyze the cutting process with a multi-tooth tool. The signals denoted by the numbers 1, 2, 3 and 28, 29, 30 correspond to the regimes of Table 1 and are obtained by examining the new tool (a, b, c) and the worn tool (r, d, e). Fig. 5 shows the wavelet spectrum calculated by ( 9 ), where the X-axis of the wavelet spectrum graph represents the time in seconds, and the Y-axis represents the frequency in rad/s. The larger the value of the spectrum is, the lighter the pattern is. smax t0  - new tool

Mode 2

0,0823 0,31129 0,09448 0,65945

Mode 3

0,13359 0,54264 0,12908 0,77467 The wear coefficient kmax for 3 modes are given in table 3. smax td  - worn tool

Mode 2

0,62313 0,09416 0,09919 0,80046

Mode 3

0,515 1,626 0,486

The results of analysis are presented in Table 3. These results make it possible to see the characteristic feature: in the lowfrequency region (550-750 rad/s), as the tool wear, kmax decreases, and in the area of conditionally medium frequencies region (1200-1500 rad/s) – increases.

The revealed regularity helps to formulate the condition for the appearance of a critical wear value when machining with a multi-tooth tool: kmax t  klow,  max   low,  kmax t  kmid ,  max   mid ,

t  td , where klow , kmid are the limit values of the wear identification coefficient for the low and medium frequency range, respectively.

In other words, as the cutting tool wear, the spectral density of the energy of the Morlet wavelet image in the low-frequency region  low increases ( kmax decreases), and in the medium frequencies region  mid decreases ( kmax increases).

5. Conclusion

A model of milling process based on Morlet decomposition of vibroacoustic signals were proposed. Analyzing of the wavelet scalogramms of the signal at various processing modes, we received stable frequency bands of local maxima: 550-750 rad/s,

Mathematical Modeling / A.I. Khaymovich, S.А. Prokhorov, А.А. Stolbova, А.I. Kondratyev 1200-1500 rad/s and 1950-2100 rad/s. Authors obtained trends to change the spectral energy density at the tool wear for the first and second frequency bands. The cross-factor CFmax can serve a numerical characteristic of change of this trend. The crossfactor determined by the dependence ( 10 ) and equal to the ratio of the average spectral density of the signal energy in the frequency bands of the local maximum of the scalogramm to the average spectral energy density throughout the frequency region of the scalogramm resolution. To identify the wear we proposed a new coefficient kmax that equal to the ratio of the cross-factors of acoustic emission signals for a new and wear tool, respectively. The coefficient of the wear identification increases where the dimensional wear increases in low-frequency region. These coefficient decreases in medium frequencies region. The experimentally determined regularity of the change a new condition that helps to improve early wear detection of the cutting tool made it possible to formalize the tool wear model with criterial constraints on the dependence.

References

[1] Machining Data Handbook. Machinability Data Center , Cincinnati, OH , 1980 .

[2] Armarego EJA , Brown RH . The Machining of Metals. New Jersey: Prentice-Hall Inc ., 1969 .

[3] Rahman M , Seah WKH , Teo TT . The machinability of Inconel 718. Journal of Materials Processing Technology 1997 ; 63 : 199 - 204 .

[4] Shaw MC . Metal Cutting Principles . Oxford University Press, 2005 .

[5] Trent EM. Metal Cutting , second ed. London: Butterworths , 1984 .

[6] Astafyeva NМ . Wavelet analysis: the basics of theory and examples of ots application . Success of physical sceinces 1996 ; 166 ( 11 ): 1145 - 1170 .

[7] Vityazev VV . Wavelet analysis of temporal series: manual . Saint-Petersburg : Publishing house of Saint-Petersburg University, 2001 ; 58 p.

[8] Dobeshi I. Ten Lectures on Wavelets . Izhevsk : SRC Regular and chaotic dinamics , 2001 ; 464 p.

[9] Koronovsky АА , Khramov АЕ . Continuous wavelet analysis and its applications . М.: Fizmatlit , 2003 ; 176 p.

[10] Mallat S. Wavelets in the signal processing: translated from English. M.: Mir , 2005 ; 671 p.

[11] Axinte DA , Andrews P. Some considerations on tool wear and workpiece surface quality of holes finished by reaming or milling in a nickel base superalloy . Proceedings of the Institution of Mechanical Engineers. Journal of Engineering Manufacture 2007 ; 221 : 591 - 603 .

[12] Axinte DA , Dewes RC . Surface integrity of hot work tool steel after highspeed milling-experimental data and empirical models . Journal of Materials Processing Technology 2002 ; 127 : 325 - 335 .

[13] Axinte DA , Gindy N , Fox K , Unanue I. Process monitoring to assist the workpiece surface quality in machining . International Journal of Machine Tools and Manufacture 2004 ; 44 : 1091 - 1108 .

[14] Beggan C , Woulfe M , Young P , Byrne G. Using acoustic emission to predict surface quality , International Journal of Advanced Manufacturing Technology 1999 ; 15 : 737 - 742 .

[15] Mantle AL , Aspinwall DK . Surface integrity of a high speed milled gamma titanium aluminide , Journal of Materials Processing Technology 2001 ; 143 - 150 .

[16] Sharman ARC , Aspinwall DK , Dewes RC , Bowen P. Workpiece surface integrity considerations when finish turning gamma titanium aluminide . Wear 2001 ; 249 : 473 - 481 .

[17] Choudhury IA , El-Baradie MA . Machinability assessment of Inconel 718 by factorial design of experiment coupled with response surface methodology . Journal of Materials Processing Technology 1999 ; 95 : 30 - 39 .

[18] Everson CE , Cheraghi SH . Application of acoustic emission for precision drilling process monitoring . International Journal of Machine Tools and Manufacture 1999 ; 39 : 371 - 387 .

[19] Axinte D , Axinte M , Tannock JDT . A multicriteria model for cutting fluid evaluation, Proceedings of the Institution of Mechanical Engineers . Journal of Engineering Manufacture 2003 ; 217 : 1341 - 1353 .

[20] Aspinwall D , Dewes R , Ng E , Sage C , Soo S. The influence of cutter orientation and workpiece angle on machinability when high-speed milling Inconel 718 under finishing conditions . International Journal of Machine Tools and Manufacture 2007 ; 47 : 1839 - 1846 .

[21] Toenshoff HK , Ianasaki I. Sensors in Manufacturing . Wiley-VCH Verlag GmbH, Weinheim , 2001 .

[22] Menon AK , Boutaghou Z-E. Time -frequency analysis of tribological systems. Part II: tribology of head-disk interactions . Tribology International 1998 ; 31 : 511 - 518 .

[23] Menon AK , Boutaghou Z-E. Time -frequency analysis of tribological systems. Part I: implementation and interpretation . Tribology International 1998 ; 31 : 501 - 510 .

[24] Cohen L. Time-Frequency Analysis . New Jersey: Prentice-Hall, 1995 .

[25] Lee SU , Robb D , Besant C. The directional Choi-Williams distribution for the analysis of rotor-vibration signals . Mechanical Systems and Signal Processing 2001 ; 15 : 789 - 811 .

[26] Wigner EP . On the quantum correlation for thermodynamic equilibrium . Physics Review 1932 ; 40 : 749 - 759 .

[27] W PR , Hammond JK . The analysis of non-stationary signals using time-frequency methods . Journal of Sound and Vibration , 1996 .

[28] Choi H-I , Williams J. Improved time-frequency representation of multicomponent signals using exponential kernels . IEEE/ASME Transactions on Acoustics, Speech and Signal processing 1989 ; 37 : 862 - 871 .

[29] Khvostikov АS , Schetinin VS . Diagnosis of cutting process by applying Wavelet - analysis of acoustic emission signal . Digital signal processing 2007 ; 4 : 40 - 43 .

[30] Yunxin Zhao LEA , Robert J , Marks II . The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals . IEEE/ASME Transactions on Acoustics, Speech and Signal processing 1990 ; 38 : 1084 - 1091 .

[31] Weston RH. A formant detection system in which signal coding properties of a neuron network are used . Journal of Sound and Vibration 1975 ; 40 : 191 - 217 .

[32] Sidorov AS . Monitoring and forecasting tool wear in mechatronic machine systems . Abstract of dissertation for the degree of Candidate of Technical Sciences. Ufa , 2007 .

[33] Pechenin VA et all. Method of controlling cutting tool wear based on signal analysis of acoustic emission for milling. Dynamics and Vibroacoustics of Machines (DVM2016).

[34] Ramakrishna RPK , Prasad P , Srinivasa PP , Shantha V . Acoustic emission technique as a means for monitoring single point cutting tool wear , 2000 .

[35] Marinescu D. Axinte A time-frequency acoustic emission-based monitoring technique to identify workpiece surface malfunctions in milling with multiple teeth cutting simultaneously . International Journal of Machine Tools & Manufacture 2009 ; 49 : 53 - 65 .

[36] Richard Y , Chiou A , Steven Y . Liang b Analysis of acoustic emission in chatter vibration with tool wear effect in turning . International Journal of Machine Tools & Manufacture 2000 ; 40 .

[37] Postnikov ЕB . Wavelet decomposition with Morlet wavelet: calculation method, based on solution of diffusive differential equations . Computer - eaided research and modelling 2009 ; 1 ( 1 ): 5 - 12 .

[38] Yakovlev АN . Introduction to wavelet decomposition: Manual . Novosibirsk: Publishing House NSTU , 2003 ; 104 p.