A comparative study on damage detection in speed-up and coast-down process of grinding

Journal of Materials Processing Technology

187–188 (2007) 30–36

A comparative study on damage detection in speed-up and coast-down

process of grinding spindle-typed rotor-bearing system

B.S.Kim a,S.H.Lee a,?,M.G.Lee a,J.Ni b,J.Y.Song c,

C.W.Lee c

a School of Mechanical Engineering,Ajou University,Suwon443-749,Republic of Korea

b S.M.Wu Manufacturing Research Center,University of Michigan,Ann Arbor,MI48109,USA

c Intelligent an

d Precision Machin

e Department,Korean Institute o

f Machinery and Materials,Daejeon305-343,Republic of Korea

Abstract

In this paper,the damage detection from non-stationary mechanical vibration signals collected during acceleration and deceleration was per-formed.A laboratory grinding spindle-typed rotor-bearing system was equipped,and modal testing was carried out to identify system characteristics and operating range.Time–frequency analysis method such as Fast Fourier Transform(FFT),Short-Time Fourier Transform(STFT),Wigner–Ville Distribution(WVD),and Discrete Wavelet Transform(DWT)was applied to vibration data of normal rotor and shaft-cracked rotor in speed-varying process and the results of feature extraction from shaft-cracked condition were also compared with those in normal condition.

Keywords:Damage detection;Speed-up and coast-down process;Vibration signal-based monitoring;Non-stationary signal processing method;Rotor-bearing system

1.Introduction

High-performance grinding process among many machin-ing methods is one of the most complicated and important cutting processes as?nal machining stage;consequently,the system monitoring and automation technology is much more necessary in order to supervise the process and machine and detect abnormalities[1].Since,vibration signals in process carry the abundant dynamic information,vibration signal-based analysis method has been widely utilized for feature extrac-tion and nondestructive damage identi?cation.However,most of the vibration signals sampled on mechanical systems are non-stationary signals containing additional information or abnormal symptom,so that it is the key how to accurately extract domi-nant features from the dynamic data[2].Up to date,a number of research results for damage detection have mainly been focused on the stationary signal process;on the other hand,little research has been accomplished for the non-stationary signal process such as speed-varying process[3].

This research is about the damage detection of a shaft-cracked rotor from vibration signals acquired in a laboratory grinding spindle-typed rotor-bearing system in speed-up and coast-down process by using various types of signal processing methods.

?Corresponding author.Tel.:+82312192954;fax:+82312192953.

E-mail address:slee@ajou.ac.kr(S.H.Lee).Coast-down is the behavior of the rotating system until the sys-tem comes to rest after power supply is cut off.The modal testing is performed for the purpose of identifying dynamic characteris-tics and settling the operating range to pass through the structural resonant frequencies of vertical and horizontal direction in test. The Fast Fourier Transform(FFT),Short-Time Fourier Trans-form(STFT),Wigner–Ville Distribution(WVD),and Wavelet Transform(WT)are applied to extract feature signals of shaft-cracked rotor from acquired time data in both processes are carried out.

2.Theoretical background

2.1.Fast Fourier Transform

The FT and its inverse are de?ned as follows[4]

F(ω)=

∞

?∞

f(t)e?iωt d t(1)

f(t)=1

2π

∞

?∞

F(ω)e?iωt dω(2)

where f(t)is a given signal in the time domain and F(ω)is the FT of the f(t)in the frequency domain.Although,the FFT is a perfect tool for?nding natural frequencies of structures,it cannot show the time information when a particular frequency component occurs.

B.S.Kim et al./Journal of Materials Processing Technology 187–188 (2007) 30–3631

2.2.Short time–frequency transform The de?nition of the STFT is [4]

STFT(t,ω)=

∞

?∞

h (u )f (t +u )e ?j ωu d u (3)

where t is the time,ωthe frequency,and h (u )is a tempo-ral window function such as rectangular,Gaussian,Blackman,

Hanning,Hamming,etc.A large window width provides good resolution in the frequency domain,but poor resolution in the time domain,and vice versa.The STFT uses a single window for all frequencies.

2.3.Wigner–Ville Distribution

The WVD can be de?ned in both the time and frequency domains.The de?nition of the WVD is [5]

W f (t,ω)= ∞?∞

t +τ2 x ?

t ?τ2 e

?j ωτd τ

(4)Fig.1.Experimental

setup.

Fig.2.Time signal,FFT,STFT,and WVD of normal and crack condition during acceleration.

32 B.S.Kim et al./Journal of Materials Processing

Technology 187–188 (2007) 30–36

Fig.3.DWT of normal and crack condition during acceleration.

where x (t )is the time signal and x *(t )is its complex con-jugate.Any real signal x (t )is not only contaminated by the noise,but also by the interference terms.Although,the WVD has the high time–frequency resolution,the applications of the WVD are restricted by the cross-term interference using the bilinear transformation.The selection of the appropriate kernel function is necessary to elimi-

nate this interference term in accordance with the signal types.

2.4.Wavelet transform

The WT of a signal f (t )is de?ned as the sum of all of the time of the signal f (t )multiplied by a scaled and shifted version of

B.S.Kim et al./Journal of Materials Processing Technology 187–188 (2007) 30–36

Fig.4.Time signal,FFT,STFT,and WVD of normal and crack condition during coast-down.

the wavelet function ψ(t ).The Continuous Wavelet Transform (CWT)of the signal f (t )is de?ned as [6]

CWT(a,b )= ∞

?∞

f (t )a ?0.5ψ

t ?b

d t (5)DWT(j,k )=1√j ∞

?∞f (t )ψ

t ?2j k

2j d t (6)The parameter a represents the scale factor which is a recipro-cal of frequency and b indicates the time shifting or translation

factor.The high frequency components in the signal f (t )can be obtained from the WT by using a small scaling parameter,and vice versa.The Discrete Wavelet Transform (DWT)can be derived from the discretization of CWT(a ,b ).In Eq.(6),a and b are replaced by 2j and 2j k .The coef?cients of the DWT can be divided into two parts:one is the approximation coef?cients and the other is the detail coef?cients.The approximation coef?-

cients are the high scale and the low frequency components of the signal f (t ),while the detail coef?cients are the low scale and the high frequency.A hierarchical set of approximation coef?cients and detail coef?cients can be obtained through the multi-level signal decomposition,and then useful information on the signal f (t )can be yielded.

3.Experimental setup and modal testing 3.1.Test apparatus

In this study,the experimental setup of the laboratory grinding spindle-typed rotor-bearing system as shown in Fig.1was implemented for damage detection through vibration signals gathered from the spot of bearing housing during speed-up and speed-down process.

The rotor device was made up of four sub-systems.Firstly,the rotating system part consisted of a shaft with the diameter of 10mm and the length of 250mm,a disk with the diameter of 76mm,width of 26mm,and the weight

34 B.S.Kim et al./Journal of Materials Processing

Technology 187–188 (2007) 30–36

Fig.5.DWT of normal and crack condition during coast-down.

of 800g,two rolling bearings located apart from each other in 100mm distance to support the disk,a motor,two speed probes,and a controller to control the rotating speed.Secondly,the data collection part consisted of an accelerometer (PCB ICP type model 333B32)attached to the bearing housing located close to the disk,a signal conditioner,and a dynamic signal collection board (NI PXI-4472).Thirdly,the signal processing part was the signal analysis code programmed by Labview https://www.360docs.net/doc/2312946375.html,stly,the structural part was composed of a frame and a base.

3.2.Modal testing

The impact testing to make out dynamic characteristics and operating range of the rotor-bearing system was made up of an impact hammer (B&K model 8202),an accelerometer (B&K charge type model 4393),and a signal analyzer (B&K model 2035).Since the vibration in the direction of radius was closely connected with the resonance of a rotor,it was very useful in understanding the dynamic behavior.From the modal testing on a grinding spindle-typed rotor-

B.S.Kim et al./Journal of Materials Processing Technology 187–188 (2007) 30–3635

bearing structure,it was found that the natural frequencies in vertical direction were29and72Hz and the natural frequencies in horizontal direction were14 and51Hz.

4.Signal processing analysis

4.1.Experimental procedures and conditions

Based on the modal testing,the operating range was set to include both structural resonant frequencies of vertical direction of29Hz and of horizontal direction of51Hz.The operating range in speed-up process was from1000to3500rpm with the acceleration speed of15,000rpm/min;on the other hand,in coast-down process was also from3500to0rpm.During accel-eration,2560data per second were collected for10s,thus the total of25,600data were applied to signal processing;similarly, during coast-down,2560data per second of vibration signals were collected for8s.The sampling frequency was2560Hz and,according to Nyquist theory,the maximum frequency of vibration signal was1280Hz.The damage applied to the rotor-bearing system was realized as a shaft crack in the depth of2mm and the width of4mm to locate18mm away from the disk. 4.2.Results of signal analysis in speed-up process

The time data and its FFT,STFT,and WVD of vibration signals from rotor-bearing system during speed-up in both the normal and shaft-cracked condition were as shown in Fig.2.In time domain,as the operating speed exceeds2500rpm,shaft-cracked rotor produces a slightly larger vibration signal than the normal rotor by means of the in?uence of resonance and crack.From FFT results,there was a dif?culty in?nding the dominant frequencies.The STFT was achieved by the setting of Hanning window,1024used in FFT calculation as the number of frequency bins,128as the time interval,and512as the window length.The WVD was accomplished under the condition of51 as the time interval and1024as the number of frequency bins[7]. Comparing analysis results by the STFT and WVD,the overall trends of characteristics were similar,so that it was dif?cult to ?nd feature signals that represent for the crack.

So far the crack information through the FFT,STFT,and WVD method has not been enough.Therefore,the DWT was carried out for damage detection of shaft-cracked rotor.The wavelet function used in this study was the Daubechies wavelet (db4)and the eighth level decompositions were applied for signal analysis.The results by the DWT were compared and illustrated in Fig.3.The feature signals of shaft-cracked rotor were distinctively identi?ed in level4and5and were weakly observed in level6.In level6,the crack information was found with the distinctive signals around the speed of2400rpm and over the speed of3000rpm.In level5,there were dominant fea-tures around the speed of1400and2000rpm and over2800rpm; on the other side,in level4,prominent signals were expressed around the speed of1600and2400rpm.

4.3.Results of signal analysis in coast-down process

The time data and FFT,STFT,and WVD from both condi-tions during coast-down were shown in Fig.4.The results of time signals and its FFT displayed similar trends like speed-up process,so that it was dif?cult to extract distinctive peak value of the damage condition;moreover,from those of STFT and WVD analysis,there was almost no difference between normal and shaft-cracked rotor signal.

It was not possible to perform effective feature extraction from shaft-cracked rotor through the FFT,STFT,and WVD in coast-down process.As speed-up condition,the DWT by using Daubechies wavelet was also applied and the results of signal analysis were as shown in Fig.5.From the results of the DWT, the characteristics of shaft-cracked rotor were clearly observed in level4,level5,and level6.In level6,narrowly concentrated signals of shaft crack were observed before the speed became higher than2800rpm.In level5,there were relatively strong features around the speed of3000,2300,and1500rpm and until the speed of2800rpm;on the other side,in level4,a large number of distinctive signals were observed in the level of3000 and2300rpm.

From the results of analysis in comparison with other tech-niques,the feature extraction from vibration data by using the DWT during speed-up and coast-down was suf?ciently useful. In speed-varying process,strong feature signals were in?uenced by the shaft crack and the structural resonant frequencies;as a result,it was veri?ed that the crack detection during acceleration and deceleration based on the structural resonant frequencies was reasonable.

5.Conclusions

In this research,a laboratory grinding spindle-typed rotor-bearing system was con?gured and structural resonant frequencies by impact testing were decided.The vibration sig-nals obtained in vertical direction of the normal rotor and shaft-cracked rotor during both speed-up and coast-down were analyzed by using the FFT,STFT,WVD,and DWT method; accordingly,the feature extraction of crack condition were carried out.Among time–frequency analysis methods,it was demonstrated that the DWT was the most effective signal processing method in detecting the damages of rotor system during acceleration and deceleration due to dominant fea-ture signals of frequency bands including structural resonant frequencies.

Acknowledgement

This work was supported by Next-generation New Technol-ogy Development Program from the Ministry of Commerce, Industry and Energy,Republic of Korea.The authors would like to thank for supporting this work.

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