Condition monitoring of rotating machinery by vibration signal processing methods

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Résumé—La détection et le diagnostic de défauts jouent un rôle important dans la sécurité, la productivité et la qualité des produits. Durant la dernière décennie, des recherches actives et considérables se sont effectuées en vue de développer des mé- thodes de détection et de diagnostic de défauts des machines tournantes. Dans ce travail, des techniques d’analyse dans les domaines : temporel, fréquentiel et temps-fréquence, sont étu- diées. Des résultats en utilisant des mesures réelles, sont pré- sentés et discutés.

Mots clefs — diagnostic de défauts, machines tournantes, domaine temporel, domaine fréquentiel, domaine temps- fréquence.

Abstract—Condition monitoring and fault diagnostics plays a very important role in the production security and the prod- uct quality. The demand for monitoring and fault diagnosis of rotating machines has increased the efforts to develop new analysis techniques. A wide variety of techniques were used for this purpose. This study will mainly investigate techniques based on time domain, frequency domain and time-frequency domain. The monitoring results using real sensor measure- ments are presented and discussed.

Key words — fault diagnosis, rotating machinery, time do- main, frequency domain, time-frequency domain.

1. INTRODUCTION

Industrial systems have become increasingly complex.

Their monitoring is essential due to the demand for high performance, great security and good reliability. Various monitoring techniques have been developed, such as dynamics, industrial noise and vibration, tribology and non-destructive techniques of structures and rotating machinery [1, 2]. In an ISO working party, it was identified that the main techniques for machine monitoring are: vibration measurements, tribo- logical measurements, electrical measurements, process and performance measurement and non-destructive testing [3].

In this work, we use the vibration measurements for fault identification in rotating machinery. Indeed, vibration analysis is generally capable of detecting more kinds of faults compared to other techniques. It also has advantages as a non-destructive, clean, relatively simple and cost-effective technique [4].

Condition monitoring by vibration analysis is essential; as the vibrations are carrying information which characterizes

the operating state of some components or mechanical parts of the machine. There are many mechanical problems associated with vibrations. Common problems are: unbalance of rotating parts, eccentric components, misalignment, bent shafts, component looseness, damaged gears, worn drive belts and defective bearings [5]. All of the above faults can cause vibration. Meanwhile, vibration causes periodic con- straints in machine parts, which lead to fatigue, wear or damage [3, 6].

Vibration monitoring is generally carried out by analyzing signals collected on the running machine. These measurements, which represent in fact some parts of the machine, are difficult to read due to the nature of the vibration signal and the noise.

A wide variety of techniques were used for fault detection and diagnosis in rotating machinery. These techniques can be classified into time domain, frequency domain, time- frequency domain, neural network and model based techniques [7, 8, 9, and 10]. This study will mainly investigate techniques based on time domain, frequency domain and time-frequency domain.

2. EXPERIMENTAL SETUP AND DATA ACQUISITION

The experiment equipment used throughout this paper is shown in Fig.1. It consists of two gears 1 and 2, four bearing housings (H1, H2, H3 and H4), coupling and disk. The system is driven by an induction motor, giving an output of 0- 1500 rpm, controlled by a variable speed drive.

In order to predict any anomalies that may occur under different measurement conditions, we collected real vibration signals from this experimental system. The vibration signals were taken on bearing housing H1 through a piezoelectric accelerometer measured the radial vibration in Vertical and Horizontal Directions (VD and HD). Each measured vibration signal is available over a window of 400 milliseconds.

Two kinds of faults were simulated in this work; mass unbalance and gear fault.

Mass unbalance is one of the most common causes of vibration. It is a condition where the centre of mass does not coincide with the centre of rotation. The unbalance creates a vibration frequency exactly equal to the rotational speed, with amplitude proportional to the amount of unbalance [11]. It is simulated in our application by an additional weight on the disk.

Condition monitoring of rotating machinery by vibration signal processing methods

H. Bendjama¹, K. Gherfi¹, D. Idiou¹, M.S. Boucherit²

1 Welding and NDT Research Centre (CSC), BP 64 Chéraga, Algiers, Algeria, h.bendjama@csc.dz.

2 Department of Automatic, Polytechnic National Scool (ENP), BP 182 El-Harrach, Algiers, Algeria, ms_boucherit@yahoo.fr.

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298 The vibrations of a gear are mainly produced by the shock between the teeth of the two wheels. Gear fault is simulated with filled between teeth. The vibration monitored on a faulty gear generally exhibits a significant level of vibration at the Gear Mesh Frequency GMF (i.e. the number of teeth on a gear multiplied by its rotational speed) and its harmonics [11].

Fig.2 (a) and (b) represent respectively a vibration signal in VD and HD collected at 900 rpm (15 Hz) from the mass unbalance and the gear fault.

3. FAULT DIAGNOSIS METHODS

Machines under operation generally induce vibration. To ensure their monitoring, we should be taken into account the analysis of these vibrations. To detect any problems and fol- low their evolution, some cases require simply a calculation or statement of an indicator followed by a comparison with a threshold. Others require a more detailed analysis by signal processing methods to locate defective parts. We present in this section some signal processing techniques appropriate for fault detection and diagnosis.

A. Temporal analysis

The significant parameter for condition monitoring of a rotating machine is the vibration level. The increase of the latter is indicative of the degradation state of the machine.

The first possible observation of a vibration signal is the temporal representation. Several parameters or indicators are defined from the temporal analysis, such as peak value, peak to peak value, root mean square value, kurtosis, and crest factor [7].

The condition monitoring using these indicators consists in appreciating the vibration level of the machine by calculat- ing for example an indicator, then comparing it with a refer- ence value. To illustrate this method, we use the kurtosis as an indicator of gear fault detection. The computed values are summarized in Table 1.

The advantage of this method is its simple use. Moreover, the evolution of a fault whose vibrational level is relatively high may be masked by the noise. The computed parameter can not then detect this fault. In addition, under a measurement of indicators, all mechanical phenomena are confused (unbalance, gear, bearing, etc.). This measure allows to track the state of a machine, but it does not establish a diagnosis.

With the rapid development of signal processing techniques, it became possible to extract useful information from the vibration data.

Fig.1 Illustration of experimental system

Fig.2 Vibration signals in VD (left) and HD (right): (a) mass unbalance and (b) gear fault

Table.1 Kurtosis values of gear signals

VD HD

Without fault

With fault

Without fault

With fault

3.00 5.76 3.41 7.25

B. Spectral analysis

The measured signal is the response of the components constituting the system. Most of the characteristic frequencies are proportional to the rotational frequency. The spectral analysis allows to identify the different frequencies of the original signal s(t). To obtain the spectrum S(w) of s(t), we apply the Fourier Transform (FT):

∫

−^+∞∞

= s(t)e− dt )

w (

S ^iwt (1) where w is the frequency.

The vibration signal of the gear fault measured at a speed of 1200rpm (20 Hz) in frequency domain is shown in Fig.3.

Obviously, there is no particularly clear demonstration i.e.

the characteristic gear fault frequency is not clear from the frequency spectrum. The identification and the monitoring of the gear fault using the spectral analysis are difficult, due to the non-stationary.

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299 C. Cepstral analysis

The cepstrum of a time domain signal is a temporal image of this signal [12]. It is defined as the inverse Fourier transform of a logarithmic, itself the forward Fourier transform of a time signal. The cepstrum is expressed by:

[

log(S(w))

]

TF ) (

C τ = ⁻¹ (2) The abscissa τ of the cepstrum has the dimensions of time

“Quefrency”.

Cepstral analysis can be a very effective aid in the analysis of spectra. It allows to distinguish faults with complex periodic spectral structures due to several amplitude modula- tions such as gears. Indeed, the gear vibration signal is often modulated by the rotational frequency of the gears.

Fig.4 shows the cepstrum of the vibration signal with gear fault. It shows a peak at the rotational frequency.

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Frequency (Hz)

Amplitude (g)

Fig.3 Spectrum of vibration signal with gear fault

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Quefrency (s)

Amplitude (g)

Fig.4 Cepstrum of vibration signal with gear fault

In the field of vibration monitoring, the analysis of stationary signals has been mainly based on the spectral analysis or FT. In practice, the most of the vibration signals are non- stationary. The spectral representation becomes limited and thus all methods based on the FT have more or less the same limits [13, 14]. In order to make a correct diagnosis, it is useful to push investigations using more appropriate techniques.

D. Envelope analysis

Envelope analysis or amplitude demodulation can be used for diagnostics of rotating machinery. It is the method of ex- tracting the modulating signal from an amplitude-modulated signal.

Envelope analysis is especially suitable for fault diagnosis inducing periodic shocks such as gears and bearings. It consists in filtering the vibration signal by a band-pass filter. The resulting signal is then processed by the Hilbert Transform (HT) in order to obtain the envelope and its spectrum. For a given signal s(t), the HT in time domain is defined as [15]:

∫

^_^ ₋ ^_^

= τ

τ τ

π t ^d

) ( s ) 1

t (

s~ (3) The analytical signal sˆ(t) of signal s(t) can be consti- tuted trough s(t) and its HT s~(t):

) t ( s~

j ) t ( s ) t (

sˆ = + (4) The process can be followed by taking the absolute value of analytic signal to generate the envelope:

2 2 s~(t) )

t ( s ) t (

sˆ = + (5) The envelope technique by filtering is selective enough since it takes into account the vibration mode with signal-to- noise ratio is high enough. The choice of the filter’s bandwidth must cover all the frequency components caused by the resonance frequency.

To test the validity and applicability of this technique, we use the vibration signal of gear fault. The rotation frequency is 20 Hz. The spectral analysis of this signal presents side- bands around the GMF (see Fig.3). The observed amplitude at this frequency is not only the level of vibration generated by fault but also by the resonance of the structure.

The identification of the nature of the anomaly shows a characteristic frequency of the gear (Fig.5). The filter is se- lected according to the resonant frequency. After filtering the signal in the bandwidth [1000-1500] Hz, the envelope spectrum presents many frequency components, at the rotation frequency of the gear and some of its harmonics. This confirms a deterioration of the gear.

The envelope method is robust to noise ratio; due to filtering around the resonance frequency. It is beneficial for the identification of the gear fault. However, this method has its drawbacks: the preliminary research of the resonance frequencies is required. To extract the fault information, the Wavelet Transform (WT) will be applied to the vibration signals.

E. Wavelet transform

WT is one of the most important methods in signal analysis. It is particularly suitable for non-stationary measures.

WT is a time-frequency analysis technique. Two variations of WT exist: Continuous Wavelet Transform (CWT) and

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300 Discrete Wavelet Transform (DWT). They are described be- low: let s(t) be the original signal; the CWT of s(t) is defined as:

a dt b ) t

t ( s a ) 1 b , a (

CWT

∫

−⁺∞^∞

∗ 



 



  −



 



= ψ (6)

where ψ^∗(t) is the conjugate function of the mother wavelet ψ(t), a and b are the dilation (scaling) and translation (shift) parameters, respectively.

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0 50 100 150

Frequency (Hz)

Amplitude (g)

Fig.5 Envelope spectrum of gear fault signal

The selection of the appropriate wavelet is very important in signals analysis. There are many functions available can be used such as Haar, Daubechies, Meyer, and Morlet functions [16]. In the present study, we used Morlet and Daubechies wavelets for fault diagnosis of gear and mass unbalance, respectively.

The identification of the gear fault is possible by using the Morlet wavelet, it is also called CWT. It can be seen from Fig.6 that the peaks at the rotation frequencies of the shaft (10 Hz) and its multiples are present in the frequency spectrum. This clearly indicates a gear fault.

DWT is derived from the discretization of CWT by discrete values of a and b, with a=a₀^m and b=nb₀a₀^m. The DWT is given by:

(

^a ^t ^nb

)

^dt

) t ( s a ) n , m (

DWT ² ₀^m ₀

m

∫

−⁺∞^∞

− −

−

= ψ (7)

The choice of a₀ =2 and b₀ =1 is particularly suitable for multiresolution analysis [17]. The DWT analyzes the signal at different scales. It employs two sets of functions, called scaling functions φ(t) and wavelet functions ψ(t), which are associated with Low pass (L) and High pass (H) filters, respectively.

n t 2 2 ) t

( ² ^m

m n

,

m = ⁻ φ ⁻ −

φ (8)

n t 2 2 ) t

( ² ^m

m n

,

m = ⁻ ψ ⁻ −

ψ (9)

In the decomposition step, we often speak of approximations and details. The discrete signal is convolved with L and H, resulting in two vectors A1 and D1 on a first level. The vector A1 is called approximate coefficient and the vector D1 is called detailed coefficient. The application of the same transform on the approximation A1 causes it to be decomposed further into approximation A2 and detail D2 coeffi- cients on a second level. Finally, the signal is decomposed at the expected level. The Approximations and the details are defined as follows:

n , n m,n m

m s,

A ⁼

∑

φ φ (10)

n , n m,n m

m s,

D ⁼

∑

ψ ψ (11) where ⋅,⋅ is the inner product.

The multiresolution analysis is applied by using the Dau- bechies wavelet of order 4 (db4). In which, level 4 decomposition is employed to extract the approximation coefficient from vibration signals. The result of db4 decomposition of the vibration signal of the mass unbalance collected at a rotation frequency of 15 Hz is given in Fig.7. Obviously, there is no particularly clear demonstration, and it is not easy to detect the fault from this figure.

Fig.8 shows the spectrum of approximation 4 (A4). It is clear that the peak at 15 Hz is present; which could be re- lated to a mass unbalance fault.

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Frequency (Hz)

Amplitude (g)

Fig.6 Spectrum of gear fault obtained with Morlet wavelet 20 Hz

10 Hz

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Fig.7 Decomposition result of vibration signal of mass unbalance with db4 wavelet

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Frequency (Hz)

Amplitude (g)

Fig.8 Spectrum of A4 with mass unbalance

4. CONCLUSIONS

This paper discusses different methods of fault detection and diagnosis in rotating machinery.

WT was presented in order to improve the monitoring results. DWT and CWT were applied on real measurement signals collected from a vibration system containing mass unbalance and gear fault. Better results are obtained by iden- tifying the type of fault.

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