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## Mathematical Methods and Modeling in Machine Fault Diagnosis

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Research Article | Open Access

Volume 2014 |Article ID 862065 | https://doi.org/10.1155/2014/862065

Hongkun Li, Xuefeng Zhang, Xiaowen Zhang, Shuhua Yang, Fujian Xu, "Pressure Pulsation Signal Analysis for Centrifugal Compressor Blade Crack Determination", Mathematical Problems in Engineering, vol. 2014, Article ID 862065, 15 pages, 2014. https://doi.org/10.1155/2014/862065

# Pressure Pulsation Signal Analysis for Centrifugal Compressor Blade Crack Determination

Revised31 May 2014
Accepted16 Jun 2014
Published19 Aug 2014

#### 1. Introduction

In this paper, PP signals are used for blade working condition classification by using EMD. Experiments are carried on to verify the effectiveness of this method in a test-rig. To verify the effectiveness of this method, strain testing is also carried on for the blade crack analysis. The structure of this paper is as follows. Section 2 introduces the theory of feature extraction for blade crack classification. Section 3 presents the simulation signal analysis. Section 4 describes our experimental setup for blade crack monitoring. Section 5 demonstrates PP signal analysis for blade condition classification. Section 6 gives concluding remarks.

#### 2. Theory and Method

##### 2.1. Empirical Mode Decomposition

EMD is developed based on instantaneous frequency calculation. It has been considered a very useful tool for the analysis of nonstationary and nonlinear signals [20]. For an arbitrary time series , it can decompose the original into many narrow-band components, each component known as intrinsic mode functions. An intrinsic mode function is used to convert it into a practically useful instantaneous frequency. The intrinsic mode function satisfies two conditions: (1) in the whole range of a data set, the number of the extreme must be equal to the number of the zero crossing points or the difference between them must be one; (2) at any given time, the mean value of the local positive extreme is equal to that of the local negative extreme. An arbitrary nonstationary and nonlinear signal can be decomposed into a series of components satisfied with the intrinsic mode function by using the local wave decomposition method. It is a sifting process and can be written as

The original data can be decomposed into an -series of intrinsic mode components plus a residual component . The residual can be either a variable or a constant. Thus, the original signal can be expressed as

After EMD, intrinsic mode function (IMF) can be obtained. FFT can be used on different IMFs analysis for CF determination. EMD can be looked as a filter on feature determination. Therefore, it is helpful to obtain the CF.

In general, centrifugal compressor casing vibration and radiation noise are closely related to blade BPF and its harmonics. It is also generated by the interference between rotor and stator during blade high speed rotation. BPF has high energy in the pressure frequency spectrum. It is the main source of centrifugal compressor noise. Its value can be determined by shaft speed multiplying the number of blade. BPF can be calculated by where is the shaft speed and is the number of blades on the impeller.

BPF is the interference between rotator and stator. As BPF is a high frequency component, the low frequency components for blade nonorder vibration can be modulated to BPF during rotation. The modulation information will appear as the sideband frequency of the BPF. For unbalanced rotor conditions, SF will also be modulated to the BPF giving a sideband frequency around the BPF for unbalanced condition. Sideband frequency could be used to determine the modulated CF. The sideband frequency produced for blade cracks is different from SF. It can be used to warn blade crack. It does not mean that there is a blade with cracks if SF is the sideband frequency for BPF. It is also difficult to classify CF just according to the spectrum for the incipient crack as the magnitude of the blade vibration is weak compared with the amplitude of BPF. Therefore, effective feature extraction is urgently needed for blade crack analysis.

##### 2.3. Blade Crack Characteristic Frequency Determination

The steps for CF determination are shown in Figure 2. Firstly, PP is monitored based on the best suitable position according to blade crack classification. This is also a key step to determine the crack information because the sensor location has a direct effect on classification accuracy. Secondly, band-pass filter is applied on signal analysis. Envelope analysis is used to filter BPF signal. Then, IMFs can be obtained by using EMD. Fast Fourier transform is used on different IMFs. In the end, CF for blade crack can be obtained. Blade strain is used to verify the effectiveness of this method.

#### 3. Simulation Signal Analysis

For a amplitude modulation signal , it can be expressed as where,  Hz,  Hz, , and . and correspond to carrier frequency and modulation frequency, respectively. The corresponding sampling frequency is 10,240 Hz for the simulation signal. Based on (4), an amplitude modulation signal can be obtained as shown in Figure 3(a). Fourier spectrum analysis is shown in Figure 3(b). The main frequency is 1500 Hz. The modulated frequency 10 Hz can be obtained by enlarging the frequency domain around the carrier 1500 Hz frequency shown in Figure 3(c). It is obvious for the sideband frequency around the carrier frequency if there is no noise interference in the signal.

Strong noise interference is added to the simulation signal as the characteristic information is usually overwhelmed by noise under practical working conditions. The obtained signal is shown in Figure 4(a). In the frequency spectrum analysis, there is clear broad frequency band noise effect shown in Figure 4(b). To determine the modulated signal, the enlargement for carrier frequency area in the spectrum is shown in Figure 4(c). Obviously, the enlarged frequency area is not clear due to the noise interference. The noise interference has an effect on the CF determination; therefore, it is difficult to classify the CF just according to sideband frequency spectrum analysis if there is strong noise interference.

Signal filter is used for the monitored signal around BPF. The filter band is 1400–1600 Hz. EMD is applied on the filter signal. IMFs can be obtained as shown in Figure 5. There is not any clear modulated frequency 10 Hz for every IMFs as shown in Figure 6. Envelope method is applied to the filter signal to filter BPF interference. EMD method is also applied on the envelope signal and IMFs can be obtained as shown in Figure 7. But there is clear modulated frequency 10 Hz as shown in Figure 8, the 5th IMFs based on EMD.

Based on above analysis, it can be convenient to determine the modulated frequency though there is strong noise interference. According to above analysis process, the blade nonorder vibration can be also monitored as it has the same property for simulation signal. Therefore, experimental verification is investigated in this research for blade nonorder vibration classification.

#### 4. Experimental Test-Rig

##### 4.1. Testing-Rig

To verify the effectiveness of this method, an experiment was carried on blade crack condition analysis by using the method based on PP signals analysis in a test-rig. The schematic diagram for the test-rig is shown in Figure 9. It contains an electric motor, fluid coupling, gearbox, and impeller. The impeller is a semiclosed one with 800 mm diameter. It is an experimental impeller for performance testing. By using fluid coupling, the rotating speed for impeller varies from 500 RPM to 9000 RPM. With the speed-up gearbox, the rotation speed of impeller can meet the designed one. The ratio between the driving and driven gears is 126/43 = 2.93. The experimental picture and hole in the diffuser for installing PP sensor are shown in Figure 10. The crack length during the experiment is 70 mm. PP, vibration, shaft speed sensors are installed to monitor the working process. There are 13 blades in this semiopen impeller. In this experiment, the speed of the impeller is 4500 RPM and 5000 RPM. The SF and BPF parameters are shown in Table 1.

 Speed (RPM) 4500 5000 Shaft frequency (Hz) 75 83.3 Blade passing frequency (Hz) 975 1083

##### 4.2. Data Acquisition

There are three PP sensors produced by PCB Piezotronics (New York, USA) to monitor the working process; it is shown in Figure 11. One is installed in the inlet pipe; the other two are installed near the diffuser in the holes shown as Figure 10. The sensitivities of the PP sensors are 0.7044 mV/Pa, 0.9845 mV/Pa, and 0.7336 mV/Pa. PP signal, vibration signal is gathered by the NI-4472 data acquisition card. It is an 8-channel synchronous data gathering system. It is also shown in Figure 11.

#### 5. Data Analysis

##### 5.1. Strain Signal Analysis

The frequency spectrum for the strain data with impeller speed 4500 RPM is shown in Figure 14. The SF of the impeller is 75 Hz. It is also clear because of the unbalance. The frequency 53 Hz is shown in the spectrum for point (b) and point (c). There is not the CF information for point (d) shown as Figure 14(d) because it is a normal blade. Point (c) is near the crack. It is clearer than point (b). It can be concluded that 53 Hz is the CF for blade vibration.

The same analysis is also carried on the impeller speed in 5000 RPM shown as Figure 15. Based on the above analysis process, the CF for blade nonorder vibration is 52.7 Hz. The CF is almost the same as speed in 4500 RPM. Therefore, it can be concluded that 53 Hz is the CF for the crack. It is a nonorder vibration for the blade and the reason of crack. There is not CF for the normal blade. Strain analysis can help us to determine the CF for blade crack. As it is not convenient in real working condition for strain monitoring, feature extraction is important to obtain the CF from other monitored signals.

##### 5.2. Pressure Pulsation Signal Analysis

PP signal is used to detect blade nonorder vibration information as for the crack. Compared the total length of the blade, the crack is very small (the diameter for the blade is 800 mm) shown in Figure 16. Sides A and B in Figure 16(b) are together with impeller. They are not separated from impeller. It is just for clear demonstration with Figure 16(b). The impeller is manufacturing with whole milling process. At the same time, the averaging thickness of the blade is 10 mm to keep the stiffness of blade. Therefore, the information is weak for blade crack. It is the reason that it is difficult to determine the blade information. It can be just found when there is blade fracture. The crack information will be modulated to BPF as mentioned above although it is weak. There is not any modulated information in time domain shown in Figure 17(a). It is clear for BPF in the spectrum analysis shown in Figure 17(b). But it is not clear for the modulated frequency as the noise interference and nonorder vibration is very weak. It is impossible to obtain the modulated frequency. Therefore, the signal filter is investigated. The filter frequency band is 900–1050 Hz. The filter signal is shown in Figure 17(c). The time domain and the frequency domain spectrum are shown in Figures 18 and 19, respectively. But there is not any information about the CF.

Envelope is used on the filtered signal. Then, EMD is used on envelope signal analysis. IMFs can be obtained shown in Figure 20. IMFs frequency spectrum analysis can clearly demonstrate the modulated frequency 53 Hz shown in Figure 21. Therefore, this method can be used to classify the crack CF for blade.

It is also with same result for 5000 RPM. Time and frequency analysis waveform for PP signal is shown in Figure 22. It is also difficult to recognize the CF. Therefore, signal filter is carried on. The filter frequency band is from 990 Hz to 1165 Hz. Then, IMFs based on EMD for envelope signal are shown in Figure 23. IMFs spectrum analysis is shown in Figure 24. It is clear for the modulated frequency 53 Hz. It has the same result with 4500 RPM. It can be verified that this method can effectively recognize the modulated nonorder vibration signal. It also demonstrates that this method can be used on feature frequency determination.

#### 6. Conclusions

In this research, PP signals are used for blade crack condition monitoring and classification. The realization of this method is demonstrated in detail. Experiments on an industrial centrifugal compressor with a cracked blade were carried out to verify the effectiveness of this method. CF of blade crack information can be obtained by using EMD and spectrum analysis to obtain the modulated frequency. Strain signal is also investigated to monitor the crack CF. It is verified that crack characteristics can be determined by using PP signal. This research puts forward a method on how to determine the blade crack CF. Further investigations will also be carried on how to apply this method on real working condition blade crack classification. It will be helpful for blade crack early warning.

#### Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

#### Acknowledgments

The work was supported by the Natural Science Foundation of China under Grant no. 51175057 and the Fundamental Research Funds for the Central Universities under Grant no. DUT14ZD204.

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