Experimental Study of Transverse Crack Fault Diagnosis in Rotating Machinery Jian-zhong Lou 1,2 Xing Li1 1 2 Department of Bio-systems Engineering, Zhejiang University, Hangzhou, China Department of Mechanical Engineering, Zhejiang Institute of Mechanical & Electrical Engineering, Hangzhou, China ([email protected] ) Abstract - The rotor transverse crack fault is one of the most typical faults of rotating machinery. The transverse crack fault mold was established to simulate the bearing fault state of transverse crack in the rotor test table of Bently in the laboratory. The main vibration characteristics were stated through the analysis of laboratory data when the bearing box was in the state of transverse crack fault. And it has been applied in practice. Where: i --displace the node along the y-axis direction Keywords - transverse crack; bearing box; rotating machinery; fault diagnosis mass matrix, damping matrix, stiffness matrix and generalized force. wi --displace the node along the x-axis direction i --the angle around the x-axis i --the angle around the y-axis M 、 C 、 K and Q respectively displace the I. INTRODUCTION The large rotating machinery is one of the most important equipment in petroleum, chemical, petrochemical, and other industries. It is also particularly important for us to diagnosis machine fault of large rotating machinery because it will cause serious economic losses and casualties. And it is very useful for people to monitor the fault diagnosis of large rotating machinery in order to avoid vicious equipment damage accidents, reduce corporate economic losses. The fundamental purpose of fault diagnosis is to ensure the large rotating machinery to run in safety, stable, long-period, full load statement. Transverse crack is the most common faults of rotating machinery and it is very important for us to get a research [1-4]. II. THE ESTABLISHMENT OF TRANSVERSE CRACK FAULT MODEL The rotor system mechanics model is the premise of obtains the rotor vibration characteristics and analysis fault mechanism of rotating machinery. Figure 1 shows the typical rotor system and its cell division. The vibration differential equation was given as follows: （1） Mq C q K q Q Where the q is the generalized displacement vector, the form of the vector q : Fig1. Typical rotor system and unit dividing The rotor with transverse crack is to reduce the overall stiffness of the rotor. There will have the effect on the system with the crack opened and closed when the rotor rotates. We looked it as a rotor with no crack when it closed. And when it fully opened, we looked it as a rotor with a slot. To establish the unit stiffness matrix of crack in the fixed coordinate system (including two parts which were the constant Kc* and variable K c* ), and f m assemble with stiffness matrix without crack unit. The stiffness matrix of transverse crack rotor system and the vibration differential equation was given as follow: Mq C q K Kc* q Q Kc* qm （3） Where: m qm is the static deformation caused by its own weight of the rotor. Cracked rotor system vibration differential equation model of the rotor crack unit was established to simplify the impact of crack on the vibration of the rotor to an external force on the rotor which was given in equation: Kc* Kc e / 2 Kc e Kc e Kc e ) cos t / 2 （4） t t m t Kc and Kc are the constant does not change m e with rotation, Author: Jian-zhong Lou (1973 -), male, lecturer in Zhejiang Institute of Mechanical & Electrical Engineering, Ph.D., Zhejiang University. m rotating. e Kc e changes periodically with the l Where E is the modulus of elasticity, l is the length of unit, Ix and Iy are the moment of inertia for x and y axes, located on the right end (L = 100mm), the crack depth is about 50% of the diameter. h sin 2t , C cos 2t From equation (3) we can be seen to contain only sin 2t and cos 2t , that means it only contains the second harmonic component. Order: Kce cos t / 2 ( Kc3e Kc1e ) / 2 t t t （4） Where: c t only contain cos3t and sin3t , that means it only contains the third harmonic component. Kc1e t only contain cos t and sin t , that means it K 1e only contains base harmonic component. c t has the same matrix form. That is: K 3e q V 0 0 c m 1 1 ,V2 0 0 2 ,V3 0 0 3 T We can see from above that the additional force Kc e qc m l which was caused by the transverse crack rotor system is same in the rotor horizontal as in the vertical directions. Phase difference is 90 degrees which is similar with the unbalanced force, but it excites the rotor with second harmonic vibration components. K c e q c m K c3e / 4 K c e / 2 K 1e / 4 K c e K c e cos t / 2 q c m l f l f m （5） The above analysis only considers the bending stiffness of the crack unit. The shear stiffness of the crack unit also has the same conclusion. The linear increase naturally has the same features. Through the analysis of the vibration differential equation of the cracked rotor system, you can see the rotor with transverse crack has the typical characteristics of the vibration and diagnostic information: The rotor with a transverse crack vibrate with high multiplier of the second harmonic, third harmonic components and cause the rotor power frequency component amplitude and phase changes. Figure 2 crack shaft used in test bench IV. EXPERIMENTAL RESULTS AND ANALYSIS Through the above experiments, the result shows that: With an opening crack on the rotor, it appeared the rotation frequency of 2 times, 3 times and high-harmonic components. When crack propagation, stiffness further reduces, amplitude of 1 time, 2 times frequency also increased. When the operating speed passed half of the critical speed, the amplitude will appear the resonance peak. In order to find the phenomenon of frequency modulation cause by the phase modulation and reducing signal frequency modulation caused by the changing of rotational speed. We collected a group of data when the rotor speeds up in the same phase. Figure 3 shows the vibration signal time-domain waveform and the Fourier spectrum under the speed of 1900RPM with rotor transverse crack. From the figures we can find the two times frequency clearly. III. FAULT SETTING AND THE PRINCIPLE Figure 2 shows the shaft with the transverse crack which was customized for this experiment. The shaft machined through the following processing. First, cut the notch in given depth in the specified location of the shaft and the notch width is about 0.12mm, then cut the slot and embedded in piece of metal with the thickness of 0.10mm and fixed it in the notch with No.502 glue which is similar to opening and closing of the crack. The location of the crack was shown in Fig.2 which was Fig3 Time-domain waveform and spectrum of vibration signal with rotor transverse crack V. ANALYSIS OF DATA One of air pressure machines in Fujian Petrochemical catalytic company was shut down in June12, 2009 because of the fault. The monitoring system recorded the data in the black box in details. From the analysis of data, we found that some time before the machine shutdown, the speed of air pressure machine fluctuations. Then the security protection system worked, and the power system of air pressure machine shut down automatically and the air compressor stopped too. Figure 4 shows the vibration waveform under normal operation, it is clear that there are 8 cycle sine waves. Its spectrum is shown in Figure 5 which has only the fundamental frequency of the vibration amplitude. The amplitude of high frequency components is very small. Figure 6 shows the vibration waveform under fault states, it is clear that the vibration waveform is different from it in normal conditions. Spectrum also contains high frequency components which were shown in Figure 7. 8. From figure 9, the vibration amplitude of the high frequency spectrum of the vibration signal increased significantly, and speed soaring at the same moment, so it can prove that the result of the malfunction of the air pressure machine is load lost, which caused by transverse crack. After technical personnel adjust the control system, reboot, and the pressure resume to normal operation. Fig.8 pressure machine speed trend in fault state Fig4 waveform in normal conditions Fig. 5 Spectrum in normal conditions Fig. 6 waveform in fault conditions Figure 9 pressure machine base frequency trend in fault state VI. CONCLUSION Fig. 7 Spectrum in fault conditions Normal speed of air pressure machine is 8300 r/min. Due to the failure of pressure control system, the speed of air pressure machine fluctuations. The protective measures of control system began to work. The air pressure machine shut down. In this process, loads begin to lose. So speed instantly rose to 10,000 rpm, and instantly went back to normal speed, as shown in Figure Through building the model to add the transverse crack in the rotor test table of Bently in the laboratory to simulate the bearing fault state of rotor transverse crack fault, through experimental results and theoretical analysis. The main vibration characteristics were stated through the analysis of laboratory data when the bearing box was in the state of transverse crack fault. This is a great help for fault diagnosis and research. REFERENCES  Wei Wei. “Typical vibration of large rotating machinery fault diagnosis”. Shenyang Chemical Industry[M]. 2000,29 (4): pp115.  Wang Ping. “Monitoring and analysis of rotary machinery orbit”. 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