Vibration signal analysis of main coolant pump flywheel based on hilbertehuang transform

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Vibration signal analysis of main coolant pump flywheel based on hilbertehuang transform. In this paper, we present a HilberteHuang transform (HHT) algorithm for flywheel vibration analysis. The simulation indicated that the proposed flywheel vibration signal analysis method performs well, which means that the method can lay the foundation for the detection and diagnosis in a reactor main coolant pump.
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Vibration signal analysis of main coolant pump flywheel based on hilbertehuang transform. In this paper, we present a HilberteHuang transform (HHT) algorithm for flywheel vibration analysis. The simulation indicated that the proposed flywheel vibration signal analysis method performs well, which means that the method can lay the foundation for the detection and diagnosis in a reactor main coolant pump..

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Nucl Eng Technol 47 (2015) 219e225 Available online at www.sciencedirect.com ScienceDirect journal homepage: http://www.journals.elsevier.com/nuclear-engineering-and-technology/ Technical Note VIBRATION SIGNAL ANALYSIS OF MAIN COOLANT PUMP FLYWHEEL BASED ON HILBERTeHUANG TRANSFORM MEIRU LIU, HONG XIA*, LIN SUN, BIN LI and YANG YANG Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, College of Nuclear Science and Technology, Harbin Engineering University, No. 145, Nantong Street, Harbin 150001, China a r t i c l e i n f o Article history: Received 10 October 2014 Received in revised form 9 December 2014 Accepted 10 December 2014 Available online 21 January 2015 Keywords: Dynamic analysis HilberteHuang transform Main coolant pump flywheel a b s t r a c t In this paper, a three-dimensional model for the dynamic analysis of a flywheel based on the finite element method is presented. The static structure analysis for the model provides stress and strain distribution cloud charts. The modal analysis provides the basis of dynamic analysis due to its ability to obtain the natural frequencies and the vibrationemade vectors of the first 10 orders. The results show the main faults are attrition and cracks, while also indicating the locations and patterns of faults. The harmonic response simulation was performed to gain the vibration response of the flywheel under operation. In this paper, we present a HilberteHuang transform (HHT) algorithm for flywheel vi-bration analysis. The simulation indicated that the proposed flywheel vibration signal analysis method performs well, which means that the method can lay the foundation for the detection and diagnosis in a reactor main coolant pump. Copyright © 2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society. 1. Introduction 2. Flywheel modeling Vibration monitoring is an important issue for the mainte- 2.1. Modeling environment selection nance and safety of main coolant pumps. Operation data show that the flywheel is mostly prone to fault in actual operation, whichaffectsthe safetyof thewhole nuclearpower plant. The critical process involved in vibration monitoring is to extract reliable features representative of the vibration signal of the flywheel. Before establishing a flywheel finite element model, we need to get a three-dimensional solid model first. For an uncom-plicated model, the CAD modeling method is generally applied. The model is then imported into the ANSYS ge-ometry module through the software interface [1]. In this study, the solid flywheel model was established using * Corresponding author. E-mail address: xiahong@hrbeu.edu.cn (H. Xia). This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any me- dium, provided the original work is properly cited. http://dx.doi.org/10.1016/j.net.2014.12.010 1738-5733/Copyright © 2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society. Special Issue on ISOFIC/ISSN2014. 220 Nucl Eng Technol 47 (2015) 219e225 Pro/E, then imported into ANSYS. In order to clarify the entire process, Fig. 1 shows the flow chart of the modeling and analysis. 2.2. Flywheel structural parameters The flywheel is composed of six parts: hub, heavy tungsten segments (HTS), shrink ring, end ring, sleeve, and thrust plate. The sectional view is shown in Fig. 2. The axisymmetric model can be established by stretching, rotating, and arraying procedure. Fig. 3 depicts the exploded solid model established by Pro/E according to the structural parameters of the flywheel. Fig. 2 e Sectional view of the flywheel. 2.3. The finite element model of the flywheel The required material parameters are listed in Table 1. 3. Static structure analysis of flywheel model Based on the above data, the flywheel finite element model is shown in Fig. 4. In order to improve the accuracy of finite element analysis, we chose tetrahedrons, hex dominant, and sweep methods to mesh the model. There are 75,052 elements and 225,351 nodes in total. In addition, the minimum edge length is 6 10 m3. According to the mesh metric data shown in Table 2, we can conclude that the mesh quality is good enough to meet the requirements. The fixed remote displacement is imposed at the upper and lower thrust plates to act as constraints. The rotational load shown in Fig. 5 is applied to the center of the hub. The displacement and stress distribution cloud charts of the calculation results are shown in Fig. 6, 7. These results indicate that the minimum displacement is 5.02 10 m4, whichoccurs in thecenter,andthe maximumdisplacementis 1.88 103 m, which occurs in the periphery. At the same time, the minimum stress is 1236.8 Pa located in the center of the lower thrust plate and the maximum stress is 1.78 107 Pa located in the keyway of the hub. Geometric Modeling Setting Material Properties From Pro/E There are three obvious faults. One of them is a crack being extended through the whole sleeve (Fig. 7A), while another is identified as the attrition existing in the keyway of the hub Setting Contacts Meshing Preprocessing Display, Modify, Refinement Modify Load Applying Static Structural Analysis Modal Analysis Finite Element Analysis Dynamical Analysis Display, Export Afterprocessing No satisfaction Yes End Fig. 1 e Flow chart of the modeling and analysis. Fig. 3 e Exploded view of the flywheel solid model. Nucl Eng Technol 47 (2015) 219e225 221 Table 1 e Flywheel material properties. Part Hub HTS Shrink ring End ring Sleeve Thrust plate Material 403SUS WHA 18Ni 625Alloy 690Alloy Graphite Density(kg/m3) 7,750 18,600 8,500 8,440 8,190 1,860 Young's Modulus(GPa) 193 350 205 206 211 11.3 Poisson's ratio 0.31 0.3 0.3 0.308 0.289 0.23 (Fig. 7B), and finally the third fault is assumed to happen at the 4.2. Modal analysis of flywheel model angle of heavy tungsten segments which contact the hub (Fig. 7C). Structural vibration can be expressed as the linear combina-tion of each order of natural vibration modes, with the lower 4. Modal analysis of flywheel model 4.1. The theory of modal analysis vibration modes having a greater influence on structure vi-bration [3]. As a result, the vibration characteristics of structural analysis usually consider the first 5e10 modes. This study extracts the first 10 natural frequencies which are shown in Table 3. Based on mechanical vibration theory, the motion differential equation for any multiple degree of freedom system is shown in Equation 1: The value of vibration type is a relative value (relative displacement value), which suggests the relative ratio of vi- bration magnitude of each point atone natural frequency. It Mq þCq þKq ¼ Q (1) Where M, C, and K are mass matrix, damping matrix, and stiffness matrix, respectively [2]. When the system has no external excitation (Q ¼ 0), the system vibration is free. Then the equation is: Mq þCq þKq ¼ 0 (2) If the damping effect is ignored, the system can be considered an undamped free system for analysis. Thus the equation is: 1600 1400 1200 1000 800 600 400 200 Mq þKq ¼ 0 (3) 0 Solving the flywheel natural frequencies and mode shapes is equivalent to solving the generalized eigenvalues and ei- genvectors of Eq. (3). -200 0 5 10 15 20 t (s) Fig. 5 e Rotational velocity. Fig. 4 e Flywheel finite element model. Table 2 e Mesh metric. Item Average Standard deviation Element quality 0.66 0.30 Jacobian ratio 1.09 0.18 Warping factor 8.38 106 2.03 105 Fig. 6 e Displacement distribution cloud chart. 222 Nucl Eng Technol 47 (2015) 219e225 Table 3 e The first 10 natural frequencies. Order Frequency (Hz) 1 1.08 2 197.2 3 197.66 4 326.23 5 596.47 6 610.49 7 612.66 8 702.3 9 703.28 10 720.47 Critical speed (r/min) 65 11,832 11,860 19,574 35,788 36,629 36,760 42,138 42,197 43,228 vibration, the second and third orders show swinging vibra-tion, while the fourth and fifth orders show thrust plate expansion (see Figs. 9e11). 5. Harmonic response analysis of flywheel model 5.1. The basic theory of harmonic response analysis Harmonic analysis is used for rotating equipment to deter-mine a structure response under the known sinusoidal (harmonic) load [5]. When the spindle undergoes forced vibration, the main consequence will be vibrations in the spindle drive hub and HTS, and cracks will occur on the contact surface where stress is concentrated (as explained in Section 4). At this point, the general motion Equation 1 turns into Equation 4 in the harmonic response: u2M þiuC þ Kq1 þiq2 ¼ Q1 þiQ2 (4) Subscripts 1 and 2 express the real and imaginary com-ponents, respectively. 5.2. The harmonic response signals The vibration was measured by accelerometers mounted on the flywheel. Fig. 13 shows one of the amplitude spectra of vibration signals. However, due to the strong noise, the spectrum is quite complex and consists of many peaks. It is difficult to find any strong indication regarding the flywheel condition. 5.3. The HHT of vibration signals analysis Fig. 7 e Stress distribution cloud chart. reflects the transportation of the natural vibration frequency, not the actual vibration value [4]. Figs. 8e12 show the vibration mode corresponding to the The HilberteHuang transform (HHT) consists of two parts: empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). It is potentially viable for TFR of nonlinear and non-stationary data. In addition, it has produced sharper results and has revealed true physical meaning compared with most other existing techniques in all the cases analyzed [6]. Since EMD decomposes signals into intrinsic mode functions (IMF) according to the order from high to low first to fifth orders of frequency. The first order exhibits shrink frequency [7], the applied EMDethreshold approach Nucl Eng Technol 47 (2015) 219e225 223 Fig. 8 e Mode of vibration under the first natural frequency. Fig. 9 e Mode of vibration under the second natural frequency. Fig. 10 e Mode of vibration under the third natural frequency.

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