VIBRODIAGNOSTICS OF COMPRESSOR VALVES VIA MUSIC PSEUDO-SPECTRA A.A. Khvostov, V.I. Ryazhskih, I.A. Kazmin, N.A. Degtyarev, A.V. Ivanov MESC AF N.E. Zhukovsky and Y.A. Gagarin Air Force Academy, Voronezh, Russia Abstract. The aer resents a mathematical mo of a iston comressor which is art of nitrogen-oxygen gas generator. Taking into account the structural arameters of the comressor, as well as the suction and ressurization valves, such mo allows to obtain the dynamics of the ressure amlitude under the comressor s iston together with the vibration velocity and vibration acceleration that are transmitted in the form of mechanical affections to the equiment (such mechanical affections can be observed using the corresonding sensors). Also we investigate the seudo-sectra of vibration signals using the MUSIC algorithm for the set of arameters of comressor s mo (such arameters determine the evolution of a defect). Keywords: vibrodiagnostics, iston comressors, nitrogen oxygen roducing station, seudosectrum, suction and ivery comressor valves. Citation: Khvostov AA, Ryazhskih VI, Kazmin IA, Degtyarev NA, Ivanov AV. Vibrodiagnostics of Comressor Valves via MUSIC Pseudo-sectra. CEUR Worksho Proceedings, 016; 1638: 588-59. DOI: 10.1887/1613-0073-016-1638-588-59 Introduction The analysis of oeration of the Nitrogen-Oxygen Gas Generator (NOGG) has shown that one of the major reasons for stoage is a fault in the high-ressure neumatic systems. At the same time the main reason for failure in the high ressure neumatic system is the failure of the valves in suction and ressurization lines. In this way the quality of oeration of the valves substantially determines the efficiency of comressor s oeration as well as the NOGG oeration. The defects of valves lead to an increase of energy exended for ushing of the gas, as well as to reducing the comressor efficiency together with the fact that the cost of air roduction at certain ressure grows [1]. The existing systems of vibration diagnostics use individual algorithms for detection of each kind of defect at the initial stage of its evolution. These algorithms allow to carry out the functional diagnostics for the objects at the nominal regime of the comressor s oeration []. This allows to redict the technical condition of equiment and to revent the station failure at a critical moment [3]. Information Technology and Nanotechnology (ITNT-016) 588
However, it is necessary to develo a mathematical mo of neumatic equiment taking into account the evolution of the robable major defects. This will allow to identify the main vibration features of the valve s failures. Also such a mathematical mo will allow to construct the algorithms for information rocessing from the vibration sensors and to investigate the sectra of the recorded signals (this allows to make a decision about the system state via the set of vibration features of the defects) [4]. 1 Mathematical mo of comressor In order to make a simulation of the evolution of defects of the valves in suction and ressurization lines we develoed a mathematical mo of the comressor taking into account the valve s defects evolution. In this mo of comressor we considered the following main functional elements of the system: comressor s iston which moves in the cylinder under affection of the crank mechanism; suction and ressurization valves of the comressor that are moving under the force caused by the difference of the ressure between the chamber under the iston and the suction line (or ressurization line); volume of the chamber under the iston which deends on the ressure. The equation of motion of the iston (1) relative to the coordinate x is constructed on the basis of the force balance (the comressor is laced in a horizontal osition, the rojection of gravity force on the x-axis is zero). The dynamics of P com is described by the equation () which is based on the equation of state for an ideal gas with constant mass taking into account the isothermal conditions [5]. In order to make a qualitatively analysis of the real rocesses we use a simlified calculation scheme for selfacting valves [6,7]. In this scheme the valve is relaced with a conventional hole without friction and heat transfer losses. The gas flow in the valve is determined by the areas of the holes S, S. For each valve we introduce a new coordinate system, namely x 1 (x ) for suction (ressurization) valve. The motion of the lates of the valves with weights m 1, m under the gravity force, viscous friction, sring reac- c and inertia is described by the equations (3) and (5). The change of ressure tion val1 in the chamber due to the exiration through the suction and ressurization valves is described by the equations (4), (6) that are obtained using the equation of state for an ideal gas, as well as the deendence (on the seed and hole s area) of the amount of gas flowing through the variable section S x D, S x D [1] slice 1 [] slice valve, where D, D are the diameters of suction and ressurization valves, resectively. Information Technology and Nanotechnology (ITNT-016) 589
d x dx m sign ; (1) frm g S Pcom F ext [1] [] dpcom Pcom Prel Prel dx ; () ( H H dv х) 0 x H ; d x1 dx1 sr. 1 suc com m c x S ( P P ); (3) 0 x1 Xкл 1; [1] dprel RT Psuc Pcom x1dvalve 1 sign( P ); (4) [1] [1] suc Pcom V d x dx sr. com m c x S ( P P ); (5) 0 x X; [] dp rel RT P Pcom xdvalve sign( P ); (6) [] [] Pcom V dx dx1 x(0) x0, ( t 0) xv0, x1 (0) x01, ( t 0) xv01, dx x (0) x0, ( t 0) xv0; [1] [1] [] [] Pcom (0) Pcom 0, P (0) P 0, P (0) P 0. Here x is the coordinate, t is the time, m is a weight of the iston, S is the area of the edge surface of the iston, sign(z) is the standard signum-function, fr is the friction coefficient, F ext is the force affection from the crank mechanism, P com is the ressure in the chamber under the iston, H is the stroke, H dv is the dislacement relative to the x-axis which corresonds to the "dead" volume of the chamber, [1] [] P, P are the ressure losses due to the air flow through the suction and ressurization valves,, are the daming coefficient of the valve (it deends on the constructive features of the valve, viscosity and density of a gas surrounding the [1] [] late), is the density of the gas,, are the coefficients of hydraulic resistance of the valves, X, X are the maximum strokes of the valves, P suc is the ressure in suction line, P is the ressure in ressurization line. Numerical simulation The mathematical mo is realized in MathWorks Simulink simulation software. The numerical exeriments included the following stes: Information Technology and Nanotechnology (ITNT-016) 590
1. Start the simulation rocess and recording the signals of ressure s amlitude together with the seed of its variation and corresonding acceleration.. Recording of the arrays of amlitudes, velocities, and accelerations as a gauge signal (this signal corresonds to the oeration of healthy comressor) in the database (DB) of vibration signals. 3. Simulation of the valve s defect by changing the corresonding arameter in the mathematical mo and start the rocess of simulation. 4. Calculation of the sectra of vibration signals from the DB for each of the simulated defects. Formation of DB of the vibration signals sectra. 5. Grahic and arametric reresentation of the obtained sectra and evaluation of significance of differences in the sectra due to the valve s defect. 6. Making decision on the ossibility of diagnosis of the defect by the selected vibration features in the sectrum of the analyzed signal. In order to construct the sectrum of the signals of ressure s amlitude, velocity and acceleration in the chamber under the iston of the comressor we use the MUSIC (MultileSIgnal Classification) algorithm. It is designed for sectral analysis of the signals that are reresented by the sum of multile sine waves (multile comlex exonents in general case) with white noise [8]. This method is based on the analysis of the eigenvalues and eigenvectors of the signal s correlation matrix [9]. The main advantage of this algorithm is the ability to determine the frequencies and levels (amlitude and ower) of the harmonic comonents (in addition to ability to obtain the sectrum as it is) [10]. The resulting deendence of the signal level on the frequency is called as the seudosectrum. In addition, the arameter setting of MUSIC allows to use it as a filter with tunable sensitivity (it determines by the order of sectral transformation) to comonents of the signal s harmonics. During the numerical simulation we have carried out the search rocess for the arameters of MUSIC algorithm that allow to identify the valve s failure in suction or ressurization lines. In order to calculate the seudo-sectrum we used the function music(). In order to calculate the frequencies and ower of harmonics in the sectrum we used the rootmusic()-function from the libraries of Signal Processing Toolbox of the MathWorks Matlab ackage [11]. 3 Results Our numerical investigations showed the ossibility to estimate the degree of defect s evolution for various valve s defects in the comressor of NOGG (namely, the NOGG-70M) using the arameters of seudo-sectra obtained by the MUSIC algorithm. The main arameters that corresond to defects in the valves (due to its aging or breakage) are: valve s sring stiffness, the flow section area, the resonse time and the weight of the valve. We obtained the fact that the lowering of the order of transform (reduction of the number of aroximating harmonics) u to 10-0 allows to get the sectrum without the comonents that corresond to high-frequency noise in the signal. It should also Information Technology and Nanotechnology (ITNT-016) 591
be ointed out that for the considered simulations of defects the arameters of the sectra of vibration velocity for the ressure under the iston are most sensitive (see the fig. 1). Fig. 1. Pseudo-sectra of vibration velocity for ressure under comressor s iston obtained by MUSIC algorithm References 1. Plastinin PI. Piston comressors, vol. 1. Theory and calculations. Moscow: Koloss Publisher, 006. [In Russian]. Kostyukov VN, Naumenko AP. Vibrodiagnostics of Piston Comressors. Comressors and Pneumatics, 00; 3: 30-31. [In Russian] 3. Filliov IV. Research of vibration rocesses in oil-injected screw comressors. Science and Education of Bauman MSTU, 014; 10: 60-69. [In Russian] 4. Zhuravlyov OA, Komarov SYu, Poov KN, Prokofyev AB. Develoment of the automated method of vibration characteristics of ower lants. Comuter Otics, 001; 1: 143-149. [In Russian] 5. Grigoryev VA. Industrial ower and thermal engineering. reference book. Moscow: Energoatomizdat Publisher, 1991. [In Russian] 6. Kondratyev TF. The valves of iston comressors. Leningrad: Mashinostroenie Publisher, 1983. [In Russian] 7. Dodin YuS, Klochkov VI, Lukyanica AI. The valves of iston comressors. Novomoskovsk: D. Meneev University of Chemical Technology of Russia, 009. [In Russian] 8. Sergienko AB. Digital Signal Processing. St. Petersburg: Piter Pulisher, 007. [In Russian] 9. Jian X, Zhang C, Zhao B, Zhu B. The alication of MUSIC algorithm in sectrum reconstruction and interferogram rocessing. Otics Communications, 008; 9: 44-48. 10. Cheney M. The Linear Samling Method and the MUSIC Algorithm. Inverse Problems, 001; 4(17). 11. MathWorks (official site). URL: htt://matlab.ru/ (Date of insect 0.03.016). Information Technology and Nanotechnology (ITNT-016) 59