=Paper=
{{Paper
|id=Vol-1638/Paper71
|storemode=property
|title=Vibrodiagnostics of compressor valves via music pseudo-spectra s
|pdfUrl=https://ceur-ws.org/Vol-1638/Paper71.pdf
|volume=Vol-1638
|authors=Anatoliy A. Khvostov,Victor I. Ryazhskih,Igor A. Kazmin,Nikolay A. Degtyarev,Alexey V. Ivanov
}}
==Vibrodiagnostics of compressor valves via music pseudo-spectra s==
https://ceur-ws.org/Vol-1638/Paper71.pdf
Mathematical Modeling
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 paper presents a mathematical model of a piston compressor
which is part of nitrogen-oxygen gas generator. Taking into account the struc-
tural parameters of the compressor, as well as the suction and pressurization
valves, such model allows to obtain the dynamics of the pressure amplitude un-
der the compressor’s piston together with the vibration velocity and vibration
acceleration that are transmitted in the form of mechanical affections to the
equipment (such mechanical affections can be observed using the correspond-
ing sensors). Also we investigate the pseudo-spectra of vibration signals using
the MUSIC algorithm for the set of parameters of compressor’s model (such pa-
rameters determine the evolution of a defect).
Keywords: vibrodiagnostics, piston compressors, nitrogen oxygen producing
station, pseudospectrum, suction and delivery compressor valves.
Citation: Khvostov AA, Ryazhskih VI, Kazmin IA, Degtyarev NA, Ivanov
AV. Vibrodiagnostics of Compressor Valves via MUSIC Pseudo-spectra.
CEUR Workshop Proceedings, 2016; 1638: 588-592. DOI: 10.18287/1613-
0073-2016-1638-588-592
Introduction
The analysis of operation of the Nitrogen-Oxygen Gas Generator (NOGG) has shown
that one of the major reasons for stoppage is a fault in the high-pressure pneumatic
systems. At the same time the main reason for failure in the high pressure pneumatic
system is the failure of the valves in suction and pressurization lines.
In this way the quality of operation of the valves substantially determines the efficien-
cy of compressor’s operation as well as the NOGG operation. The defects of valves
lead to an increase of energy expended for pushing of the gas, as well as to reducing
the compressor efficiency together with the fact that the cost of air production at cer-
tain pressure 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 compressor’s operation [2]. This allows to predict the technical
condition of equipment and to prevent the station failure at a critical moment [3].
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However, it is necessary to develop a mathematical model of pneumatic equipment
taking into account the evolution of the probable major defects. This will allow to
identify the main vibration features of the valve’s failures. Also such a mathematical
model will allow to construct the algorithms for information processing from the vi-
bration sensors and to investigate the spectra 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 model of compressor
In order to make a simulation of the evolution of defects of the valves in suction and
pressurization lines we developed a mathematical model of the compressor taking into
account the valve’s defects evolution.
In this model of compressor we considered the following main functional elements of
the system: compressor’s piston which moves in the cylinder under affection of the
crank mechanism; suction and pressurization valves of the compressor that are mov-
ing under the force caused by the difference of the pressure between the chamber
under the piston and the suction line (or pressurization line); volume of the chamber
under the piston which depends on the pressure.
The equation of motion of the piston (1) relative to the coordinate x is constructed on
the basis of the force balance (the compressor is placed in a horizontal position, the
projection of gravity force on the x-axis is zero). The dynamics of Pcomp is described
by the equation (2) which is based on the equation of state for an ideal gas with con-
stant mass taking into account the isothermal conditions [5]. In order to make a quali-
tatively analysis of the real processes we use a simplified calculation scheme for self-
acting valves [6,7]. In this scheme the valve is replaced with a conventional hole
without friction and heat transfer losses. The gas flow in the valve is determined by
the areas of the holes Svalve1, Svalve2. For each valve we introduce a new coordinate
system, namely x1 (x2) for suction (pressurization) valve. The motion of the plates of
the valves with weights m1, m2 under the gravity force, viscous friction, spring reac-
tion cval1 and inertia is described by the equations (3) and (5). The change of pressure
in the chamber due to the expiration through the suction and pressurization valves is
described by the equations (4), (6) that are obtained using the equation of state for an
ideal gas, as well as the dependence (on the speed and hole’s area) of the amount of
[1]
gas flowing through the variable section Sslice x1 Dvalve1 , Sslice
[2]
x2 Dvalve 2 , where
Dvalve1 , Dvalve 2 are the diameters of suction and pressurization valves, respectively.
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d2x dx
m p 2 fr m p gsign S p Pcomp F ext ; (1)
dt dt
dPcomp Pcomp Prel[1] Prel[2] dx
; (2)
dt ( H p H dv х) dt
0 x H p ;
2
mvalve1 d x1 valve1 dx1 c spr .valve1 x1 Svalve1 ( Psuc Pcomp ); (3)
dt 2 dt
0 x X ;
1 кл1
[1]
dPrel x D RT 2 Psuc Pcomp
sign( Psuc Pcomp ); (4)
dt 1 valve1
V [1] [1]
d 2 x2 dx
mvalve 2 2
valve 2 2 c spr .valve 2 x2 Svalve 2 ( Pdel Pcomp ); (5)
dt dt
0 x2 X valve 2 ;
dP[2] RT 2 Pdel Pcomp
rel x2 Dvalve 2 [2] sign( Pdel Pcomp ); (6)
dt V [2]
dx
x(0) x0 , dx (t 0) xv 0 , x1 (0) x01 , 1 (t 0) xv 01 ,
dt dt
dx2
x2 (0) x02 , (t 0) xv 02 ;
dt
P (0) P
comp 0 , Pdel (0) Pdel 0 , Pdel (0) Pdel 0 .
[1] [1] [2] [2]
comp
Here x is the coordinate, t is the time, mp is a weight of the piston, S p is the area of
the edge surface of the piston, sign(z) is the standard signum-function, fr is the fric-
tion coefficient, Fext is the force affection from the crank mechanism, Pcomp is the
pressure in the chamber under the piston, H p is the stroke, H dv is the displacement
relative to the x-axis which corresponds to the "dead" volume of the chamber,
[1] [2]
Pdel , Pdel are the pressure losses due to the air flow through the suction and pressuri-
zation valves, valve1 , valve 2 are the damping coefficient of the valve (it depends on the
constructive features of the valve, viscosity and density of a gas surrounding the
plate), is the density of the gas, [1] , [2] are the coefficients of hydraulic re-
sistance of the valves, X valve 2 , X valve1 are the maximum strokes of the valves, Psuc is
the pressure in suction line, Pdel is the pressure in pressurization line.
2 Numerical simulation
The mathematical model is realized in MathWorks Simulink™ simulation software.
The numerical experiments included the following steps:
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1. Start the simulation process and recording the signals of pressure’s amplitude to-
gether with the speed of its variation and corresponding acceleration.
2. Recording of the arrays of amplitudes, velocities, and accelerations as a gauge sig-
nal (this signal corresponds to the operation of healthy compressor) in the database
(DB) of vibration signals.
3. Simulation of the valve’s defect by changing the corresponding parameter in the
mathematical model and start the process of simulation.
4. Calculation of the spectra of vibration signals from the DB for each of the simulat-
ed defects. Formation of DB of the vibration signals spectra.
5. Graphic and parametric representation of the obtained spectra and evaluation of
significance of differences in the spectra due to the valve’s defect.
6. Making decision on the possibility of diagnosis of the defect by the selected vibra-
tion features in the spectrum of the analyzed signal.
In order to construct the spectrum of the signals of pressure’s amplitude, velocity and
acceleration in the chamber under the piston of the compressor we use the MUSIC
(MultipleSIgnal Classification) algorithm. It is designed for spectral analysis of the
signals that are represented by the sum of multiple sine waves (multiple complex
exponents 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 (amplitude and power) of the harmonic components (in addition to ability to
obtain the spectrum as it is) [10].
The resulting dependence of the signal level on the frequency is called as the pseudo-
spectrum. In addition, the parameter setting of MUSIC allows to use it as a filter with
tunable sensitivity (it determines by the order of spectral transformation) to compo-
nents of the signal’s harmonics.
During the numerical simulation we have carried out the search process for the pa-
rameters of MUSIC algorithm that allow to identify the valve’s failure in suction or
pressurization lines. In order to calculate the pseudo-spectrum we used the function
pmusic(). In order to calculate the frequencies and power of harmonics in the spec-
trum we used the rootmusic()-function from the libraries of Signal Processing
Toolbox of the MathWorks Matlab™ package [11].
3 Results
Our numerical investigations showed the possibility to estimate the degree of defect’s
evolution for various valve’s defects in the compressor of NOGG (namely, the
NOGG-70M) using the parameters of pseudo-spectra obtained by the MUSIC algo-
rithm. The main parameters that correspond to defects in the valves (due to its aging
or breakage) are: valve’s spring stiffness, the flow section area, the response time and
the weight of the valve.
We obtained the fact that the lowering of the order of transform (reduction of the
number of approximating harmonics) up to 10-20 allows to get the spectrum without
the components that correspond to high-frequency noise in the signal. It should also
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be pointed out that for the considered simulations of defects the parameters of the
spectra of vibration velocity for the pressure under the piston are most sensitive (see
the fig. 1).
Fig. 1. Pseudo-spectra of vibration velocity for pressure under compressor’s piston obtained by
MUSIC algorithm
References
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