Measuring and testing – Vibration – Resonance – frequency – or amplitude study
Reexamination Certificate
2003-02-12
2004-03-16
Moller, Richard A. (Department: 2856)
Measuring and testing
Vibration
Resonance, frequency, or amplitude study
C073S593000
Reexamination Certificate
active
06705168
ABSTRACT:
This invention relates to the technical domain of measuring, recording and studying the vibrations of a bearing block or the rotor of a rotating machine.
In this domain, it is known how to use at least two position sensors placed relative to the bearing block so as to measure the shaft displacements, for example to study the rotational behavior of a shaft guided by an oil bearing block. The two position sensors are then arranged in the same plane, approximately perpendicular to the direction of rotation, along two approximately orthogonal measurement directions X and Y. The sensors are used to make a series of measurements x(t) and y(t) that can be considered as being the instantaneous coordinates of the axis of the shaft supported by the bearing block. Two seismic sensors, for example accelerometers, can also be used for the study of the vibrations of the bearing block. It is also known how to use means of measuring the rotation speed &ohgr;(t) of the shaft, in order to complete this information.
After acquisition, the measured magnitudes are recorded on an appropriate support or data storage device. Considering the large number of measurements made, it then may be necessary to compress data to reduce the volume.
In general, this compression is done by calculating a DFT (Discrete Fourier Transform) for each of the two series x(t) and y(t) to obtain a spectral decomposition of the x(t) and y(t) series in amplitude and phase according to an amplitude-phase couple [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;y(f
i
)], in which f
i
corresponds to frequency values distributed on the frequency spectrum and is usually chosen so as to correspond to integer multiples or an integer fraction of the rotation speed.
This type of processing by a Fourier Transform can significantly reduce the data volume to be stored to the extent that it is possible to record the spectral amplitude-phase decomposition that includes a limited number of terms, instead of the measurements themselves.
However in practice, in cases in which prolonged test campaigns are carried out involving a large number of measurements, it was found that the individual spectral decomposition of each measurement series x(t), y(t) represents a relatively large data volume and for which the compression factor is not sufficient.
Furthermore, individual spectral decomposition data for x(t) and y(t) measurements cannot be used directly to make a detailed analysis of the behavior of the bearing block or the rotating element being studied.
Therefore, it appears necessary to have a new processing technique capable firstly of reducing the volume of data to be stored without introducing any bias or excessive distortion, while providing data that can be used directly and in particular that are useful for an intuitive analysis of the behavior of the rotating element being studied.
In order to achieve these objectives, the invention relates to a process for processing measurements of the vibration of a rotor of a rotating machine, of the type consisting particularly of:
using a record of at least one pair of two series of measurements x(t) and y(t) made using at least one pair of two position sensors placed relative to the rotor and arranged approximately in the same plane and with two approximately orthogonal measurement directions X and Y,
calculate a DFT (Discrete Fourier Transform) of each of the two series x(t) and y(t) to obtain a spectral decomposition of the series x(t) and y(t) in amplitude and phase according to two series of amplitude-phase pairs [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;y(f
i
)], where f
i
corresponds to frequency values distributed on the frequency spectrum,
According to the invention, this process also consists of:
starting from spectral decompositions [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;y(f
i
)], calculating a spectral decomposition in elementary elliptical trajectories of the displacement of the rotor axis, defined by a series of sets of at least three data [Emax(f
i
), Emin(f
i
), E&phgr;(f
i
)] where:
Emax(f
i
) is the maximum radius of the elementary ellipse at frequency f
i
,
Emin(f
i
) is the minimum radius of the elementary ellipse at frequency f
i
,
E&phgr;(f
i
) corresponds to the value of the orientation angle of the principal axis of the elementary ellipse (between 0 and 180°), and may be positive or negative depending on the direction of movement around the ellipse,
save the series [Emax(f
i
), Emin (f
i
), E&phgr;(f
i
)].
It appears that this new processing process has the advantage that it reduces the volume of data to be stored by about a quarter, because three parameters Emax(fi), Emin(fi), E&phgr;(f
i
) replace the four parameters [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;y(f
i
)] in the spectral decomposition.
Furthermore, the three data [Emax(f
i
), Emin(f
i
), E&phgr;(f
i
)] supply characteristic magnitudes of the elementary ellipse corresponding to the trajectory for frequency f
i
in the X, Y plane of the axis of the rotating element being studied, for each frequency f
i
in the spectral decomposition.
Thus, knowledge of these three parameters is a means of almost immediately perceiving the behavior of the rotating element being studied at frequency f
i
.
According to the invention, the [Emax(f
i
), Emin(f
i
), E&phgr;(f
i
)] coefficients may be calculated in different ways starting from spectral decompositions [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;y(f
i
)].
Thus, according to a first variant embodiment, the processing in the method according to the invention is as follows:
use a FFT (Fast Fourier Transform) algorithm using complex numbers, and applied to the signal x(t)+jy(t),
make a spectral decomposition of the rotation movement, firstly for positive frequencies and secondly for negative frequencies, giving two series [A(f
i
), &PHgr;(f
i
)] and [A(−f
i
), &PHgr;(−f
i
)],
starting from positive frequency spectra and negative frequency spectra, calculate the spectral decomposition into elementary ellipses using the following formulas:
Emax
(
f
i
)=[
A
(
f
i
)+
A
(
f
i
)]/2
Emin
(
f
i
)=
Abs
[(
A
(
f
i
)−
A
(−
f
i
)]/2]
S
(
f
i
)=
Sign[A
(
f
i
)−
A
(−
f
i
)]
E&phgr;
o
(
f
i
)=[&PHgr;(
f
i
)+&PHgr;(−
f
i
)]/2
E
&phgr;(
f
i
)=
S
(
f
i
)×
E&phgr;
o
(
f
i
)
According to a second variant embodiment of the method, the processing is done particularly as follows:
make a DFT-sin (Discrete Fourier Transform in sine) of the x(t) and y(t) series to obtain a spectral decomposition [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;y(f
i
)] in sine,
use the sine spectral compositions to make a spectral decomposition into elementary ellipses [Emax(f
i
), Emin(f
i
), E&phgr;(f
i
)].
According to another characteristic of the invention, the measurements x(t) and y(t), are made jointly with a measurement of the rotation speed &ohgr; of the rotor being studied to determine the behavior of the rotor as a function of its rotation speed &ohgr;.
And, according to another characteristic of the invention, the processing method consists particularly of the following steps:
make a record of several pairs of series of measurements x(t) and y(t), each pair [x(t), y(t)] being associated with a rotation speed &ohgr;(t) of the rotor
associating the corresponding rotation speed &ohgr; with the spectral decomposition of each pair x(t), y(t), into amplitude-phase [Ax(f
i
), &PHgr;x(f
i
)] and [Ay(f
i
), &PHgr;x(f
i
)]
associating the rotation speed &ohgr; with the spectral decomposition into elementary elliptical trajectories [Emax(f
i
), Emin(f
i
), E&phgr;(f
i
)]
record the set [&ohgr;[Emax(f
i
), Emin(f
i
), E&phgr;(f
i
)]].
The results of the calculation steps, and particularly the spectral decomp
Labeyrie Patrick
Poizat Philippe
Dennison Schultz Dougherty & MacDonald
Moller Richard A.
Ol db Acoustics & Vibration
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