**Application of the generalized vibration spectra for rotating machine condition monitoring**

by

A. Yu. Azovtsev, A.V. Barkov, N.A. Barkova, S.N. Rogov

VAST, Inc. St. Petersburg, Russia

**Abstract**

*The efficiency of machine condition monitoring is determined by the sensitivity of the
methods used for the analysis of signal to the appearance of the defects that decrease the
residual service life of the machine and its units. The traditional way to ensure the reliability
of the monitoring is based on the increase of the number of different types of measurements
and methods of signal analysis. But still another solution of this problem is available. It is
based on the development of the basic method of the analysis of the vibration signal that is
adapted to the problem of monitoring condition of the machine. This method is extremely
sensitive to the appearance of nearly all types of defects in the machine. Below such a
method of the rotating machines vibration analysis based on the measurement of the
generalized spectrum is justified.*

For monitoring condition of rotating machines that have a stable rotation frequency, it is usual to use the method of spectral analysis of the vibration signal. This method has a number of advantages. First is the ability to separate the vibration components of sources which are from different units of the machine. The most efficient method for this is narrow band spectrum analysis with the frequency resolution of about one tenth of the rotation frequency of the unit under control. In this situation, the variations of the rotation frequency should not exceed 0.1%-0.5% of its mean value. It is possible to ensure such a stable rotation frequency, especially on transport, only during the process of vibration measurements (100-200 seconds), but from one measurement to another the rotation frequency usually has variations in a wider range. So, the problem is that the choice of the method of the signal analysis should ensure the ability to compare the results of periodic diagnostic measurements and preserve all the important diagnostic information that is present in the vibration signal.

Many years of investigations of the influence of the incipient defects of the rotating machines (the defects on the initial stages of their development) on the oscillating forces and the resultant excited vibrations show that, in the most cases, the main forces and the power of the vibration components excited by these forces does not change significantly due to the appearance of the incipient defects. At the same time, small defects have a notable influence on a number of other characteristics of the oscillating forces and vibration of the machine units. Here are the main types of such influence in the descending order of the value of diagnostic information [1]:

- the amplitude modulation of the oscillating forces and corresponding vibration components of the rotating machine.
- the appearance of pulsating moments in the rotating units and thus a frequency modulation of the vibration components.
- changes in the form of the oscillating forces and appearance or increase of new harmonic components in the vibration excited by these forces.
- the increase of the oscillating forces and the corresponding components in the vibration spectrum and appearance of new components.

It is possible to detect the defects of rotating machines using monitoring only in cases where the natural random fluctuations of the periodically measured vibration parameters are less than the regular changes caused by the defect appearance. The basic method of signal analysis must assure the maximum reliability of the defects detection on the background of the measured vibration parameters fluctuations that can be caused by:

- the change in the rotation frequency of the machine between the periodic measurements.
- the change in the mode of operation of the machine including changes in load, temperature, etc.
- the appearance of construction and technological deviations during manufacturing, assembling or repairing of some units of the machine,
- different measurement conditions including the position of measurement point, method of transducer mounting, calibration of the instruments, etc.
- the influence of extraneous signals including vibration of other machines, electric fields, etc.

Thus, the method most sensitive to the appearance of incipient defects in the rotating machines is the narrow band spectrum analysis of the vibration signal. Using this method, it is possible to detect the main types of modulation, the change of the shape of oscillation forces and the appearance of new components in the vibration spectrum. But, at the same time, the fluctuations of some parameters of the narrow band vibration spectra due to above mentioned reasons can be so strong that they make the defect detection very hard. Besides narrow band vibration spectra, constant percentage bandwidth spectra are used for monitoring condition of rotating machines. One example is third octave spectra. The fluctuation of the parameters in such spectra, especially if the variations of the rotation speed does not exceed 10%, is much lower than in the narrow band spectra. But at the same time, it is impossible to detect some defect symptoms by the analysis of such spectra, for example, amplitude or frequency modulation of a certain vibration component.

So, it becomes evident that here occurs a problem of an optimal method of spectral analysis of the vibration signal for monitoring condition of the rotating machines. The desired spectrum should be as informative as a narrow band spectrum and, at the same time, the fluctuations of the diagnostic parameters when the rotation frequency or load or a method of the transducer mounting changes should be minimal.

Many years experience in rotating machinery condition monitoring using vibration shows that the
Generalized vibration spectrum gives the best result in the monitoring condition of the rotating
machines. This kind of spectrum is formed from the narrow band spectrum and has a number of
properties typical to a third octave spectra. Every component of the generalized spectrum is formed
from the narrow band components that belong to one third octave band with a generalized
geometric mean frequency. The amplitudes of the narrow band spectrum components within this
band are multiplied, but not added (their energies are not summed) as is done when the third octave
spectra are formed from the narrow band spectra. The resulting amplitude of the generalized
spectrum component Aofi is equal to [2]:

(1)

where A*f*_{j} - is the amplitude of the *j* component of the narrow band spectrum in the frequency band
corresponding to the generalized spectrum component.

*N*_{i} - the number of the narrow band spectrum components in the certain band corresponding to the
generalized spectrum component.

The amplitude A^{o}*f*_{i} of the generalized spectrum is uniformly sensitive to the changes or appearance
of both the weak or strong vibration components within a certain frequency band. Thus A^{o}*f*_{i} is
sensitive to the appearance of weak side bands that occur in the vibration spectrum when the
strong harmonic component (carrier) is modulated by some signal and to any other components in
the vibration spectrum.

When this algorithm (1) was optimized, some weighting coefficients were implemented on the
amplitudes of the strong harmonic components within the band corresponding to the generalized
spectrum component. Taking into account that the amplitudes of the vibration are usually measured
in dB, the amplitude of the generalized spectrum component corresponding to the mean geometric
frequency *f*_{i} can be expressed by:

(2)

where *Lf*_{j} is the level of the *j* component of the narrow band spectrum

*c*_{j}=1+*N*_{j}/10 - the weight coefficient for strong harmonic components

*c*_{j}* *=1 for random components.

After the weight coefficients were implemented on the strong harmonic components, a very
important problem appeared- how to distinguish the harmonic components in the initial narrow
band vibration spectrum. An empirical rule can be used for this purpose. A spectrum component
can be assumed to be harmonic if it exceeds the random components by 10 dB. An example of a
generalized spectrum together with the initial narrow band spectrum is presented on figure 1. When
a defect occurred in one of the gears in a gearbox, the teeth harmonics f_{z} and 2f_{z} were modulated
by the rotation frequency of this gear, f_{r}. A number of side bands can be found in the narrow band
spectrum (Fig.1b). In the generalized vibration spectrum we see the increase of levels of the
corresponding components with f_{z} and 2f_{z}.

Fig 1a(above). An Example of the Generalized spectra application in the monitoring condition of a gearbox - a narrow band spectrum of a gearbox with no defect.

Fig. 1b(above). A narrow band spectrum of the same gearbox with a worn gear.

Figue 1c(above). The generalized spectrum of the gearbox. Grayed bars represent the increase of the generalized spectra components corresponding to the development of the wear of a gear.

As the generalized vibration spectrum contains the main diagnostic information, it is possible to use it not only for detection of changes in the vibration state of the machine, but also to identify the reasons for such changes - to make the diagnostics of the rotating machines. The only weak point of the generalized and narrow band spectra analysis is that these methods are not sensitive to the amplitude modulation of the random vibration components. This problem can be overcome by the analysis of both the generalized vibration spectrum and the narrow band spectrum of the envelope of random vibration components measured in the reference points of the machine.

The generalized vibration spectra are widely used in the stationary and portable diagnostic systems developed by the VAST, Inc. There can be some peculiarities concerning the choice of the frequency band used for the vibration measurements. So, for the monitoring condition of the machine as a whole, it is recommended to measure vibration in the special reference points of the machine up to 20-40 harmonics of the rotation frequency. For the monitoring condition and diagnostics of separate units of the machine, it is recommended to use generalized spectra measured up to 20—40 harmonic of the rotation frequency and even higher frequencies that are determined by the construction peculiarities of the unit. For example, up to 2-3 harmonic of the teeth frequencies in the gearboxes, blade passage frequencies in the turbines and pumps, slot pass frequencies in electric machines etc. The measurements should be made in the control measurement points on the cases of the machines.

**Summary**

The application of the generalized vibration spectra for the monitoring condition of the rotating machines can solve the following problems:

- decrease the amount of work on the analysis of the measured vibration and simplify the problem of its automatization with no loss of diagnostic information.
- minimize the number of measurement points on the machine.
- enlarge the list of defect types that can be detected and identify the types of defects.

The use of generalized spectra analysis in the stationary and portable monitoring condition and diagnostic complexes produced by VAST, Inc. has enabled the cost of the systems to be significantly reduced and the efficiency of the defects detection and identification to be significantly increased.

**Bibliography**

1. ALEXANDROV A., BARKOV A., BARKOVA N., SCHAFRANSKY V. - Vibration and Vibrodiagnostics of Electrical Equipment on Ships, - Sudostroenie, Leningrad, 1986.

2. BARKOV A., BARKOVA N., ROGOV S. - "Generalized Spectra - A New Concept For Improved Condition Monitoring"- Proceedings of the 18TH Annual Meeting of the Vibration Institute, Hershey, PA, 1994.