**Optimization of Monitoring and Diagnostics Methods for Rotating Machines using
Vibration and Noise Measurements**

by

Alexei Barkov, VAST, Inc., 22, Rozenshteina str., St. Petersburg, 198095, Russia

**Abstract**

*Current machinery condition monitoring and diagnostics methods use both simple energy
models of signals applied for the detection of changes in the machine condition and more
complicated ones that can detect and identify incipient defects. An analysis of the limitations
on the choice of signal analysis methods for on-line and off-line condition monitoring
methods is presented in this paper. Special attention is paid to the multiplicative signal
models that are very effective in the identification of the defects in the off-line monitoring
systems that allow making a condition prediction for a long period between noise and
vibration measurements.*

**Introduction**

Currently, three types of condition monitoring systems using vibration and noise measurements are widely used. The first type includes means of alarm protection of the equipment from the vibration and (or) noise that also guarantee shut down of the equipment on the initial stage of the breakdown. The second includes on-line systems for the detection of dangerous changes in the machine condition that will provide a sufficient time interval to adopt a decision for the equipment shutdown or maintenance. The third type includes both on- and off-line systems for defect detection, identification, and monitoring on the early stages of the defectdevelopment. Different methods of noise and vibration signal measurements and analysis can affect the efficiency of the monitoring system.

**Common Methods**

The simplest method for the detection of changes in the machine condition is the comparison of the measured vibration energy to a defined level that splits the set of machine conditions between defective conditions and good conditions. This is also the fastest method as the measurement can be made during only one revolution of the machine shaft. It is very typical that this energetic method already includes the basics of the most efficient spectrum analysis of the signals and measurements of vibration (noise) are conducted in parallel in a number of frequency bands. This is a basic method for all types of alarm protection systems for machinery. Typically, optimization of this method and systems is determined by the economic factors and is achieved by the choice of measurement points on the exact machine and the number of frequency bands for the parallel analysis of the signals.

In on-line systems for the condition monitoring of the rotating machines, the energetic method for detection of changes remains the main one used concurrently with the narrow band frequency analysis. Usually, developed defects, at least those close to the breakdown of the equipment, change the spectral composition of the vibration signal so that certain spectrum components exceed defect levels determined originally during the initial stage of the machine operation with the monitoring system. In this case, optimization of the system can be made basically, not by the optimization of signal analysis methods, but by the optimization of the system structure, i.e. determining the minimum number of vibration (noise) measurement points that will guarantee satisfactory probability of either missing defects or of false alarms, i.e. alarm signals when there is no danger. The reasons for possible false alarms include fluctuations of vibration (noise), spectrum components levels due to the changes in external conditions such as load, temperature, startup or shutdown of other machines, etc. In the off-line monitoring systems, when the same methods of signal analysis are used, the probability of defect missing or false alarms is higher. The first reason is that the measurements are made much less frequently. The second reason is that transducer is fixed each time measurements are made, introducing additional fluctuations in the levels of spectrum components, especially in the high frequency range. This is the reason why additional methods of vibration and noise signal analysis based on more complicated models of signals are used in the modern systems of vibroacoustical monitoring of the machine condition in addition to common energetic methods.

**Nonlinear Models**

What are the models of signals and methods of their analysis that can be the best prospects for
condition monitoring and diagnostics of machinery? First of all, there are non-linear models: an
additive-multiplicative combination of periodic and random stationary signals and analysis methods
that can separate the signal types with minimum loss of information. Research work made in recent
years show that a number of processes that generate oscillation forces can be well described by
such models [1]. At the same time, conversion of forces into vibration (noise) and its propagation
to the measurement point is adequately depicted by the linear models. The most general signal
model of the additive-multiplicative type with the simplest components can be represented as

(1) where

*x(t)* - measured vibration (noise) signal

- simplest modulated component

- simplest modulation component

*c*_{i} - coefficient responsible for relationship between additive and multiplicative components.

In this way, the most frequently observed amplitude modulated vibration and noise signals can be described. In practice, in the majority of cases the modulated components in the vibration (noise) signal are present in both defective and defectless machines and modulation components occur only when a defect develops or the machine operation mode is disrupted. Modulation components contain information on both type and severity of a defect. A significant advantage of measurements and analysis of such signals is the absence of absolute measurements and the parameters of the modulation process can benormalized to the parameters of modulated process. This brings up a situation when on-line and off-line systems will produce measurements with the same level of errors and defect detection and identification can be made by a single vibration (noise) measurement.

Let us consider some practical examples of diagnostic problems that can be successfully solved
using the above models. The simplest example is the detection of gear defects involving contact
between gears[2]. The gear teeth frequency vibrations can be represented using the model of
equation (1) where:

- harmonics of the teeth frequency,

- rotation frequency harmonics of the defective gearing, and

*c*_{i} -1 - modulation index of the teeth harmonics that indicates the defect severity.

The set of harmonics determines the defect type. The sidebands of the teeth harmonics in
the narrow band spectrum should be considered to find and to determine *c*_{i} from figure 1.

*Figure 1. Vibration spectrum of a gearbox with a gear defect.*

For the same purpose, it is possible to use cepstral analysis that is very sensitive to the appearance of the multiple harmonics or a number of sideband harmonics in the analyzed signal [2]. The same model can be applied to the detection of defects in the rotor winding of the induction motor [1].

A more complicated example is the detection of faults in a geared coupling when shock loads on
shaft and bearings occur several times during a shaft revolution. When the defects are well
developed, the amplitude of these loads is changed very slowly and randomly with time. As a
result, the spectrum components of the vibration signal at the rotation frequency widen significantly
in the frequency axis due to the amplitude modulation [3] as shown on fig.2 . A mathematical model
of this process can be represented by the model of equation (1) where

- j harmonic of the shaft rotation frequency,

- random stationary process with the maximum spectral density on the much lower
frequencies than the rotation speed.

*Figure 2a(above). Vibration spectra of a geared coupling with an incipient defect.
Figure 2b(above). Vibration spectra of a severely worn geared coupling.*

Much more complicated is the method of detection of rolling element bearings faults using high
frequency random vibration excited by friction forces [4]. The model of amplitude modulated
random vibration is applied in this case, here

- stationary random signal,

- periodic modulating process and

*c*_{i} - partial modulating indexes of the random vibration.

The complexity of this method is determined by the fact that simple spectral analysis is not sufficient
for the analysis of modulation in this case. Prior to spectral analysis, the random components
excited by friction forces should be extracted and their envelope should be formed. The spectral
analysis itself should be carried out with a high frequency resolution as the harmonic components of
the modulation process are rather weak compared to random components of the modulated signal
converted in the envelope detector [5]. A typical envelope spectrum is presented on figure 3. The
frequencies of the harmonic components in the envelope spectrum determine the defect type of the
rolling element bearing and their amplitudes determine defect severity. When a good bearing is
considered, the envelope spectrum has no harmonic components.

*Figure 3a(above). Envelope spectra of a good rolling element bearing.*

*Figure 3b(above). Envelope spectrum of a severely worn rolling element bearing.*

The considered signal model is applied for the diagnostics of a number of machine units when there is mechanical, hydrodynamic or aerodynamical friction [1,3]. Besides the above three kinds of additive-multiplicative signal models, some other models represented by equation (1) are used in practical problems. In this way, modulation process as a sign function enables us to describe vibration of electromagnetic origin in electric machines with such defects as saturation of active core or vibration of pump impeller due to the liquid cavitation [1]. Modulation process as a delta function may describe vibration excited by shock pulses in the defective units. In some practical cases when slide bearings and working wheels of the pumps are diagnosed, the same model when both and are stationary random processes is used [6]. In all of the considered, practical, diagnostic problems detection, identification of type and severity of a defect can be accomplished by comparison of parameters of modulation and modulated processes, i.e. by relative, thus, single measurements. In this case, as proved by experience, the efficiency of incipient defects detection is much higher compared to one using energetic methods. This means that at least in the off-line monitoring and diagnostic systems for the rotating machines a methods based on nonlinear models of forces and vibration excited by them should be used.

The question of what are the optimal methods of the signal analysis for the on-line monitoring and diagnostic systems should be considered taking into account the costs of system installation and operation. The models described here usually require measurements of the high frequency vibration on the case of each machine unit to be diagnosed, though common monitoring systems usually use only low frequency (below 1-3 kHz) measurements in a small number of control points on a machine. The simplest solution seems to be in combination of on-line and off-line monitoring systems. The tasks for both systems should be separated into machine condition monitoring and identification of the detected defects. In this case, the operator of the off-line diagnostic system can be responsible for the planning of maintenance and repair works on the enterprise.

**Conclusions**

- While choosing condition monitoring methods a special attention should be paid on the nonlinear signal models and those methods of signal measurement and analysis that will ensure minimum losses of the diagnostic information.
- A number of the defects in the rotating machine units can be detected and identifies by a single vibration measurement using nonlinear signal model as an additive-multiplicative combination of a simple components. The main difficulty in this case is the extraction from the measured signal components excited by the defective unit.
- Most successfully these methods can be used in the off-line monitoring and diagnostic systems ensuring the detection and identification of the incipient defects that is essential for the long term prediction of the save operation period for the machine between diagnostic measurements.
- These methods not always can be recommended to be used in the on-line monitoring systems because of the economic reasons as often they require to increase the number of measurement points to measure the vibration on case of every machine unit under control.

**References**:

1. A.A. Alexandrov, A.V. Barkov, N.A. Barkova, V.A. Shafransky, Vibration and Vibrodiagnostics of Electrical Equipment in Ships, -Sudostroenie (Shipbuilding), Leningrad, 1986.

2. John S. Mitchell, An Introduction to Machinery Analysis and Monitoring, Tulsa:PennWell Books, 1993.

3. A.V. Barkov, N.A. Barkova, “Peculiarities of Gearing diagnostics by the bearings’ vibration signal”, Presented at the 20th Annual Meeting of the Vibration Institute, 1996.

4. A.V. Barkov, N.A. Barkova, J.S. Mitchel, “Condition Assessment and Life Prediction of Rolling Element Bearings”, Sound & Vibration, June (part1), September (part2), 1995.

5. Application software, DREAM (Diagnostic Rolling Element Analysis Module) User's Manual, VAST, Inc., St. Petersburg, Russia, 1992.

6. Application software for rotating machines monitoring, VAST_RM User's Manual, VAST, Inc., St. Petersburg, Russia, 1994.