A. Y. Azovtsev and A. V. Barkov
VibroAcoustical Systems and Technologies, Saint Petersburg, Russia
D. L. Carter of Boulder, Colorado


Detailed diagnostics of rolling element bearings can be made by the analysis of the bearing friction forces which are the most sensitive indicator of bearing defects. The direct analysis of these friction forces in an operating machine is a very complicated problem which why it is much easier to analyze the vibration excited by these forces. As this vibration is a quasi-random process, the most informative approach is the analysis of the envelope of the broadband vibrations. Unfortunately, a number of error producing technical problems can occur that limit the effectiveness of most existing instrumentation used for bearing analysis. The analysis of these errors sources and methods to avoid them that have been developed and used by the authors are presented in this paper.

Mathematical model of the envelope signal.

The friction forces in a good bearing are stable in time as neither the friction coefficient nor the applied loads depend on the rotation angle of the surfaces of friction. As a consequence, the vibration excited by friction is stable in the frequency band used for the envelope analysis, , having a center frequency equal to w0. As a first approximation, we can say that the spectral density of the signal in this band is . Then the envelope of the considered vibration will have a DC component with the following amplitude:


and random components for the frequencies << w0 will have the spectral density:


The value does not depend significantly on the band pass filter shape that is used for the separation of the part of a signal used for envelope analysis in the D band.

When the bearing has non-uniform wear, the friction coefficient in the bearing is dependent on the rotation angle of friction surfaces. A similar dependency can be observed in the load applied to the bearing when there are defects of installation of the bearing or defects of other parts of the machine. As the result, the RMS average vibration varies with time. The simplest expression for this may be presented in the following form [1] :


where ,

= modulation index and = modulation frequency.

In this case, the DC component of the envelope spectrum together with the random vibration components on the other frequencies does not change, but the following harmonic components can be found in the envelope spectrum:


The widely misused analogy of bearing demodulation to amplitude modulated radio is valid in this situation. An example of the envelope spectrum in this case with a modulation index of 11% is presented on figure 1a. Here you can see a harmonic component of the frequency, . Its RMS value can be presented as:


Here Dw1 is the frequency resolution of the analysis.

The appearance of shock pulses can be considered as instantaneous increases of the friction forces due to the changes in applied loads. In this case, the spectral analysis will reveal a more complicated situation. An example of such an envelope spectrum is presented on the figure 1b.

On the other frequencies, the RMS average of the random components can be determined by the first part of the equation (5). In this case the modulation index is correlated with the relationship of to in the following way:


Equation (6) allows us to determine the modulation index of the random vibration by the relationships of RMS average values of the envelope spectrum component Aw that are uniquely related to the defect severity in the bearing [2]. The type of the bearing's defect can be determined by the frequencies of the harmonic components in the envelope spectrum of the random vibration and additionally by the relationships between the amplitudes of different components.

The influence of other vibration components on the results of diagnostics.

When the frequency band that is used for envelope detection contains only random vibration components excited by friction forces, then the absence of harmonic components in the envelope spectrum guaranties the absence of the defects in the considered bearing except for possible defects of lubrication. When the measured frequency band contains some vibration components from other sources, the situation may change dramatically, possibly causing significant errors in diagnostics.

There are three main cases when such interfering vibration components may spoil the results of diagnostics.

The first and most complicated problem occurs when random vibration components from other units of the machine occur in the data such as when the data includes turbine and pump flow signals. The diagnostic accuracy in this case can suffer in two ways. First, the modulation index of the overall vibration decreases which leads to underestimating of the defect severity. Second, the defect type may also be misrepresented if the random vibration from other units is also modulated with their own frequencies. In some such cases, it may be practical to improve diagnostic accuracy by additional processing of the data after detection.

The second case is related to the appearance of a group of rather small harmonic components that do not significantly influence the overall vibration level in the frequency band selected for demodulation. Consider this case of the example of two harmonic components, and . In this case the envelope spectrum will contain a harmonic component:


The maximum amplitude in the envelope spectrum will be in case when A1 = A2 = A. Then if the value of A is roughly equal or greater than half of random vibration level in the selected band:


the envelope spectrum will contain an additional harmonic component with the with the frequency equal to that can lead to an error in the identification of the defect type.

The most complicated case for diagnostics is the situation where there are harmonic components that determine the overall vibration level in the band selected for envelope detection. So, if in the considered frequency band there is a strong harmonic component with amplitude equal to , when the signal undergoes non-linear transformation such as an envelope detection, the spectral density of the random components increase in the following way: (9)

where (10)

At the same time, the level of the harmonic components decrease in the following manner: (11)

which means that when the q is greater than 3, the envelope spectrum will contain no discernible harmonic components with the frequency W0. In this case, it is impossible to determine whether there is diagnostically useful modulation of the random vibration or not from the analysis of the envelope spectrum. In figure 2a, you can see a high resolution spectrum with bearing data from an electric motor. Figure 2b, which contains a set of harmonic series of such frequencies, is the envelope spectrum of the data in 2a using a 5 KHz band pass filter prior to demodulation.

This last fact is the main reason for not recognizing bearing defects by practitioners who use most of the commonly available vibration analyzers. To eliminate possible errors, it is necessary to make vibration measurements at such points on the machine housings and in selected frequency bands that do not have strong harmonic components or else use other measures such as advanced digital filter techniques to remove the non-random harmonic components before demodulation. Figure 2c is the envelope spectrum of the data in figure 2a, again bandpass filtered at 5 KHz, but with the harmonic components removed prior to demodulation. Note that the data in figure 2b contains both the obvious primary interference frequencies and also significant lower level distortion products that are eliminated in figure 2c.

How to detect an error.

It is rather easy to detect cases when there are strong harmonic components in the considered frequency band. One way is to measure the normal narrow band spectrum and determine whether there are harmonic components that exceed the random vibration level by more than 10 dB. The other way is to compare the DC component of the envelope spectrum and the mean background level of random components in it. Their difference should not exceed 6 dB or


The case when there is a group of the smaller harmonic components in the selected frequency band is more difficult to detect. To do this, we recommend using either a zoom fft spectrum with a four times resolution increase or a normal spectrum of comparably higher resolution to view the spectrum. Problems with diagnostics may occur if, in the selected frequency band, there exist at least two harmonic components that exceed the random vibration level on more than four dB. This case may also be detected by comparing the frequencies in the envelope spectrum with the characteristic bearing frequencies. If they do not coincide, it is worth considering changing either the frequency band used for demodulation or the measurement point location.

The most complicated case occurs when the measured data contains random vibration components from other parts of the machine other than the bearing being tested. In the majority of cases, this case can be detected by comparison of envelope spectra measured on the bearing shield and the unit that produces interfering signal. If identical lines are found in both spectra and the vibration level on the bearing housing is at least 6 dB less than on the other unit, it is probable that the vibration detected on the bearing shield is produced by another unit, for example, in the flow part of a pump. Such situations usually occur only in machines with strong sources of vibration excited by hydrodynamic or aerodynamic flow and only in the bearings that are installed very close to these flows.

Often, when this interference situation appears to occur, these components are the result of loading of the bearing that exceeds the capacity of the bearing lubricant. In such cases, it may be useful to vary the lubricant condition to see if this changes the data. Figure 3a is a plot of data that appears to have interference from air flow in a Joy Vane Axial Fan. In this case, the diagnostic software is unable to make a diagnosis since the envelope spectrum does not conform to data expected for the bearing and shaft frequency used and displays this information in figure 3b. Figure 3c shows new data recorded after an increase in lubricant level. In this case, the diagnostic program, returns the diagnosis displayed in figure 3d of a medium level of “revolution around outer race”, a normal condition for this fan at high thrust loads.

How to eliminate possible errors.

There are two main ways to solve this problem. The first one is to control the portion of the frequency spectrum that is used for envelope detection and, if necessary, to change the frequency band used and perhaps also the location of the measurement point on the bearing housing. The next way is to separate the random and harmonic parts of vibration signal in the selected frequency band and demodulate only the random parts that signal. Of these two methods, the second is more effective.

To use the first method, it is necessary to use a rather narrow frequency band for demodulation, typically 25-50% from the center frequency. In this case, the envelope detector is usually equipped with the hardware band pass filters with the corresponding passband width, for example of 1/3 octave filters. The set of these filters should also cover all the high frequency range. Unfortunately, only a small portion of the available instrumentation has such filters for the envelope detector. We are aware only of analyzers produced by Bruel & Kjaer and Diagnostics Instruments in current production with such 1/3 octave filters. Also, when choosing the measurement point location it is necessary to measure the normal spectrum with high frequency resolution in the frequency band used for envelope detection. If some harmonic components comparable to the energy of random vibration are found, another frequency band for envelope detection or a different measurement point location should be chosen.

The second method requires rather complicated digital signal processing. In this method, the frequency band is first determined and then all the non-random harmonic components are found and removed so that only the random components are left for envelope detection [3],[4]. Significant calculation power is required to implement this approach. The best way to do it is to use spectrum analyzers based on the 486 or Pentium computer which allow such processing to be done at "real-time" data rates or to use specialized signal processors. Vibration Specialty Corporation equipment supports this filter method.


A widely held view exists that the diagnostics of rolling element bearings by the analysis of the envelope spectrum of high frequency vibration is not very reliable and sometimes diagnosis erroneous defects is not necessarily accurate. This view is just a consequence of errors in measurements of the envelope spectra when in there are some harmonic components from other machine units in the frequency band used for demodulation.

These errors frequently occur when the customers are using instruments that either do not have selective filters before the envelope detectors or these filters only have a very wide pass band that do not enable customer to select the frequency band with no harmonic components. Even using analyzers with programmable 1/3 octave or other band pass filters in their envelope detectors cannot guarantee elimination of all possible errors in diagnostics. To minimize these errors, analysis of the direct spectrum of the bearing vibration prior to an envelope spectrum measurement is recommended. The main purpose of this is the selection of the best frequency band for envelope detection that does not contain any harmonic components. If such bands can not be found, changing the location of the measurement point is recommended. The experience of more than one hundred of VAST's clients in Russia who follow this procedure when using the DREAM for automatic diagnostics of rolling element bearings has proved that even its automatic algorithms can guarantee correct identification of defect types in 70 to 80% of cases[6]. This success rate coincides with the results of tests of DREAM software conducted in 1993 in the Canadian Naval Engineering Testing Establishment with the Bruel and Kjaer type 2148 analyzer equipped with a envelope detector having thirteen different 1/3 octave bandpass filters who reported a correct defect type identification rate of 70% in DREAM's automatic diagnostic mode[7]. Note that these percentages refer to the correct diagnosis of specific defects with the percentage of defective bearings detected being significantly greater.

A more effective technical solution to eliminate diagnostic errors is to separate the random and harmonic components in the vibration signal in the desired band and demodulate only the random parts of the vibration signal, a process that can be done automatically when the data is collected. Algorithms to do this have developed and are available systems that have PC compatible architecture and 486 or better CPUs. These algorithms may also be also applied to more specialized signal processing devices. Using these algorithms, the rate of correct identifications of different defect types in the automatic mode provided by the DREAM software exceeds 90%, making the need for operator selection of the frequency band for demodulation unnecessary except for very unusual cases.

1. Alexandrov A., Barkov A., Barkova N., Shafransky V. "Vibration and Vibrodiagnostics of Electric Equipment on Ships", Sudostroenie (Shipbuilding), Leningrad, 1986.

2. Azovtsev Yu., Barkov A., Yudin I. "Automatic Diagnostics and Condition Prediction of Rolling Element Bearings Using Enveloping Methods", presented at the 18th annual meeting of the Vibration Institute, June, 1994.

3. Duncan L. Carter, U. S. Patent Number 5,477,730, “Rolling Element Bearing Condition Testing Method and Apparatus” issued December 26, 1995.

4. Duncan L. Carter, “A New Method For Processing Rolling Element Bearing Signals”, presented at the 20th annual meeting of the Vibration Institute, June, 1996.

5. Duncan L. Carter, “Some Instrumentation Considerations In Anti-friction Bearing Condition Analysis”, presented at the 17th annual meeting of the Vibration Institute, June, 1993.

6. A. Barkov, N. Barkova, J. Mitchell, "Condition Assessment and Life Prediction of Rolling Element Bearings", Sound and Vibration, June, September, 1995.

7. R. Archmbault, "A New Method for Reliable Detection, Diagnosis and Prognosis of Bearing Faults", presented at the 18th annual meeting of the Vibration Institute, June, 1994.

Figures 1, 2, and 3 below.

Figure 1a (above).  Data is from an NTN 205-1W8 bearing with a shaft 
rotation frequency of 33.5 Hertz.  The diagnostic shoftware, DREAM, 
returns a diagnosis of a MEDIUM level of  REVOLUTION AROUND OUTER RACE, 
primarily a thrust load symptom.
Vertical axis scales are in decibels with 1G = 90 db and horizontal axis 
scales are in Hertz. 
Figure 1b (below).  Data is from an NTN 205-1W8 bearing with a shaft 
rotation frequency of 33.5 Hertz.  The diagnostic shoftware, DREAM, 
returns a diagnosis of a SEVERE level of  CAVITIES ON OUTER RACE.



Figures 3a and 3b above are original DREAM diagnostic screens for a Joy Vane Axial Fan bearing. 
Figures 3c and 3d below, same as above after lubricant level increase.

Return to home page Return to bibliography page