Condition Assessment and Life Prediction of Rolling Element Bearings - Part 1

Alexej Barkov and Natalja Barkova, VibroAcoustical Systems and Technologies, St.Petersburg, Russia,

Edited by John S. Mitchell, Contributing Editor for Sound & Vibration

Vibration based condition assessment of rolling element bearings in the West has largely been constructed from empirical "trial and error"observations. The extraordinary work in the article shows the basis in fact for many of the methods that have been used effectively over the years.

Methods that define current condition and predict safe operating life accurately, with fewest measurements and least cost must be the prime objectives of machine condition assessment technology. These objectives are closest to fulfillment on rolling element bearings. This article compares vibration based methods for rolling element bearing diagnostics, condition assessment and lifetime prediction. The comparison is conducted in three areas:

The work described is based on research conducted in Russia on about 1,000 machines, half new and half operating for several years. Currently, the data base includes about 100,000 bearings with complete historical information on maintenance, defect development, replacement and visual inspection. The authors hope that the results of this comprehensive work will aid in understanding the factors that determine the life of a rolling element bearing, provide more insight into the characteristics and methods for identifying defects and aid a user in choosing the best methods and means for condition assessment and lifetime prediction.

Characteristics Of Flaw Induced Bearing Vibration

The choice of the optimal method for condition assessment and lifetime prediction is determined by the vibration characteristics associated with specific defects and how they can be recognized earliest and with least ambiguity. A typical rolling element bearing can produce vibration from six primary types of dynamic forces:

Each has its own optimum method of separation from within a vibration signal.

Rolling Surface Irregularities and Defects. The first type of vibration is excited by rolling surface irregularities and defects. When the rotor is rotating in the bearing it moves along the direction of the static load repeating the form of the rolling surfaces. This is the so called kinematic vibration of the shaft in the rolling element bearing [1,2]. Depending on which rolling surface has the irregularities the bearing will excite vibration at the following well-known defect frequencies:

Cage rotating frequency:

(1)

where: is the diameter of the rolling elements

is the diameter of the cage

is the diameter of the outer race

is the diameter of the inner race

is the contact angle between the rolling elements and rolling surfaces and RPM/60 is the shaft rotating frequency (expressed in Hz).

Rotational frequency of the rolling elements (BSF):

(2)

Ball-pass frequency on the outer race (BPFO):

(3) where: z is the number of rolling elements.

Ball-pass frequency on the inner race (BPFI):

(4)

Very often, especially when the load is variable, vibration at other frequencies are excited in the bearing. These frequencies are the harmonics and sum and difference combinations of the preceding frequencies.

Stiffness Variations in Bearing Components. The second type of rolling element bearing vibration is similar to the first, but it is defined by unequal stiffness on different parts of the rolling surfaces or the bearing as a whole. The simplest example is the variation in stiffness where the load applied to the bearing periodically changes during rotation as the number of rolling elements in the load zone varies.

Shock Pulses when Lubrication Layer is Disrupted. Periodic shock pulses excite two types of bearing element oscillations. Forced oscillations are excited by the leading front of the shock pulse. These are followed by damped natural oscillations. The impact at the leading edge of the shock pulse produces components across a wide range of frequencies. The second, damped oscillation appears in a narrow frequency band near the natural frequencies.

Figure 1 illustrates the two types of vibration in both the time and frequency domain. The top horizontal row shows the broadband excitation produced by the fast rise time leading front of the impact shock pulse. The second row illustrates the excitation produced by decaying natural frequencies. The third row shows how the two effects combine in the real signal. If shock pulses occur at equal time intervals, their spectra consist of a set of harmonic components. These spectra are illustrated in the second vertical column on figure 1. In reality the interval between the shock pulses change randomly. The spectra illustrated in figure 1 have small random changes that are only about one half the period of their natural oscillations. In this case the spectrum of the signal will be continuous, as shown in the third column of figure 1. As one more point of interest, the width of the resonant spectrum is determined by the rate at which the damped oscillations decay. The wider the resonant oscillations the more quickly they decay.

Time SignalsStrictly Periodic Signal SpectraSpectra of Signals with Random Modulation of Intervals Between Pulses in Limits of Half the Period of Natural Oscillation

Figure 1a(above). Symmetrical pulse excitation representing the leading edge of a shock pulse.

Time SignalsStrictly Periodic Signal SpectraSpectra of Signals with Random Modulation of Intervals Between Pulses in Limits of Half the Period of Natural Oscillation

Figure 1b(above). Symmetrical pulse excitation representing the damped natural oscillation of a bearing element.

Time SignalsStrictly Periodic Signal SpectraSpectra of Signals with Random Modulation of Intervals Between Pulses in Limits of Half the Period of Natural Oscillation

Figure 1c(above). Real form of rolling element bearing oscillations excited by shock pulses.

Vibration excited by shock pulses can be used for detecting bearing defects [3]. It is possible to detect several types of rolling surface wear defects with shock pulse excitation at the beginning stage of their development. Defect recognition and identification can be accomplished from low, middle and high frequency vibration. It must be recognized however that rolling element bearing defects do not always produce shock pulses. For example, installation defects such as misalignment of the fixed race and uneven radial tension (housing out of round) are not characterized by shock pulse excitation. Further, wear of the outer or inner races that modulate friction forces but do not produce shock pulses may be missed from 20% to 40% of the time. Thus, sole reliance on shock pulse excitation for defect recognition may delay earliest detection until the defect has progressed or additional defects have appeared.

Friction Force Excitation. The fourth type of rolling element bearing vibration is excited by friction forces which are a set of short shock pulses randomly distributed in time, duration and form. As the contact of the rolling surfaces proceeds through a layer of lubrication the shape of the pulses are smoothed in comparison with the shock pulses generated by surface defects. Random vibration components, excited simultaneously by friction forces at frequencies higher than 20 kHz -- 30 kHz, are very weak. The frequencies of the largest random vibration components are usually in the band of 2 kHz -- 10 kHz. They are higher with higher velocity of rolling element movement in the bearing [2].

Even if the spectrum of the input pulse contains a broad band of frequencies, friction forces limit excitation to forced oscillation. Resonance of the bearing elements or the bearing itself amplifies these oscillations and the random vibration spectrum exhibits the characteristics of multiple resonances. The widths of the resonant frequency bands are defined by the Q (amplification) factor of the excited elements, but not by the characteristics of the friction forces. As a result, it does not convey any additional information about the defects. The magnitude of bearing vibration at the resonant frequencies of the rolling elements or the fixed race is defined by friction forces, not by short shock pulses. Only when the amplitudes of the shock pulses exceed the amplitudes of the friction forces by more than 10 times do the contribution of shock pulses and friction forces within the vibration signal become equivalent.

Rotor Oscillation Forces. The fifth type of vibration is excited by rotor oscillation forces applied to the bearing. The rotor self-oscillation appears when there is excessive bearing clearance. In this case friction forces move the rotor from its equilibrium position and it begins to make pendulum oscillations around the original position [2]. The self-oscillation frequency is usually lower than rotating frequency and is determined by rotor characteristics and the magnitude of the bearing clearance. Since other oscillation forces are also applied to the rotor, they synchronize the self-oscillations. As a result, the self-oscillation frequency typically coincides with one of the known fractional frequencies. The half frequency of rotational frequency (1/2 RPM), or the second order of the cage frequency (2 FTF) are typical examples. Self-oscillations create additional machine vibration components at these low frequencies. They also change the parameters of the friction forces and the high frequency vibration excited by the friction forces.

Interactions with Other Components. Bearing vibration can sometimes affect the appearance of vibration components generated elsewhere in the machine. For example, rotor oscillations caused by unevenness of the bearing surfaces lead to variations in the rotor and stator clearances. These clearance variations excite additional forces and vibration. Oscillations of a motor rotor may produce varying electromagnetic forces. Oscillations of a pump impeller can lead to pressure pulsations in the pumped liquid. There are further examples of bearing induced rotor oscillations that are converted into vibration of other machine components. However, the use of secondary components of machine vibration for condition assessment is justified only in specific, highly specialized cases such as remote monitoring of reactor cooling pumps. Applications of this type, while successful, are not discussed further in this article.

Methods Of Identifying Flaw Characteristics

Vibration characteristics, excited by dynamic forces within rolling element bearings and other rotating machine components are usually identified by one or a combination of four known methods. Frequency analysis is the first method. Success is based on the assumption that each defect produces a unique complement of frequencies and that these frequencies can be separated from the background. The second utilizes location to define the origin of vibration, especially at high frequencies. The third method is based on the time or phase relationship of the vibration. A fourth method utilizes a two stage, calculated or derived variable. Envelope detection, Kurtosis and K factor are examples.

Frequency analysis of a vibration signal recorded on the bearing housing is a frequently used method to separate bearing excitation from vibration originated elsewhere in the machine. This analysis is customarily accomplished to about the fifth harmonic of the highest frequency defined by expressions 1 - 4 (BPFI). Figure 2 shows a vibration frequency spectrum recorded on a machine with a rotor mounted in bearings of two different types. This picture illustrates the difficulty of identifying individual components within a complex spectrum and determining the reasons for their presence.

Figure 2(above). Vibration spectrum from a machine with two different types of bearings.

In addition to identifying rolling element bearing defects by frequency, localization methods may be used. These methods rely on the principle that kinematic vibration, excited by the bearing, has its maximum magnitude along the direction of static load while other components can differ in their direction. However, this approach is very seldom used in practice because it does not always provide a unique result.

The characteristics of rolling element bearing defects, excited by shock pulses, are most efficiently extracted as high frequency components. It is sufficient to measure these signals externally on a bearing housing in mechanical contact with the fixed race. If shock pulses are being generated within a bearing, almost all vibration at frequencies higher than 20 kHz to 30 kHz is originated by these pulses. High frequency vibration originated from other sources such as flow instability and cavitation, reach the measurement point very attenuated due to surface transmission losses on the machine case.

The only practical method for extracting the vibration excitation generated by rolling friction forces is based on space signal separation methods. To achieve separation it is necessary to measure high frequency vibration at a point on the bearing housing and filter the signal. The filter bandwidth is set to limit the signal such that the spectral density of the random signal is maximum and the harmonic vibration components excited by other forces within the bearing or transmitted from elsewhere in the machine are minimum. To eliminate large harmonic components in the filtered signal it is necessary to use a relatively narrow band filter (about 25-50%). It is also necessary to choose the center frequency of the filter by examining the vibration spectrum and selecting a frequency band with the fewest large harmonic components. More about this later.

From the preceding it can be seen that bearing characteristics can be extracted from vibration signals and used for detecting defects. Low frequency harmonic vibration components are usually extracted with spectral analysis. High frequency random vibration components can be extracted by localization (space separation). Difficulties with the first method occur when other components, unrelated to bearing condition, are present at essentially the same frequencies. Difficulties with the second occur when it is impossible to fix the transducer to the bearing housing. Better to use separation after dividing the signal into middle and high frequency parts. Cepstrum analysis can be used for the low and middle frequency signals with crest factor (peak/rms) used for the high frequency portion of the signal [1].

Methods For Extracting And Assessing Flaw Characteristics

Overall Level. Measuring the level of high frequency vibration, excited by shock pulses, and the magnitude of the crest (peak) factor, are quite enough when detecting changes in rolling element bearing condition with minimal expense is the sole objective of condition assessment. However, it must be recognized that overall measurements may not be sufficient to evaluate defect depth (severity) because the magnitude of high frequency vibration is much more dependent on the rise time of the leading edge of the shock pulse than the amplitude of the pulse. This dependency becomes much stronger with increasing frequency of the measured vibration.

The means for measuring overall level is rather simple and the time required to make the measurements is only a few seconds. Acceptance standards can be constructed by two main methods. The first uses known algorithms for calculating the levels of high frequency bearing vibration and the value of the crest (peak) factor for beginning, medium and severe defects. Bearing dimensions and rotating speed must be taken into account. The second method consists of several measurements recorded on a bearing known to be in good condition. This is followed by introducing defects at varying levels of severity according to a priori statistical information familiar to designers of diagnostic methods.

Difficulties with these methods appear most often on machines operating at low rotational frequencies and on machines where loads are applied to the bearings by other machines (shaft misalignment). In both cases, the certainty of condition assessment based on overall level sharply decreases in the final stage of a bearing's service life, when several defects are developing in parallel.

Crest Factor. Considerations involved with bearing condition prediction after defects appear are illustrated on figure 3. The typical time variation of crest (peak) factor and high frequency vibration are shown from the moment a wear defect appears up to bearing failure. These curves illustrate clearly that substantial bearing life remains after the crest (peak) factor has reached its maximum value and begins to decrease and that high frequency vibration is the best predictor of remaining life. These results can be improved by measuring the k-factor.

Figure 3(above) Typical relationship of crest (peak) factor and the magnitude of high frequency vibration to bearing operating life.

k Factor. A large part of the uncertainty in condition assessment is due to the fact that the distribution of excitation shifts as defects worsen and spread during the final stages of bearing life. Although total excitation continues to increase, the increase occurs mainly in the rms portion of the signal. Peaks rise more slowly and may even decrease as impact producing discontinuities are worn away. This phenomenon produces the often observed, and highly misleading, reduction in peak measured vibration and crest factor as condition worsens that was mentioned in the previous paragraph. A solution, called k factor, has been patented by Professor Adolf Sturm while at the Technsche Hoch Schule in Zittau Germany. K factor is defined as peak times rms. As a result, increases in either the rms or peak magnitude within a complex signal will result in an increase in the measured k factor.

Spectrum. Spectrum analysis is used to extract the bearing defect frequencies and their harmonics in the low and middle frequency bands. The difficulty is that part of the bearing defect frequencies may be close to frequencies excited by other components in the machine and therefore hard to identify. Figure 4a(below) shows the low frequency vibration spectrum of a bearing with a spall on the outer race. The magnitudes of the vibration defect frequencies, excited by shock pulses, significantly exceed all other components. High frequency vibration components, excited by shock pulse and friction forces, require localization (space separation) methods followed by spectrum analysis.

Figure 4a(above). Spectrum of a bearing of a spall on the outer race.


Figure 4b(above) Cepstrum of a bearing of a spall on the outer race (same raw data as fig.4a).

Cepstrum. As mentioned in the preceding paragraph, it is often very difficult to separate and identify the source of a complex array of bearing defect frequencies and their low order harmonics within a vibration signal. Better methods extract low frequency excitation from a high frequency signal or use specialized methods of signal analysis to identify the source of multiple harmonics. A cepstrum (double spectrum) analysis is a highly effective method to reduce the complex harmonic content of shock pulse vibrations excited by a bearing flaw. Figure 4b illustrates the power of a cepstrum to simplify a complex signal and identify the source of components that are related by a common difference in frequency [1].

Cepstral methods have characteristics that can be used to advantage. These include the fact that each machine has its own frequency band where bearing defects are manifested most clearly. The cepstrum method also has disadvantages. First, there are a large number of harmonic components unrelated to bearing condition in the low and middle frequencies. Some of them coincide in frequency with the bearing vibration components and create obstacles to identifying the type of defect. Second, there is no direct correspondence between the magnitude of the vibration cepstrum components and defect severity. The advantages and disadvantages of this method are illustrated in figure 5 where the cepstra of three defective bearings are shown. All factors considered, performing cepstrum analysis of a vibration signal, filtered with a bandpass optimized for the machine, increases the effectiveness of condition assessment.

Figure 5a(above). Cepstrum of a rolling element bearing with incipient wear of outer race.

Figure 5b(above). Cepstrum of a rolling element bearing with medium wear of outer race.

Figure 5c(above). Cepstrum of a rolling element bearing with severe wear of outer race and incipient wear of inner race.

 Envelope Detection. Several alternative methods for detecting and identifying rolling element bearing defects from high frequency vibration pulses, excited by shocks, have been developed. One method, based on spectral analysis of the envelope produced by high frequency shock excitation has proven particularly useful [4]. The envelope method has significant advantages including the ability to separate symptoms that characterize several defects developing simultaneously in a bearing. This greatly increases the certainty of defect identification and largely solves the problem of long term bearing condition prediction.

For defect identification, the envelope spectrum must be measured in a frequency band from zero up to 2-3 orders of the BPFI (ball pass frequency on inner race). For many bearings this spectrum bandwidth can exceed the width of the rolling element resonance. When this occurs, the use of vibration at resonance for envelope processing will distort the identifying symptoms of the defects that produce friction force modulation. Fewer mistakes will be made in defect identification by using vibration in a wider frequency band that is free of resonances and strong harmonic vibration excitation transmitted from other components. It is also possible to gain coincidence between acceptance threshold values for different types of defects by carefully selecting the center vibration frequency used to obtain the envelope. Both the modulation of friction forces and the presence of shock pulses will be included. Currently, the optimal frequency band is considered to be about 25-50% of the center frequency. Due to this relationship, 1/3 octave band pass filters are frequently used in envelope detectors.

Figure 6 shows the time signal and high frequency enveloped vibration spectrum obtained from a bearing with a worn outer race. Figure 7 shows the same presentation for a bearing with a spall on the outer race. These figures clearly illustrate that bearing wear does not necessarily produce shock pulses but has the appearance of a smooth, periodically changing vibration level. Bearing wear mainly appears as a prominent first harmonic component at the BPFO frequency, defined by expression (3), in an enveloped high frequency vibration spectrum. When the bearing has cavities (spalls) then a set of harmonics with frequencies kBPFO appear indicating the presence of shock pulses in the bearing.


Figure 6a(above). Band limited time signal of a rolling element bearing with wear of the outer race.


Figure 6b(above). Band limited envelope spectrum of a rolling element bearing with wear of the outer race.


Figure 7a(above). Band limited time signal of a rolling element bearing with a spall on the outer race.


Figure 7b(above). Band limited envelope spectrum of a rolling element bearing with a spall on the outer race.

Two complications can occur when the envelope spectrum is used to detect changes in rolling element bearing condition:

  1. In some machines, construction influences the shock pulses generated by bearings. As an example, a geared transmission, especially with high rotational frequencies, transfers loads at the gearing zone to the bearings. Modulation of the friction forces and shock pulses due to the impacts of one surface with another must be taken into account when analyzing the high frequency envelope spectrum and constructing the acceptance standards.
  2.  Multiple harmonic components are often present in a high frequency bearing vibration spectrum. This results in harmonic components in the enveloped vibration spectrum that also have to be taken into account during analysis. Alternately the vibration measurements can be made at higher frequencies where the presence of intensive harmonic components is diminished. However, at higher frequencies the relative contribution of random vibration, excited by friction forces, sharply decreases and the vibration components, excited by shock pulses, become the dominant source within the vibration signal. Shock pulses do not convey all the defects of rolling element bearings. Thus, some defects may escape early detection until other, shock pulse producing, defects have developed.

Detecting And Identifying Changes In Condition And Flaw Characteristics

Bearing Defect Frequencies. As mentioned previously, detecting changes in bearing condition during operation can be accomplished with low, middle or high frequency vibration characteristics excited by the bearing. The first type of vibration is excited primarily by rotor oscillations caused by irregularities of the rolling surfaces and by shocks as the defective surfaces impact against each other. Two main obstacles must be overcome. The first is due to the complexity of a typical bearing vibration signal. Within a complex signal it can be quite difficult to separate components excited by the bearing from those originating from other interactions and transmitted from elsewhere in the machine. The second is connected with the fact that bearings mounted in a machine never have ideal rolling surfaces. As a result, vibration components, characteristic of bearing defects, also may be present in the spectra of non-defective bearings. These components also may be different depending on the construction of the machine.

When defect detection is accomplished using the harmonic content of the low frequency bearing vibration signal, the optimum bandwidth for observing harmonics of the defect frequencies calculated from expressions (1-4) should be limited to the fourth through the tenth orders. Vibration harmonics with multiples of less then four are usually due to manufacturing tolerances -- deviations between actual and ideal bearing rolling surfaces. Experience has demonstrated that excluding unbalance, the magnitude of harmonic components below the fourth order average about 3 - 6 dB lower on new machines with defect free bearings compared to older machines and increase only during the final stages of a bearing's life. Harmonic multiples from four to ten times the bearing defect frequencies have proven to be the most accurate and responsive measures of condition. Magnitudes typically increase with increasing load applied to the rolling surfaces (mounting defects), and at the initial stages of wear on these surfaces. Higher harmonics, with multiples more than 10 to 20, are usually the consequences of shock pulses, represent only a portion of bearing defects and are best detected from a high frequency vibration signal. It should be noted that shock pulses, detected at high frequencies are not necessarily accompanied by high order harmonics of the defect frequencies (above 10 to 20).

Bearing defect frequency harmonics with multiples ranging from about 4 to 10 are often used in machine condition monitoring systems for early detection and identification of rolling element bearing wear defects. In these systems, a combination of bearing vibration components are defined for each type of defect to be monitored.

High Frequency Shock Pulse and Friction Forces. High frequency bearing vibration is excited by the shock pulses and friction forces. In a nondefective rolling element bearing there are no shock pulses and the friction forces are stable in time. At the high frequencies, condition assessment standards for rolling element bearings can be established on the basis that vibration level does not depend on the angular position of the rotor. Under these conditions there is no amplitude modulation of the vibration signal. When several rolling surface defects occur, shock pulses and modulation of the vibration signal by one or a group of frequencies, defined by expressions 1 - 4, appear. The modulation process produces multiple harmonic frequencies in the enveloped vibration spectrum which make it possible to detect and identify the defect. As mentioned earlier, up to a point in bearing life, condition can be assessed by measuring the ratio between the peak and mean values of high frequency vibration (crest-factor) excited by shock pulses, figure 3.

Shock pulse repetition frequency is one of the methods that can be used to identify the type of defect from a high frequency vibration signal. This approach is efficient but has certain limitations. When there is a stable load applied to the bearing and only one defect exciting the shock pulses, the magnitude of the shocks do not change significantly with rotor rotation. Amplitude modulation may or may not be present. In some cases the number of shocks registered per unit time do not define the type of bearing defect.

Examples of the latter include a cavity on the inner race combined with rotor unbalance. In this case shock pulses are amplitude modulated by the rotational frequency. At high values of amplitude modulation (large unbalance, minor defect) the pulse repetition frequency will be less than BPFI. Under these conditions a frequency component and the defect producing the component are likely to be misidentified.

Simultaneous cavities on inner and outer races are a second example. In this case the pulse repetition frequency will not coincide with either BPFI or BPFO but their sum (BPFI + BPFO). Maximum errors will occur when amplitudes of the pulses excited by the cavities on the inner and outer races are very different.

The magnitude of shock pulse excitation is used for condition assessment. In wide frequency band vibration, excited by the leading front of shock pulses, an increase in level is the main characteristic that identifies the appearance of a defect.

At high frequencies that are a factor of two or three higher than the natural frequencies of the rolling elements, shock pulse excitation is the primary source of bearing defect vibration. Shock pulse excitation produces an amplitude modulated high frequency signal that can be quantitatively assessed most effectively from an enveloped spectrum described in the next section [2, 3]. With rolling element defects present, harmonic components will appear in an enveloped high frequency vibration spectrum that are absent when there are no defects in the bearing.

Frequencies nearer the natural frequencies of bearing components contain vibration excited by friction forces that respond to all bearing defects. Friction forces also can be recognized as amplitude modulation from an enveloped high frequency bearing vibration spectrum. Close to the natural frequencies the contribution of shock pulses and friction forces is about 1:3 with severe defects present. The reason is that the shock pulses are very short duration and their rms amplitude is small.

When the high frequency bearing vibration, excited by shock pulses and friction forces, has been extracted for analysis the same methods used for condition assessment and prediction from low frequency vibration can be employed.

In many monitoring systems bearing defects are detected and identified by shock pulse excitation using a cepstral analysis of the low and middle frequency vibration [1, 2]. Major advantages of this method include the fact that vibration does not necessarily have to be measured on the bearing housing and the number of measurements required for condition assessment are minimized.

Enveloped Spectrum. Rolling element bearing condition assessment utilizing a high frequency, enveloped vibration spectrum combines two methods. The methods are differentiated from each other by the frequency band of measured vibration, diagnostic symptoms and the method of constructing acceptance standards. The first method is based on high frequency vibration, excited by shock pulses. The second is based on high frequency vibration, excited by friction forces [6]. Defects mentioned earlier that are characterized by shock pulse excitation are identified by the first method. The second method detects and identifies all bearing defects that occur as a result of installation and operation of the bearing. To provide an understanding of the principles of developing representative acceptance standards used for these two kinds of enveloping methods, it is necessary to describe their main differences.

The first difference is defined by the frequency band of the measured vibration. It is well known that shock pulses excite vibration in a wide range of frequencies - most strongly at the natural frequencies of the impacting elements. Since the rolling elements always take part in the impacting process, bearing analysis can be accomplished utilizing vibration excitation in either of two frequency bands. First, the previously mentioned high frequencies two to three times higher than the natural frequencies of the rolling elements and the fixed race. Second, from components within a comparatively narrow frequency band centered on one of the natural frequencies. Experience with these two methods demonstrates that condition assessment conclusions, derived from enveloped vibration in different frequency bands, can be different.

Several characteristics can be used to define the type of defects on the rolling surfaces. Frequencies of the harmonic components in the envelope detected spectrum, the number of the higher harmonics of these components, the increase in magnitude with the appearance of shock pulses, and the ratio of their levels all provide valuable diagnostic information. The frequencies of these components, depending on the defect type and the load applied to the bearing, coincide with the values that are calculated by expressions (1-4) or sum and difference combinations of these frequencies. Possible combinations can reach several hundred.

The primary diagnostic symptoms of bearing defects utilizing vibration frequencies near the natural frequencies of the rolling elements are quite different. As stated in the previous section, high frequency random vibration is defined mainly by friction forces and can be used effectively for assessing the quality of bearing lubrication, but not defects on the rolling surfaces. Random vibration excited by shock pulses produced by defects on the rolling surfaces has similar features to amplitude modulated vibration excited by friction forces. The high frequency envelope method of defect detection and identification is equally valid for vibration signals that contain excitation from shock pulses, friction forces or a mixture of the two.

Measured vibration components often coincide with a high Q resonance of the bearing or other machine elements. Figure 8 shows a bearing vibration spectrum that illustrates the difficulties in choosing the frequency band for condition assessment measurements and analysis of random vibration, excited by friction forces. The rotating frequency of the bearing is 25 Hz and the maximum spectral density should be between frequencies of about 5 kHz and 10 kHz. The optimal center frequency, where there are neither harmonic components nor resonances, is about 7.5 kHz. However, when standard 1/3 octave filters are used it is necessary to choose between filters with center frequencies of either 6.3 kHz or 8.0 kHz. In this situation it is better to choose the 6.3 kHz center frequency filter because only one vibration harmonic is included within this band and it will not disturb the extracted signal.

Figure 8(above). Bearing vibration spectrum illustrating optimum selection of the envelope detector center frequency.

Standards for Assessing Condition and Lifetime

Considerations. Prior to developing vibration condition assessment standards that can distinguish between good and faulty bearings, it is necessary to choose requirements for diagnostics and condition prediction. Four primary considerations can be identified depending on the principal interest and objective:

Effective long term prediction of rolling element bearing condition relies on the detection and identification of all defects that can influence the residual service life. Smooth deviations of the form of rolling surfaces affect bearing vibration but do not influence its service life. These deviations are detected mainly by low frequency vibration. The appearance of shock pulses identifies rolling surface defects which influence the bearing service life.

There are two types of bearing lifetime prediction. A long term lifetime prediction can be made for up to 20% of a bearing's specific service life using envelope methods. Predicting the service life remaining at any point in time is very approximate and can be estimated only after at least two developed defects have appeared. This second prediction of residual lifetime can be improved by incorporating a direct analysis of medium frequency level, crest factor, trends of both values, defect frequency harmonics and an envelope spectrum analysis.

Comparative condition assessment standards must be constructed in accordance with several considerations. The method chosen for diagnostics, types of excitation from oscillating forces in the bearing, methods for separating bearing defect characteristics from excitation originated elsewhere in the machine and the stage of bearing operating life all must be considered.

Installation and Operating Defects. Different types of defects influence the bearing's residual service life differently. Thus, identifying defect type and estimating severity is the main way to increase certainty of the lifetime prediction. Defect identification and residual life prediction must begin with installation defects that increase loads applied to the rolling surfaces of a bearing and include all rolling surface wear defects. The first group includes race misalignment, increased radial tension (tight fit), and the slip of bearing races in the mounting (loose fit). Shaft misalignment that results in increased static loads applied to the bearing and a bent shaft that produces rotating forces are additional installation type defects. Rotating loads can accelerate wear on all the rolling surfaces, fixed and rotating races, rolling elements and the cage. Cavities (spalls) and cracks can appear on all the rolling surfaces. In addition to wear on the rolling surfaces, lubrication defects such as too little or too much, impurities and aging can appear. All contribute to accelerated bearing wear.

To assure an accurate prediction of bearing condition it is necessary to confirm the absence of installation defects that decrease service life at the initial stage of machine operation. If there are no initial defects, normal operation can be safely predicted for a period of time. The predicted normal operating time is slightly less than the minimum time required for development of all possible defects from their origin to shortly before failure. This time becomes the standard for long term prediction of rolling element bearing condition.

Installation and operating defects, except cage defects, directly influence the harmonic properties of the oscillating and friction forces. An increase in the severity of a defect will produce shock pulses. Cage defects may be a result of rolling element defects. Alternately, cage wear alters the spacing between rolling elements. Thus, cage defects can also be detected from a vibration signal.

Detection and identification of installation defects is complicated. The reason is that comparative standards are constructed from vibration characteristics measured not on the specific bearing but from a large group of machines with the same general construction. In this case, natural variations in the vibration levels between different machines in the group can be so large (up to 20 dB, a factor of 10 have been observed) that the variations due to installation defects are imperceptible. Due to the amount of work necessary to define condition assessment standards for a wide variety of machine configurations, this work is accomplished most efficiently at the machine manufacturers during acceptance testing.

As a rule, installation defects shorten bearing service life. These defects should be detected during the machine manufacturers initial testing as an abnormal magnitude of mid frequency bearing vibration. Unfortunately, not all the machine manufacturers make initial bearing vibration measurements so the user must detect potential installation defects to gain assurance of long term condition prediction. Pre operational testing following installation or repairs is also advantageous to identify defects due to conditions such as improper mounting and shaft misalignment. The accuracy of condition prediction increases if all initial defects are identified. Gaining this assurance requires assessing bearing condition utilizing the random vibration envelope spectrum excited by friction forces. In this case it is necessary to take into account a significant factor that affects friction forces in a new bearing. These forces do not depend on the rotation angle of the bearing when the friction coefficient is the same at any contact point of the rolling elements and the rolling races. In new bearings the quality of the rolling surfaces can differ slightly, and a certain period of time (bearing run in) has to pass before the surface roughness becomes equal. This is why characteristics indicative of wear defects can appear in the enveloped random vibration spectrum during the first hours of bearing operation. It makes the detection of installation defects slightly more difficult. However, after a few hours of run in operation only the characteristics of installation defects will remain in the vibration envelope spectrum.

Condition Assessment Standards - Low Frequency. Standards on which to base condition assessment and prediction from information conveyed by low and middle frequency vibration must be constructed for each bearing. It also means that constructing a vibration acceptance standard for a nondefective bearing requires many vibration measurements before a defect appears. That is why bearing condition assessment utilizing low and middle frequency vibration is comparatively complex and the cost is large. At the same time the use of these methods has advantages - primarily the ability to assess condition of the entire machine and the bearings from the same vibration signal. For this reason, low frequency vibration is frequently used in many machine condition monitoring systems. In addition, condition acceptance standards may be developed that are useful for detecting changes in bearing condition, determining the defect type and its severity, and for predicting short term trouble free operation. It is evident however, that more detailed acceptance standards are necessary to identify and solve complex problems.

Experience has shown that qualitatively better results can be achieved from vibration condition assessment by observing two principles. Detect potentially life limiting defects at their earliest stages (incipient defects) and watch and analyze trends as each of the defects develop.

A condition assessment reference or baseline standard consisting of a set of vibration cepstral components, constructed individually for each machine at the beginning of operation, is very valuable to assess later changes.

Condition Assessment Standards - High Frequency. A condition assessment standard also must be developed for shock pulse excitation. Crest (peak) factor is the best quantitative measure of condition derived from shock pulse excitation early in bearing life. Shock pulse repetition frequency is the condition assessment standard for defect identification.

The presence of amplitude modulation indicates rolling surface defects. Prior history is not required. This conclusion is possible only when condition assessment and prediction are based on friction forces and defines the main advantage of the envelope method - the ability to detect amplitude modulation and thereby perform an accurate assessment of condition with one vibration measurement. Thus, the high frequency envelope method provides the basis for the most objective standards of condition assessment and prediction.

Comparative condition assessment standards have been developed for the high frequency envelope method from a group of rolling element bearings with loads limited to static or synchronous rotating loads, installed on all types of machines. In general, the standards are dependent on the rotational frequency and the bearing diameter. However, this dependence is a weak one.

The most accurate comparative standards for determining the severity of a bearing defect are based on the magnitude of modulation, m. The magnitude of modulation of a random vibration signal is defined by the difference L between the levels of the maximum harmonic component Li within the enveloped spectrum and the background (MSV) Lb calculated from the following expression, figure 6, [2]:

0<m<1 (5)

where: L is the difference between the level of the harmonic component fi and the level of the background of the envelope spectrum; fA is the width of the spectral line of the analyzer of the envelope; fB is the frequency band extracted from the spectrum in the input circuit of the envelope detector.

From the preceding expression, threshold values to detect and determine the severity of a defect well prior to failure can be defined for each bearing from the magnitude of modulation within a high frequency envelope spectrum without any prior measurements of it's enveloped spectra. To detect defects at the beginning stage of bearing life the high frequency envelope spectrum modulation threshold values should be fixed at a level of approximately m = 15%. Methods for detecting and identifying defects will recognize the presence of a defect beginning from a threshold of about 1% modulation. Thus, the means to solve the challenge of long term rolling element bearing condition assessment and life prediction is clearly available.

Predicting Short Term Residual Life. Before selecting a method for short term rolling element bearing condition prediction, it is necessary to decide on the stage of service life that condition prediction will be required. The method will be different for a bearing with a large operational life remaining compared to a bearing in degraded condition close to failure.

As stated earlier, short term prediction of normal operating lifetime for a bearing without developed defects can be based on measurements of high frequency vibration, excited by shock pulses. From periodic measurements of crest (peak) factor it is possible, if there are no shock pulses, to predict non-failure operation for a time interval up to 3-5% of the statistical service life. When shock pulses are detected, the interval between predictive measurements must be reduced by several times. When the crest factor stops increasing (see k factor discussion) this method must be discontinued and replaced by a more rigorous method of condition assessment. It is important to note that when shock pulses are first detected the residual service life of the bearing may still be quite large. Therefore, in most cases the bearing does not yet require replacement but must be monitored more closely. Methods of diagnostics, condition assessment and prediction that provide accurate results during the last stages of a bearing's service life must be employed.

Bearing Lifetime Prediction. Known methods of detecting and identifying bearing defects and their use for short and long term condition prediction use two groups of standards. The first includes standards for nondefective bearings. The second includes criteria for assessing the condition of bearings with defects of different types and severity. The first group of criteria can be constructed by three different methods based on expert estimate algorithms, algorithms of preliminary learning and self-learning algorithms. The second group of criteria is usually constructed from an expert estimation that represents an array of diagnostic symptoms for each type of defect and the threshold values for defects of different severity. Only after a long period of operation of a specific machine, and an investigation of its defects, is the user able to make adjustments to the expert estimates of defect symptoms, severity and predicted intervals of nondefective bearing operation.

At the beginning stage of bearing operation the initial measurements are compared to general standards for nondefective bearings to gain an assessment of condition and predict lifetime. Accuracy during this period is somewhat less than later in bearing life when condition characteristics defining the specific bearing have been developed. Early life condition assessment is less accurate for two principal reasons. First, there are the large number of vibration components in a low frequency spectrum close to the bearing frequencies and their harmonics (see figure 2). This complicates the analysis of a new bearing. Second, in a new bearing the correspondence between observed vibration levels with the severity of detected defects is not yet established. This occurs because the measured vibration level is modified by the mechanical properties of the machine and will increase if the oscillation force frequency happens to coincide with a natural frequency.

The ratio between the amplitudes of different groups of harmonics defines the link between the severity of defects that are developing simultaneously. As was demonstrated in figure 3, the magnitude of the crest (peak) factor of the high frequency vibration signal does not define severity when several defects develop simultaneously. That is why the crest (peak) factor is not included in the list of diagnostic parameters when the spectrum of the enveloped vibration is used for condition assessment.

During the final stage of bearing life with defects present, condition assessment and prediction can be accomplished by using the levels of bearing vibration components discussed earlier. In particular, high frequency shock pulse vibration is often used for rolling element bearing diagnostics and condition assessment. For short term prediction it is necessary to analyze the trends that characterize the rate at which periodically measured vibration components are increasing and estimate the time at which the level will reach a threshold value. The threshold level is usually set up according to the rules established by the condition assessment method.

During the final stage of rolling element bearing operation, the fundamental defect frequencies calculated from expressions 1 - 4 can be used for condition assessment. At this point in bearing life the magnitude of the wear defects exceed the manufacturers tolerances for rolling surface irregularities. More important, the magnitudes of components at the fundamental defect frequencies in the before failure stage of the bearing provides a precise estimate of the residual service life of the bearing.

Predicting long term bearing lifetime when there are no defects in the bearing is relatively simple. The means of condition assessment must ensure a minimum probability of missing a defect present in the bearing and define a standard for a minimum duration of defect free operation.

Such a standard has been derived on the basis of a statistical analysis of bearing diagnoses conducted in the before failure condition. Developing the data for a valid standard requires detailed analysis throughout the service life of a bearing with all defects identified and severity assessed. Unfortunately there is very little published in this area. Part two of this article will document the results of detailed condition assessment accomplished on rolling element bearings with the high frequency, random, enveloped vibration spectrum method previously described. The work was performed in Russia over the last five years and included over 100,000 bearings in an actual operating environment.

References

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

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

3. U.S. Patent No. 3554012, “Method and Arrangement for Determining the Mechanical State of Machines”, E. O. Shoel, Tumba, Sweden, 1971.

4. U.S. Patent No. 3842663, “Demodulated Resonance Analysis System”, Darrell R. Hartig, John W. Taylor, 1974.

5. Barkov, A. V., “The Diagnostics and Condition Prediction of the Rolling Element Bearings by the Vibration Signal,” Sudostroenie (Shipbuilding), No. 3 (1985): 21-23.

6. Barkov, A. V., Barkova,N. A., “Assessing the Condition and Lifetime of Rolling Element Bearings From a Single Measurement,” Proceedings of the 19th Annual Meeting, Vibration Institute, 1995.

Part 2 of this two part article.

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