Diagnostics of Gearing and Geared Couplings Using Envelope Spectrum Methods

Dr. Alexej V. Barkov, Dr. Natalia A. Barkova

VibroAcoustical Systems and Technologies, (VAST), Inc., Saint-Petersburg, Russia


Difficulties appeared when random vibration envelope spectrum algorithms for identifying defects in rolling element bearings were applied to gearing. Additional lines appeared in the envelope spectrum due to dynamic loads applied to the bearings from the gearing. Additionally, spectral lines associated with rolling element bearing occasionally disappeared from the spectrum. Special investigations were conducted to solve these problems. As a result, technical solutions to eliminate possible errors in bearing diagnostics were proposed as well as new gearing diagnostic algorithms. The main results of these investigations are discussed in this paper.

Traditional solutions

In this paper the term gearing is applied to one stage of reduction gearing consisting of two meshing gears. It also applies to gear type couplings that do not change the rotational frequency of the driven shaft against the driver shaft. The main focus is on defects that have to be detected in a timely fashion. These include mesh defects that change the condition of contact between teeth in the mesh zone, and individual tooth defects, particularly wear, cracks and spalling (pitting).

Traditional diagnostic methods for fault detection use the main groups of vibration harmonics that are excited by shocks as teeth engage in mesh. In gear type couplings they are the harmonics of shaft rotational frequencies. Rotational frequencies and harmonics of each of the meshing gears, harmonics of the gear mesh frequency and the harmonics of the contact frequency between two faulty zones on the gears are commonly observed in reduction gear spectra. The latter frequency is a very low subharmonic of the rotational frequencies of the two gears. Usually this frequency is one-half to one-tenth of either shaft rotational frequencies.

In gear-type couplings with defects, shocks at the shaft rotational frequency and its multiples increases shaft, bearing housing and supporting structure vibration at a number of harmonic frequencies. Increased structural vibration containing a large number of rotating frequency harmonics is the traditional symptom used to detect defects on gear type couplings.

When defects are present that change the condition of the contact between teeth in mesh, vibration increases at the gear mesh frequency and its multiples. Defects include, displacement of one gear against another, misalignment of shafts and bad lubrication. This increase is also a traditional diagnostic symptom of gear defects.

If a specific tooth is worn, cracked or a part of a tooth is missing, then once during each revolution of the faulted gear a shock will occur between the gears. Vibration of the gear supporting structure will increase at multiples of the rotational frequency of the faulted gear. This increase is a traditional diagnostic symptom of the faults identified above. In addition, vibration at multiples of gear mesh frequency are modulated at a period equal to the faulted gear rotational frequency. Consequently, the gear mesh harmonics develop side bands spaced at an interval equal to the rotational frequency of the gear.

Finally, when both meshing gears have flawed teeth, the defective areas on the two gears are engaged in mesh once in several revolutions. Called the tooth repeat or hunting tooth frequency [1], the event produces a strong shock vibration. Bearings and the supporting structure are excited at the fundamental and multiples of the tooth repeat frequency.

Narrow band frequency analysis, cepstral analysis, and a frequency spectrum analysis of the high frequency vibration envelope extracted with a band pass filter, are traditional methods for gearing analysis. Each enables detecting the harmonics series as well as sidebands. All three methods are widely used for gearing monitoring and diagnostics.

It is not always possible to measure all these vibration components. This is especially true on low speed gear transmissions, when the shaft rotating frequency and its multiples are below 10-20 Hz. In this area of the spectrum it is very difficult to extract the vibration of the diagnosed machine from a background that may include vibration from other machines. Under these conditions it becomes necessary to gain diagnostic information by analysis of the gear mesh frequency, harmonics of gear mesh frequency and side bands. However, this information is often not complete. Consequently, the quality of diagnostics is significantly reduced. For example, in addition to defects in the mesh, an increase in the level of the gear mesh vibration components can be the result of bearing wear.. Bearing wear can cause the gear shafts to go out of parallel or a shift in the gears relative to each other along their axes. Finally, a change in the amplitude at mesh frequency often occurs upon changes in load with no defects present. The appearance of side bands around the gear mesh harmonics can also be the result of bearing wear accompanied by movement of the gear shaft. Gear operation where the shaft axes experience self sustained oscillations within the limits of bearing clearances is another source of sidebands.

Thus, traditional diagnostic solutions are not ideal when applied to gear transmissions. There are benefits to search for new, more efficient diagnostic methods for identifying gear flaws.

New Approaches in Diagnostics

During diagnostics of rolling element bearings in gear-boxes using an envelope spectrum of the bearing case vibration the authors often came across a situation where the diagnostic results indicated a decreased severity of defects. There were even cases when symptoms of known, severe bearing defects were not observed in the envelope spectrum. These cases indicated the DREAM diagnostic software had limitations that produced less than optimum results on gear box bearings.

Very soon the reasons for the diagnostic errors were discovered. The envelope detector filter passed the high amplitude harmonic multiples of gear mesh frequency in addition to the random vibration components needed for accurate bearing diagnostics. The harmonic components that are within the frequency band of the envelope detectors filter influence the harmonic composition of the envelope spectrum. One of the characteristics of this influence is a decrease in the contribution to the envelope spectrum of the signals that modulate the random vibration. Sometimes they even disappear from the envelope spectrum [2]. Since the modulation of random vibration is utilized as a primary indication of defects and also to assess defect severity, much information is lost.

To eliminate potential errors in rolling element bearing diagnostics it was proposed to use an envelope detector filter with a band pass of about 20-25%. Optimally, the filter should be located in a frequency region where there are no strong harmonic components present in the signal. This produces a reliable diagnosis of rolling element bearings in gear boxes, and also provides a means to detect the shock loads applied to the bearings by the gear meshing. It also provides a new approach to gear mesh diagnostics.

The top trace in figure 1 is a gear box rolling element bearing vibration spectrum recorded on a rolling mill stand at the West-Siberian metallurgical plant. Directly below are three envelope spectra of the vibration signal with different frequencies of the envelope detector filter. The first envelope spectrum was measured in the third octave frequency band with a center frequency coinciding with the third order gear mesh frequency component. No harmonic components are present in this envelope spectrum, so we might conclude that there are no defects in the bearing or gear mesh. However, the envelope spectrum measured in the frequency band between the third and fourth orders contains shock pulses. The shock pulses are not at the rotating frequency of the bearing on which the vibration signal was obtained but rather at the rotating frequency of the meshing gear. The envelope spectrum also contains a series of orders of the BPFO. This indicates cavities (pitting) on the outer race. The enveloped vibration spectrum recorded on the other bearing of the same shaft contains only multiples of the meshing shaft rotating frequency. Thus, both bearings are influenced by shock loads transmitted from faulted teeth located on the meshing gear. This analysis of the spectra presented in figure 1, leads to the following conclusion: Shock loads induced by mesh defects can be detected at all bearings associated with a mesh by choosing the correct frequency band for the envelope detector. In this example, the mesh shock loads do not interfere with the detection of bearing rolling surface flaws.

Figure 1(above). Autospectrum and three envelope spectra of the rolling elemet bearing of a gear-box. Vertical units are in Gs-acceleration.

This conclusion has been confirmed by many tests where similar results were gained on gear boxes equipped with fluid film bearings. An analysis of the enveloped vibration spectra recorded at the bearings also gave very good results on low rotating speed gear boxes. Dynamic loads transferred to the bearings from low speed gearing typically have lesser losses than in high rotating speed gear boxes.

Furthermore, a similar analysis of the influence of defects in geared, tooth type couplings indicates that envelope spectrum analysis provides a good means to detect coupling faults. Envelope detection works efficiently with any rotational speed of the coupled shafts.

Diagnostic Tasks

The first diagnostic task is selecting the frequency band in which the envelope of the vibration signal is formed. As previously noted, this frequency band should be chosen to exclude harmonic components, for which RMS values are higher than the half value of the sum of all the random components in the frequency band. Otherwise, the shock load applied to the bearing and bearing faults are impossible to detect with high reliability.

Estimating defect severity is the second task in diagnostics. This requires analyzing the vibration envelope of all the gear box bearings. A crucial point is that the shock load, applied to the rolling contact surfaces of different bearings can be different depending on the bearing clearance. Bearing clearance limits the free displacement of the shaft in response to torque load acting along the circumference of the gear. As shock load is transferred through the gear mesh to all the bearings, the severity of a gear mesh defect is best defined at the bearing. At this location the modulation of the friction forces and random vibration by the rotational frequency of the faulty gear is maximum. The observation that the maximum value of the vibration amplitude modulation may not appear at the flawed gear's bearings is confirmed by the envelope spectrum shown in Figure 2. This vibration spectrum was recorded from a gear box on the Saint-Petersburg metro escalator. The first stage, highest rotating speed, gear is flawed. Note that symptoms of the first stage gear flaw are strongest in the third stage vibration envelope.

The third task is separating the diagnostic characteristics of bearing, gear and coupling defects that produce the same symptom, namely random vibration modulation by shaft rotating frequencies and their multiples. In rolling element bearings these are wear of the inner (rotating) race. On fluid film bearings and gear couplings, virtually all types of defects, including specific tooth defects, produce more or less the same characteristics. Three rules have been constructed to link vibration characteristics to one of the specific defects mentioned.

The first rule concerns bearings. If the defect is in the bearing, the modulation almost always appears only in the random vibration of this bearing. Only when the defect is very severe do shaft oscillations become so strong that they deform the lubrication layer of a nondefective bearing at the other end of the shaft. When this occurs, modulation of the friction forces and random vibration will also appear at this bearing.

The second rule concerns the couplings. With a faulted coupling the deformation of the lubrication layer occurs in the bearings of both coupled shafts to a different degree depending on the relative shaft displacements. Thus, modulation of the friction forces by vibration at the rotating frequency and its multiples will be detected at different levels on the bearings at each end of a faulted coupling.

The third rule concerns gearing. When the teeth of a gear are defective, vibration modulation at the rotating frequency of the faulted gear and its multiples is detected on both the bearings of this shaft as well as the shaft meshing with the faulted gear. Moreover, the appearance of modulation by the same frequency is also possible in the bearings of other shafts within the gear box.

The fourth and last task is identifying and diagnosing flaws on gearing equipped with fluid film bearings that have a thicker lubrication layer than rolling element bearings. Because of the thicker lubrication film, shock loads, especially in high speed gears, are greatly attenuated through the lubrication layer. As a result, modulation of the friction forces can be both extremely weak and reasonably smooth. For this reason the qualitative relations between the severity of a gear flaw, the modulation amplitude of the vibration signal and the number of multiples in the vibration envelope spectrum should be quantified for different types of gearing. To establish representative criteria, quantitative data comparing the relation between the levels of the autospectrum components and the severity of the gear defects can be used. By comparing data relating the influence of severe gear flaws on gear box vibration and on modulation of random vibration at the bearings, it is possible to set level criteria in the envelope spectrum for severe defects. With these criteria it is possible to define levels for incipient (weak) defects that will ensure their timely detection.

Practical Results

For several years the authors have achieved positive results on gearing and geared couplings, especially on low speed machines, with diagnostics conducted using the methods described. In the pulp and paper and metallurgy industries where the rotational speed of the machines can be as slow as several revolutions per minute, this approach appeared to be the only successful method that solved practical problems effectively. This experience in diagnostics has led to several conclusions that characterize the influence of defects on the vibration envelope spectrum recorded on the bearings of gearing and geared machines. These conclusions can be demonstrated with examples.

First, we shall describe the influence of gear wear on vibration and its envelope spectrum. Intensive wear of geared coupling teeth is frequently observed when the shafts have major operating misalignment. With wear, the coupling centerline changes angle spasmodically several times during one shaft revolution. This action applies a shock load to the bearing that results in the appearance of several multiples of the rotating frequency in the bearing vibration spectrum and its envelope.

Figure 3 shows the vibration spectrum and high frequency envelope spectra recorded on the intermediate shaft rolling element bearing of a gear that connects an electric motor to a rolling mill stand at the West Siberian metallurgical plant. With an incipient (weak) defect, just after detection, the number of spasmodic displacements of the shaft axis was five in one revolution. This is seen in the top vibration spectrum and in the envelope spectrum third from the top. During defect development the number of changes decreases to two in one revolution and the duration of the transient processes increases. In addition, random changes of amplitudes and duration of shock loads applied to the bearings, occur. The width of the lines of the multiples of rotating frequency in the autospectrum and the envelope spectrum of the high frequency random vibration signal both increase. All this is seen from the second vibration spectrum and its envelope in figure 3. If grease is added to the coupling shortly after detection of the beginning stage of a flaw spasmodic displacements of the shaft axis can disappear for some time or significantly decrease in amplitude.

Tooth defects in geared transmissions influence vibration in a different way than tooth defects in geared couplings. There is also a common symptom -- the appearance of shock loads applied to the bearings at multiples of rotating frequency. Differences are primarily in two areas: First, the shock load appears several times per revolution in a geared coupling, but only once per revolution in a geared transmission. Second, the magnitude fluctuations of shock loading in a geared transmission are minimal and therefore the spectral lines do not widen as large as in gear couplings.

In addition to these symptoms, gear faults typically produce rotating frequency amplitude modulation of multiples of gear-mesh frequency simultaneously with shock loads applied to the bearing. For developed faults on two gears, especially in high speed geared transmissions, the appearance of shock loads, applied to the bearings is also typical. The primary frequency will be the contact frequency produced by two defective zones on the meshing gears. This observation is illustrated in figure 4. Figure 4 shows vibration spectra and their high frequency envelope spectra recorded on faulty gearing in an IL-96 jet engine measured at the Moscow Sheremetyevo airport.

It is important to consider that components at gear mesh frequency are encountered only rarely in bearing vibration envelope spectra. This is explained by the fact that the dynamic load applied to the bearing at gear mesh frequency is much less than the constant load when the amplitude of friction force's modulation is small. However, if components at gear mesh frequency are detected in the bearing vibration envelope spectrum the earlier consideration of incorrect selection of the frequency band for envelope spectrum formation must be investigated.

Selecting the machine operating mode, including both rotating speed, and the magnitude of load is equally important. Experience has shown that diagnostics of geared couplings are best conducted at no load operation. Shock load symptoms at the bearings that identify beginning stages of wear appear more often under no load conditions on then on a loaded machine. In bevel gear boxes where there is a change in location of tooth contact under load, it is best to select a consistent, normal operating for analysis. In other cases, illustrated in figure 5, the magnitude of the shock load applied to the bearing occurs only when the faulted surface of the gear in the contact area. Thus, an estimate of defect severity can be in error if conditions of load are not comparable. This typical situation took place when diagnostics were conducted on the Saint-Petersburg metro car trailer bogie with two methods -- under real load conditions and running under no load with the car supported on jacks.


Practical experience in gear diagnostics using high frequency bearing vibration envelope spectra leads to the following conclusions:

  1. Traditional methods of gear diagnostics using narrow band vibration spectra, cepstra and envelope spectra of gear mesh vibration do not always assure early fault detection and identification, especially on machines operating at low rotating speed.
  2. Diagnostics based on envelope spectra of the high frequency random vibration signal increases the certainty of defect detection and identification on geared machines at the earliest stages of development, including low rotational speed machines. Components within an envelope spectrum are most sensitive to the appearance of flaw induced shock loads applied to the bearings, especially at low frequencies.
  3. It is necessary to be certain that there are no major harmonics in the frequency band utilized to develop the envelope spectrum.
  4. Separating bearing, gear and coupling defects that have the same vibration envelope spectrum diagnostic symptoms requires a combined analysis and of bearings and meshing gears with potential faults.


[1] John S. Mitchell, “Introduction to Machinery Analysis and Monitoring” Tulsa, PennWell Publishing, 1993, page 230

[2] Barkov, A. V., Barkova, N. A. Automatic Diagnostics of Rolling Element Bearings Using Enveloping Methods, Proceedings 18th Annual Meeting, The Vibration Institute, June 21-23, 1994

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