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The damages of ball and roller bearings can be attributed to various reasons: faulty assembly, technological errors during the assembly of shaft components, steam impact, overload, excessive speed, poor or missing lubrication, material and manufacturing defects. However, fundamentally, the operational load of the bearing itself – depending on the bearing's service life – eventually leads to material fatigue, followed by initially minor and then rapidly increasing damages.
When a bearing is damaged, vibrations occur, and their frequency depends on which bearing component the failure occurred. The fault frequencies – often referred to as bearing frequencies or bearing fault frequencies – can be easily calculated if certain basic geometric dimensions of the bearing are known.
The following data is required to calculate fault frequencies:
Most Common Bearing Faults
The following bearing fault frequencies (fundamental train frequencies) exist:
The most common bearing fault is damage to the outer ring, as in most cases the outer ring is stationary, and the load (e.g., weight of the rotating part) always acts on the same point of the outer ring through the rollers. The calculation of fault frequencies depends on whether the inner or outer ring of the bearing rotates.
Due to the axial forces acting in individual machines, force transmission does not occur at the contact angle specified in the bearing specification. The contact point shifts minimally to the side, thus changing the actual contact angle. This affects the expected fault frequencies obtained by calculation. In practice, this mainly occurs with high axial loads, where axial forces increase the contact angle, affecting the development of fault frequencies. The effect is quite small, up to 2 percent, but even at this point, the calculated fault frequencies do not exactly match the frequencies measured in reality. In most common cases (inner ring rotates, outer ring is stationary), vibration frequencies characteristic of bearing faults can be estimated with an accuracy of ±20 percent based on the following equations:
Calculation Example
The shaft speed is 2940 revolutions per minute, which corresponds to 49 Hz, the outer ring of the bearing is stationary, and the inner ring rotates. The number of balls in the bearing is Z=8, the diameter of the balls is d=6.75 mm, the diameter of the rolling path is D=28.5 mm, the contact angle Q=0 degrees.
The diagram shows the spectrum appearance of the fault frequencies of the bearing in a simplified (schematic) form as presented in the example. The fault frequencies of the outer ring (BPFO) are slightly highlighted to distinguish them from the fault frequencies of the inner ring (BPFI). The appearance of bearing problems in the frequency spectrum varies depending on whether it is a mild – incipient – fault phenomenon or an established – severe – fault. Accordingly, further theoretical aspects need to be addressed.
Occurrence of Bearing Fault Frequencies The basket frequency rarely occurs dominantly. Basket damages often appear in the form of modulation around the other bearing frequencies (roller, inner, or outer ring frequencies) with the basket frequency. If the rolling over the bearing damages occurs with continuously changing load, occasionally the speed modulations of the bearing fault frequency can be observed.
During the operation of a healthy machine, the fundamental frequencies of the bearing are usually not present. The incipient damage of the bearing manifests itself with high-frequency multiples of the bearing fault frequencies, and as the damage worsens, the fundamental frequencies of the bearing become more pronounced. In the case of bearing damage, periodic impact excitations always result in multiples of the impact frequency (in our case, the fundamental frequencies of the bearing). However, if a purely sinusoidal excitation occurs (e.g., due to balancing forces), only the fundamental frequency of the excitation force appears in the spectrum.
For example, if the bearing components deform due to stress, sinusoidal force effects can be expected during the rolling of the rollers. This is often observed in cases of tensioning sleeves being assembled with too small clearances after repairs, or in heavily loaded, deformed bearing seat units (e.g., belt drives). In such cases, only the fundamental frequency of the bearing faults appears in the spectrum.
In the case of too small bearing clearance, primarily the fault frequency of the outer ring becomes visible. The actually loaded bearing component is the cage, the reason for which is the following: due to the too small clearance, the bearing stress must be borne by the cage, as it needs to press the rollers through the smallest clearance. Therefore, in the end, the fundamental frequency of the cage should appear, but this is not true in most cases. The reason for this is that the cage needs to press each roller individually through the narrow cross-section, thus the cage frequency occurs multiple times, precisely the product of the cage frequency and the number of rollers. This is the fault frequency of the outer ring.
Noises and vibrations in gear drives
Gear drives do not transmit forces completely linearly. Although the transmission of torque is slip-free, minimal speed fluctuations (torsional pulsations) occur with each tooth engagement, leading to pulsations in force transmission. Even in undamaged teeth, pulsating forces are generated, resulting in the "usual" noises and vibrations. The strength of these pulsating forces depends on various factors:
When determining the condition of drives and gears, the design parameters (type of gearing and tooth design) and operating conditions (load) are often considered given. Emphasis is usually placed on the surface properties of the teeth. The cause-and-effect relationships detailed below can be utilized for this purpose.
Impact impulses during tooth contact
When two teeth come into contact, the so-called tooth contact impact occurs. This natural force action occurs with every tooth engagement. Its strength depends on the magnitude of the load, the tooth overlap in helical gearing, and the tooth shape itself. With undamaged teeth, nearly pure sinusoidal excitation occurs, which appears in the spectrum as the tooth contact frequency. The tooth contact frequency, often referred to as the gear mesh frequency, can be calculated based on the following equation: Ff= n1 / 60 × Z1 = n2 / 60 × Z2 where Ff is the tooth contact frequency, n1 is the speed of shaft 1, Z1 is the number of teeth on gear 1 of shaft 1, N2 is the speed of shaft 2, Z2 is the number of teeth on gear 2 of shaft 2. The tooth contact frequency corresponds to the number of teeth contacting each other in one second. Vibration at the tooth frequency is a natural (thus unavoidable) characteristic of gear transmissions.
Impact impulses due to gear damage
If one or more teeth are damaged, additional impact excitations occur beyond the "natural" tooth frequency when the "rolling over" takes place at these defective locations. Since generally more impacts occur per tooth, primarily multiples of the tooth frequency appear, despite the fact that sinusoidal force action is not present here. Practical experience shows that in the case of minor damage to one or a few teeth, the values of the multiples of the tooth frequency increase. Tooth repetition frequency If one or more faulty teeth are present on both meshing gears, in addition to the tooth frequency and its harmonics, the tooth repetition frequency also appears, if there is a tooth pair where particularly high vibration impulses occur during engagement. The tooth repetition frequency is the product of the greatest common divisor of the gear teeth and the product of the teeth of the meshing gears. It should be noted that during the design of transmissions, every manufacturer strives to ensure that - to eliminate uneven wear - the same teeth meet as infrequently as possible. This is achieved by having the smallest common divisor of the two gear teeth as large as possible, which can be achieved by using prime numbers of teeth. Torsional vibrations due to damage on the teeth All gear drives exhibit torsional vibrations. This is manifested in the oscillation of the driven shafts' speeds. The cause is the non-100% linear force transmission and the surface roughness of the teeth resulting from the manufacturing technology. Torsional vibrations are very small in the case of an undamaged gear drive. However, if multiple teeth are damaged, in addition to the impact impulses described earlier and the resulting tooth frequency sidebands, an increase in torsional vibrations can be observed. Torsional vibrations cause changes in the tooth frequency, meaning that the teeth do not engage at uniform intervals. This phenomenon is manifested in the vibration spectrum in the form of frequency modulation: the tooth frequency (tooth contact frequency) is modulated ("mixed") with the rotation frequency of the damaged gear. The modulation becomes visible in the form of sidebands at the frequency distance from the tooth frequency. The frequency spectrum may look like the diagram above (schematically depicted). Unfortunately, the situation is not quite as simple: since the teeth carry the force effects resulting from the - as indicated in our example - imbalance and misalignment, this also generates torsional vibrations, and thus the modulation of the tooth frequency with the rotation frequencies of the two shafts also appears here. Therefore, the sidebands resulting from torsional vibrations clearly indicate severe tooth defects only if the gear drive itself is not subjected to torsional stress.
Fault diagnosis based on vibration analysis
For single-stage drives, the mentioned frequencies and their sidebands need to be examined. In the case of multi-stage gear drives, the frequencies generated by each stage are calculated successively: the output rotational frequency of the previous stage is always the input rotational frequency of the next stage. Based on this method, the mesh frequency and its modulations for all stages can be determined. (However, the number of sidebands increases significantly because even the last stage "sees" the mesh frequency and its modulations of the first stage. This means additional modulation for the mesh frequency associated with the last stage, beyond the effects from the input and output sides.) It is self-evident that discovering and separating the above frequencies requires a vibration analyzer with sufficient resolution and frequency bandwidth. The more stages in the drive, the higher resolution (up to 3200, 6400, or even 12,800 line spectra) will be needed.
For spur gear transmissions, radial, helical, or herringbone gear drives, axial vibrations are sought in the case of helical gears, while in structures with inclined gears, vibrations are sought in both directions at the mesh frequency and its harmonics, as well as their appearing frequency modulations as sidebands.
The spacing (frequency) of the sidebands characterizes the type and location of the fault, for example, modulation proportional to the speed of the driving, intermediate, or driven shafts is related to problems with these elements, while modulations at different frequencies may be related to speed or load fluctuations, and the frequency modulating the mesh frequencies is characteristic of gear faults.
Sidebands closely grouped around mesh frequencies mostly indicate faulty gear tooth shapes. "Wide" (high-frequency) sidebands indicate impulsive, random impacts or sudden load changes causing vibrations, with possible causes such as broken teeth. In the case of more than one fault, intermodulation sidebands may also occur, arising from the sums or differences of fault modulation frequencies.
Rahne Eric (PIM Ltd.) pim-ltd.com, machineryexpert.com
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