Bearing Dynamics and Sound

 

This post covers Bearing Dynamics and Sound. It’s takes excerpts from Timken’s pdf publication of the material here.

Preface

A growing awareness of noise pollution, prompted in part by
government regulations, has been noticeable during recent years.
One is hard-pressed to single out an industry that has not been
affected, either as a user or a supplier.

In its role as a supplier, The Timken Company can look back on a
long history–predating the current emphasis on noise abatement
by many years–of actively practicing noise control. This philosophy
is exemplified not only by an extensive sound test program in its
production facilities but also by an ongoing commitment to research
in both fundamental and practical aspects of bearing related sound.

It is very useful to picture the bearing as playing one of two very distinct
roles. In one of these, its passive role as a transmitter, the bearing
merely provides a path for energy transfer between the rotating and
the stationary member, while in the second or active role, it causes
its immediate environment to be excited by virtue of its rotation. It is
important to recognize this distinction, particularly in situations calling
for a diagnosis. Essentially, bearings play a significant role in the
transmission of vibration in rotating equipment, however, they usually
are not the predominant source of vibration.

The bearing as a transmitter Simply put, a bearing may be thought of as a massless spring/ damper connecting a shaft to its housing. Typically, the interest lies in determining how vibration is transferred from housing to shaft or vice versa. For example, the excitation of meshing gears is carried along the shaft, through the bearing and to the exposed housing surface, where some of the energy is converted to airborne noise. Tapered roller and angular contact ball bearings enjoy an advantage not found in other types of rolling element bearings. Since two bearings typically are adjusted against one another, the setting will govern the axial force. This influences the stiffness of the bearings and thereby the stiffness of the system. By merely varying the bearing setting, it may be possible to shift any unwelcome resonances out of the frequency range of interest. Maximum stiffnesses of approximately 1.75 x 109 N/m (10 x 106 lbf/in) are common in tapered roller bearings. In manipulating the system stiffness, it is essential that the stiffness of the bearing supports (housing) be taken into account. In simple conceptual terms:

While the prediction of stiffness in bearings is cumbersome at best, dealing with their damping characteristics is even more elusive. It has been demonstrated, however, that bearing setting will affect the amount of damping which can be realized.

Here is some important nomenclature used in later formulas:

The Bearing as an Exciter:

The excitation potential of any rolling element bearing is determined primarily by the topography of its rolling surfaces. For example, a severe force pulse would result if a gross imperfection, such as a spall of sufficient size, were present in an operating bearing. Similarly, small imperfections such as brinell marks, nicks and any other deviations from perfect roundness of the components, will cause smaller fluctuation in the dynamic force. Hertzian theory tells us that even minute deformations can result in forces of significant magnitude. Therefore, this is the mechanism causing the bearing to act as an exciter. Surface irregularities of various origins lead to dynamic forces. These forces do not remain localized but are transmitted quite readily into the supporting structure. The dependence upon a number of rather unwieldy variables prohibits the mathematical determination of the magnitude of these forces in any one bearing. Their frequencies can be determined very accurately, though, from the gross dimensions of the bearing and its operating speed. Three constants can be defined in terms of either the angles or the diameters of the bearing depending on the bearing type:

These constants, along with the operating speed (S), the number of rollers or balls (Z) and a harmonic index (i), permit the calculation of certain frequencies. They, in turn, identify specific disturbances (Table 1).

Measurement Considerations

The frequencies listed in Table 1 are applicable whenever a bearing is
evaluated. A typical approach employs an accelerometer attached on
or near the bearing. By performing a narrow band frequency analysis
of the acceleration signal, one can usually determine if the bearing is
damaged or meets a user established vibration criterion.

To avoid ambiguity when identifying the acceleration spikes occurring at
the above frequencies, the bandwidth must be sufficiently narrow. For
example, as the operating speed decreases, so should the bandwidth.

It is not uncommon to observe modulation, particularly when the
signal is obtained in a direction perpendicular to the axis of the
bearing. Under these circumstances, the predominant evidence will
be found at the frequencies f2i ± f5j or f2i ± f6j where i and j denote
harmonic indices.

Up to this point it has been assumed that the bearing operates with
a 360º load zone. If this is not the case, such as when operating with
radial load and internal clearance or end play, the rolling elements
moving in and out of the load zone cause a spectrum that tends to
have a “smeared” appearance.

As one of the final steps in its quality assurance program, The Timken
Company subjects its bearings to a vibration analysis in highly
specialized, accelerometer-equipped test machines.

In addition, the following rationale is employed: “The vibration
(dynamic force) level of a bearing, operating at a specific speed
and under a specific preload, is compared to and must meet an
established standard. If this is the case, then by implication the
geometric imperfections are of such small magnitude that the
bearing’s potential to act as an exciter is considered acceptable.”
Note that this implies that the merit of the bearing is strictly a function
of the geometric imperfections, not one of speed and/or load and/or
the bearing supports. The vibration signature may, of course, differ
under other combinations of speed and load.

Acoustic implications

The mechanical energy in the bearing-generated dynamic forces
and those presented to the bearing from the rotating member for
transmission to the stationary member, will first be transferred to
the structure supporting the bearing. The energy then permeates
the structure and will be partially converted to acoustic energy upon
arriving at an air/solid interface. Depending upon the mass, stiffness,
geometry and boundary crossings characterizing the structure,
the mechanical energy will undergo modifications. As a result of
this transfer function, the prevailing acoustic energy (or airborne
sound) will be a function not only of the mechanical vibration of the
bearing but also the attenuation/amplification characteristics of each
particular structure.

One such structure is the quality assurance equipment employed by
The Timken Company. Bearings are tested for vibration in a relatively
unenclosed configuration, i.e., one in which a large percentage of
the bearing surface is exposed. Clearly, this condition is acoustically
quite different from one in which the bearing is fully enclosed, as for
example, in a machine tool.

The structure greatly influences the outcome of an acoustic
measurement. Since sound is mainly caused by transverse vibration
of the housing walls, a stiffer housing tends to be less noisy than one
that is less rigid. Thus, any comparisons made or conclusions drawn
between dissimilar structures are at best haphazard. The design of
the structure can profoundly affect the overall noise characteristics
of the system. This is the most important reason for not attaching
sound level specifications, dB(A), to bearings.

Design Considerations

Usually, resonances can be shifted or minimized by selective design,
i.e., the shrewd manipulation of mass and/or stiffness. Where
possible, impedance mismatches should be part of the design. For
example, the vibration path between some electric motors and
their bases is interrupted by rubber-like inserts. Also, consideration
should be given to damping, either in the form of visco-elastic layers
or mechanical discontinuities. The latter is realized wherever bolts,
rivets or interference fits occur.

Within this context, the excitation potential of the bearing can be
optimized by a variety of different techniques. An increase in the
operating speed of a bearing causes an upward shift toward the
frequency range of maximum hearing sensitivity. Simultaneously, the
overall vibration level increases. A variation in preload/end play of the
bearing can be utilized to bring about a “most favorable” condition.
Run-in will typically result in some “quieting”. The same effect can
be observed by going from a condition of marginal lubrication to
one of “adequate” lubrication, but there is a point where additional
lubricant flow no longer produces a benefit. It is good practice to
fully enclose the bearing to minimize the direct acoustic path.
Assistance is readily available from The Timken Company engineers.
Their experience can assist the user in selecting the proper bearing.