Whitepaper written for Power Transmission Engineering by Dr. Hannes Grillenberger and published with permission from the Schaeffler Group USA
An important quality feature requires an effective assessment strategy
The noise behavior of rolling-element bearings is an important indicator of quality. Accordingly, it is a high-priority feature for customers. With the proliferation of electric motors in applications such as electric vehicles and household appliances, customers are also becoming more sensitive to bearing-induced vibrations. To effectively address these concerns, it is important to optimize bearings not only by testing but also by means of validated simulation methods. But while simulations provide useful information, they can be complicated to use. This creates a need for easy-to-use rating and limiting values that can facilitate proper bearing assessment and selection for each particular application.
The article will both provide an overview of the complex simulations applied to certain aspects of rolling-element bearing noise as well as introduce a catalog-based rating index known as the “Schaeffler Noise Index” (SGI).
Simulation methods for investigating bearing running noise
CABA3D simulation tool
Simulations of bearing noise may be done with Multi-Body-Simulation (MBS), a physics-based simulation tool that uses the power of a computer to design, evaluate and refine complex systems using sophisticated mathematical modeling and solution tools. To that end, Schaeffler has developed the CABA3D MBS tool [1, 2]. When using MBS, an accurate contact model is essential to accurately model the mechanical response of the bearing. In addition to the contact model, the inner bearing geometry significantly impacts the bearing’s stiffness and the degree of its variation. This can be an issue if the simulation is performed using commercial software, as these internal parameters may not be made available by the bearing manufacturer.
Of course, MBS is not the only method for analyzing bearing dynamics and vibration. Finite Element Analysis (FEA) is another popular simulation tool, but it requires long simulation times as transient calculations need to be performed – a significant drawback.
How waves on bearing rings affect noise
This effect is investigated using both the CABA3D MBS tool and FEA on an NU-type cylindrical roller bearing radially loaded with 37.7% of the static load rating C0. The waves are applied on the rotating inner ring with an amplitude of 9.7*10e-3% of the inner race diameter and wave numbers of 2 and 7 as well as both waves combined in phase. The inner ring is rotating at 9.3% of the bearing’s limiting speed. In these simulations, the outer ring is locked in all degrees of freedom, and the inner ring is completely free except for the constant rotation. The assessed dimension is the displacement speed of the inner ring in the radial direction perpendicular to the load direction. The graphs show the duration of the simulations for the three configurations. The strong correlation between the amplitudes and frequencies of the MBS results and the FEA results can be seen as positive.
Grinding marks on rollers
Grinding marks on rollers are typically the result of a manufacturing defect. Although such defective rollers would not be used in a bearing intended for sale, they serve as a good validation example for the simulation. The impact of the grinding marks usually masks all other effects of further tolerances and allows a comparison of testing results and the idealized simulation.
The graph in Fig. 2 shows the envelope spectrum of testing and simulation data from the radial vibration acceleration on the outer diameter of a cylindrical roller bearing with a grinding mark on one roller. The grinding mark has a depth of 0.25% of the roller diameter. The load on the bearing is 2% of C0, and the rotational speed is 7.8% of the limiting speed of the bearing. Due to the very good agreement of the spectra, the simulation can be interpreted as having been validated.
As with any comparison of data, employing the correct set of boundary conditions can be crucial because they influence the resonance of the system being analyzed. Especially when regarding absolute amplitudes, the boundary conditions must be as similar as possible. For comparisons that are made using test data, the simulation also must take into account the salient features of the test rig that was used. These “salient features” must be identified since each application is different. However, if an “A to B” comparison is being made, then the boundary conditions may also be disregarded in favor of the lower modeling effort and shorter calculation times.
Radius sorting of tapered rollers
During production, the diameter of tapered rollers can vary within a certain tolerance range, which may lead to noise. For our investigation, the radius sorting takes into account sorting spread and relative sorting. For the spread definition, an initial spread of x in the low micron range is assumed and scaled by 0, 1, 2, 4 and 8. Three different statistical sequences are generated as sort sequences, along with a scenario where all rollers (except for a larger one) have the same diameter. The sequences are scaled by the spread of the simulation.
The diameter spread effects the noise of the bearing in three different mechanisms:
1. Ring position due to roller diameters:
Due to the different roller diameters, the rings are not ideally aligned. Instead, they are tilted and shifted toward each other, which causes vibrations as the bearing is rotating. The degree of tilting and shifting is primarily dependent on the sorting spread.
2. Additional tilting of the ring:
If the relative sorting causes the support of the rings to become unstable, they may additionally tilt and, consequently, vibrate even more. This effect depends on the sorting sequence and is augmented by high diameter spreads as an unstable position becomes more likely.
3. Cage dynamics:
These simulations are done for a roller-guided cage. For a horizontal bearing axis, the cage center of mass (CoM) is shifted downward due to the effects of gravity on an ideal bearing. Depending on the roller diameters, different types of dynamics can be seen. In the red sorting simulation shown in Fig. 3, the cage guidance is passed from roller to roller. This results in a vibration of the bearing ring with the ball-passing frequency of the outer ring (BPFO) and its multiples. This can also be seen in the vibration spectrum of the ring as the guidance force is transmitted to the rings with that frequency (Fig. 4).
For the green roller sorting simulation shown in Fig. 3, the cage CoM orbits with the roller set frequency, and it is being guided by only some of the rollers. This results in vibration with the roller set frequency (fundamental train frequency/FTF) and its multiples. This can be seen for another sorting simulation, which is shown in blue in Fig. 4. Because centrifugal force has a significant impact on orbiting cages, this effect is both sorting- and speed-dependent.
Schaeffler Noise Index (SGI)
The above-mentioned possibilities regarding simulation of individual bearing noise behavior caused by typically unwanted effects are an important step toward establishing the overall noise-level calculation. Based on highly sophisticated tools, the Schaeffler Noise Index (SGI) was developed to provide a catalog-level rating tool that can quickly rate and compare bearing noise. The SGI’s development was motivated by a desire to understand which bearing emits the minimum noise for a given static load rating – a question that, until now, could only be answered through experience or measurement. With regard to experience, each case may be individually different and will usually give qualitative results. Measurement, on the other hand, is complicated and time-consuming. In contrast, the Schaeffler Noise Index is a quantitative measure that quickly provides results and offers users the opportunity to make comparisons between bearing types.
Because the SGI is derived from and certified by Schaeffler’s internal standards, it is currently only available for Schaeffler bearings. It displays the maximum permissible vibration level for reference conditions described in ISO 15242.
This definition leads to two main characteristics: Because the SGI is derived from certain basic requirements, an individual bearing usually has lower normal running noise. Individual subjective impressions in certain applications are not displayed because the SGI refers to reference conditions that describe the load case, mounting as well as assessment.
Because the SGI is normalized, it does not have a separate unit. In the catalog listing, it is displayed graphically over the static load rating C0, which offers a fast and clear overview for a given application with known load rating. The relationship to C0 is obvious as this measure links the maximum permissible load to a certain plastic deformation, which may be directly related to the emitted vibration.
The Schaeffler Noise Index is available for the main series of deep grove ball bearings, angular contact bearings as well as tapered and cylindrical roller bearings. It allows quick comparisons to be made between different bearing types, e.g., ball bearing vs. roller bearing. An SGI for additional bearing types and series is currently in development and will be published as it becomes available . Fig. 5, which features a graph of the SGI for deep groove ball bearings, clearly shows that several bearing series may be used for a given C0 = 20300N. Furthermore, the graph shows that, depending on the geometrical dimensions of the application, one particular bearing series provides the best fit (for example, the 62..-C series). For noise-sensitive applications, Schaeffler’s GenerationC bearing (designated as point 2 in the graph) is recommended because its SGI value is considerably lower than for a conventional version (designated as point 1).
To address the challenges posed by the noise behavior of rolling-element bearings, it is necessary to take a comprehensive approach that includes advanced simulations, testing methods and readily available rating values. This article provides examples of validated multi-body-simulations that help to understand the general excitation mechanisms within bearings in order to be able to optimize them during the design phase.
To that end, Schaeffler has introduced its Schaeffler Noise Index, which allows the noise emitted by a bearing at reference conditions to be quickly and easily rated. As such, the SGI offers a hands-on rating tool for designers during the application engineering stage.
About the Author
Dr. Hannes Grillenberger develops methods to calculate noise inside rolling bearings at Schaeffler. His field of research includes simulations on normal and system-excited running noise as well as all types of cage noise effects. In his role as Key Expert, Hannes is a vital part of Schaeffler’s network of R&D experts. He currently also serves as chairperson of the Rolling Element Bearing Technical Committee for the Society for Tribologists and Lubrication Engineers (STLE). Hannes holds a PhD in physics from the University of Erlangen-Nuremberg in Germany.
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