#### Calculation Methods for Dynamic Parameters of Rolling Element Bearings and Their Prediction Accuracy

Rolling element bearings are essential components in a vast range of rotating mechanical systems, providing rotational support and a wide range of methods for friction control. The performance of these bearings is crucial to the overall functionality of the machine. Therefore, predicting the dynamic behavior of rolling bearings accurately is vital to ensure their reliable operation. Figure 1 shows a general view of angular contact ball bearings.

Dynamic parameter calculation is the process of determining the bearing’s dynamic response under specific operating conditions, including load, speed, and lubrication. The calculation of these parameters is crucial for designing and selecting bearings and predicting their operating life. The main dynamic parameters are:

• Radial and axial stiffness, which is the ability of a bearing to resist deformation when subjected to radial and axial loads. This parameter is essential in ensuring that the bearing maintains its shape and does not deform excessively under the applied load.
• Damping, which is the ability of a bearing to absorb energy and dissipate it in the form of heat. This parameter is crucial in ensuring that the bearing does not overheat, leading to premature failure.

­

Moreover, bearing stiffness and damping are used for the rotor dynamic calculations of the machine supported by rolling element bearings for the accurate prediction of the rotor response under static and dynamic loads, taking into account the correct bearing characteristics.

Several methods are available for calculating dynamic parameters, each with its advantages and limitations, as shown in Figure 2.

One of these methods is the Gargiulo method [3], which is based on a mathematical model that considers the deformation of the bearing components and the interaction between the rolling elements and the races. This method is particularly useful for bearings subject to high loads or non-ideal operating conditions, such as misalignment or vibration.

The Harris method [4] is a more comprehensive approach that considers the effects of both lubrication and deformation. The Harris method is particularly useful for large or heavily loaded bearings that are subject to high stresses and deformations.

Another method is the Elasto-Hydrodynamic Lubrication (EHL) method, which considers the effects of lubrication on the contact between the bearing elements and the races. The EHL method is particularly useful for high-speed bearings, where the effects of lubrication can significantly impact the bearing performance.

Other methods, such as finite element analysis (FEA) and the boundary element method (BEM), are also used to calculate dynamic parameters. These methods are more complex and time-consuming than previous methods, as they require building separate models for each bearing, but they provide more accurate results, especially for complex bearing geometries and loading conditions.

According to an article [5], there is a simple relationship between the unknown bearing damping coefficient c and the bearing stiffness coefficient, which can be calculated. Based on this, it can be considered sufficient to calculate the stiffness coefficient and find the damping coefficient through it.

Radial stiffness measures a bearing’s ability to resist deformation under radial loads. It refers to the force needed to produce a unit of radial displacement in the bearing raceway. Bearings with high radial stiffness are less likely to deform under load, leading to reduced vibration amplitudes and increased fatigue life. Factors such as the bearing design, material, and geometrical model all influence radial stiffness. Geometrical parameters like the number of rolling elements, their size and spacing, and the curvature of the raceways also play a crucial role.

Numerical techniques like computer simulations can be used to calculate rolling bearing dynamic parameters. AxSTREAM Bearing™ is a software package that allows for radial stiffness calculations of various types of rolling-element bearings, including angular contact ball bearings, self-aligning ball bearings, cylindrical roller bearings, and tapered roller bearings, as shown in Figure 3.

In conclusion, accurate calculation of rolling bearing dynamic parameters is critical for reliable operation. Several methods are available, each with their advantages and limitations. The appropriate method should be selected based on the bearing’s geometry, operating conditions, and accuracy requirements. It’s essential to ensure the accuracy of input data and assumptions made to achieve reliable predictions. AxSTREAM Bearing™ provides advanced methods for calculating radial stiffness, resulting in more accurate predictions of dynamic parameters. To learn more about AxSTREAM RotorDynamics™ and AxSTREAM Bearing™, contact our team at Info@SoftInWay.com.

References

1. (2010). SKF Rolling Bearings Handbook (No. 17000/1 EN). Retrieved from https://www.skf.com/binaries/pub12/Images/0901d196802809de-Rolling-bearings—17000_1-EN_tcm_12-121486.pdf
2. International Organization for Standardization. (2007). Rolling bearings — Dynamic load ratings and rating life (ISO Standard No. 281:2007). Retrieved from https://www.iso.org/standard/38102.html
3. Gargiulo, E.P.,Jr., A Simple Way to Estimate Bearing Stiffness, Machine Design, 1980, pp.107-110.
4. Harris T.A. Rolling Bearing Analysis. 4-th edition. 2001.
5. SKF Evolution. (2021, February 10). Damping in a Rolling Bearing Arrangement. Retrieved from https://evolution.skf.com/damping-in-a-rolling-bearing-arrangement/