Bearing Vibration by Forced Rotation

While a bearing performs by rotation, this rotation generates vibration as well.
Vibration is affected by RPM, and its frequency, is called "Vibration by forced rotation"

Calculation of vibration by forced rotation in a ball bearing

In a ball bearing vibration is generated in axial, radial, and rotating directions. In certain bearing applications, vibration can have a significant effect.
This vibration sometimes causes other parts of the assemblies to resonate as vibration energy is emitted.
Understanding the bearing application characteristics well is an important part of selecting the right bearing specification for any application.

Formula for Bearing Inner Ring Rotation

Formula for Bearing Outer Ring Rotation

To simplify, cos α0 = 1 could be used.

The calculations below are examples.

example.1 : When the inner ring of an R-1560X2ZZ bearing is rotated at 1800RPM, vibration caused by ball or retainer revolution is calculated as follows:

As the difference in each ball gets bigger, vibration in the rotating direction also increases.
(Figure 1, 2)

example.2 : The amplitude of vibration at the vibration position calculated above for this R-1560X2ZZ bearing increases when the inner and outer ring raceways deform to hexagonal, heptagonal, and octagonal shapes. (Figure 3, 4, 5, and 6)

These calculations are very helpful to analyze bearing vibration, speed fluctuation, noise, and so on.