Miniature & Small ball bearings 15. Vibration by forced rotation
Although a bearing performs by rotation, vibration is also generated during the rotation. The vibration, which is affected by RPM, and its frequency, is called "Vibration by forced rotation"
Calculation of vibration by forced rotation
The vibration is generated in axial, radial, and rotating directions. The vibration has great impact on some applications.
This vibration sometimes causes other parts of the assemblies to resonate as vibration energy is emitted.
It is necessary to understand the application characteristics well in order to select a suitable bearing, and its specification.
Formula for inner ring rotation
Formula for outer ring rotation
D_{w} : Ball diameter (mm)
D_{pw} : Pitch circle diameter (mm)
α_{0} : Nominal contact angle (°)
Z : number of balls
n : Integer number
fr : Inner ring rotation speed (Hz)
Fr : Outer Ring rotation speed (Hz)
To simplify, cos α_{0} = 1 could be used.
The calculations below are examples.
example.1 :
When the inner ring of an R1560X2ZZ 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 151, 152)
example.2 :
The amplitude of vibration at the vibration position calculated above for this R1560X2ZZ bearing increases when the inner and outer ring raceways deform to hexagonal, heptagonal, and octagonal shapes. (Figure 153, 154, 155, and 156)
These calculations are very helpful to analyze vibration, speed fluctuation, noise, and so on.

normal vibration in rotating direction
Figure 151

vibration in rotating direction
if the difference in each ball is huge
Figure 152

Outer ring raceway deformation
(Triangle)
Figure 153

Inner ring raceway deformation
(hexagonal shape)
Figure 154

Inner ring raceway deformation
(heptagonal shape)
Figure 155

Inner ring raceway deformation
(octagonal shape)
Figure 156