Selecting a bearing
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
| Vibration caused by ball revolution (fa) |
| 1 |
 |
1 - |
Dw |
cos α0 |
 |
fr |
| 2 |
Dpw |
|
| Vibration caused by retainer rotation (fb) |
same as fa |
| Vibration caused by ball rotation (fc) |
| 1 |
|
Dpw |
- |
Dw |
cos2 α0 |
|
fr |
| 2 |
Dw |
Dpw |
|
| Vibration caused by ball pass (fd) |
Zfa
Z (fr - fa) |
| Vibration caused by inner ring raceway dents or bumps (fe) | |
| Vibration in Axial direction (fet) |
nZ (fr - fa) |
| Vibration in Radial direction (fer) |
fet ± fr |
| Vibration caused by outer ring raceway dents or bumps (ff) | nZfa |
| Vibration caused by ball surface dents or bumps (fg) | |
| Vibration in Axial direction (fgt) |
2nfc |
| Vibration in Radial direction (fgr) |
fgt ± fa |
Formula for outer ring rotation
| Vibration caused by ball revolution (Fa) |
| 1 |
|
1 + |
Dw |
cos α0 |
|
Fr |
| 2 |
Dpw |
|
| Vibration caused by retainer rotation (Fb) |
same as Fa |
| Vibration caused by ball rotation (Fc) |
| 1 |
|
Dpw |
- |
Dw |
cos2 α0 |
|
Fr |
| 2 |
Dw |
Dpw |
|
| Vibration caused by ball pass (Fd) |
ZFa
Z (Fr - Fa) |
| Vibration caused by inner ring raceway dents or bumps (Fe) | nZFa |
| Vibration caused by outer ring raceway dents or bumps (Ff) | |
| Vibration in axial direction (Fft) |
nZ (Fr - Fa) |
| Vibration in radial direction (Ffr) |
Fft ± Fr |
| Vibration caused by ball surface dents or bumps (Fg) | |
| Vibration in axial direction (Fgt) |
2nFc |
| Vibration in radial direction (Fgr) |
Fgt ± Fa |
| Dw | : Ball diameter (mm) |
Z | : number of balls |
| DPW | : Pitch circle diameter (mm) |
n | : Integer number |
| α0 | : Nominal contact angle (°) |
fr | : Inner ring rotation speed (Hz) |
| | |
Fr | : Outer Ring rotation speed (Hz) |
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:
| fa = |
1 |
|
1 - |
2.778 |
× 1 |
|
× 30 = 11 Hz |
| 2 |
10.5 |
As the difference in each ball gets bigger, vibration in the rotating direction also increases.
(Figure 15-1, 15-2)
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 15-3, 15-4, 15-5, and 15-6)
These calculations are very helpful to analyze vibration, speed fluctuation, noise, and so on.
normal vibration in rotating direction
Figure 15-1
vibration in rotating direction if the difference in each ball is huge
Figure 15-2
Outer ring raceway deformation (Triangle)
Figure 15-3
Inner ring raceway deformation (hexagonal shape)
Figure 15-4
Inner ring raceway deformation (heptagonal shape)
Figure 15-5
Inner ring raceway deformation (octagonal shape)
Figure 15-6
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