Bearing Frequency-Calculation-Methods for Vibration Analysis with MPB10

When investigating the frequency range of a machine, especially its bearings, with our
Condition Monitoring Sensor Multi-Physics-Box (MPB10), the question often arises as to which vibration frequencies should be observed.

In general it is not necessary to know these frequencies, because by teaching the MPB10, ideally when the motor is in good condition after installation, it is possible to set the alarm thresholds for single frequencies and/or complete frequency ranges slightly higher than the current frequency levels and the MPB10 will generate an alarm if the frequencies change due to e.g. wear down.

If the dimensions of a bearing are known, the basic measurements of the bearing can be used to calculate typical vibration frequencies if a one-point damage occurs at some time. Detailed bearing properties can be found in the motor's specification documents or if the product name of the bearing is known, by searching for the datasheet at the bearing manufacturer's website.

In this article four cases of damage are focused: 

• Rotation of the inner ring - fixed outer ring
  • A local damage on the outer rings' raceway of the bearing
  • A local damage on the inner rings' raceway of the bearing
• Rotation of the outer ring - fixed inner ring
  • A local damage on the outer rings' raceway of the bearing
  • A local damage on the inner rings' raceway of the bearing
• Appendix regarding the mentioned calculations

On the picture below, a schematic ball bearing is shown. Each element of a typical bearing are mentioned and might be useful for the formulas and the further descriptions.

With a rotation of the inner ring (fixed outer ring), the characteristic frequencies for local bearing damage on the inner rings' raceway or on the outer rings' raceway can be calculated.

The formula symbols are described in the Appendix chapter.

The frequency of a local damage on the outer ring is equal to the
turning frequency of the bearings cage. 
Due to the fact a bearing has more than one rolling element, the resulting frequency has to be multiplied with the number of bearing elements.

The frequency of a local damage on the inner ring is equal to the turning frequency of the inner ring minus the turning frequency of the bearings cage.

Also, the number of bearing elements have to be considered.

Important note:

There are bearings with one more rows of rolling elements. If this is the case, the following has to be considered:

If the damage is a kind of line/scratch or crack over all/multiple raceways on the inner ring or outer ring, the overall number of elements should be used for calculation. If the damage is just a point on one of the raceways, the elements number of one row should be used for the calculation.

With a rotation of the outer ring (fixed inner ring), the characteristic frequencies for local bearing damage on the inner rings' raceway or on the outer rings' raceway can be calculated.

The formula symbols are described in the Appendix chapter.

The frequency of a local damage on the inner ring is equal to the
turning frequency of the bearings cage. 
Due to the fact a bearing has more than one rolling element, the resulting frequency has to be multiplied with the number of bearing elements.

The frequency of a local damage on the outer ring is equal to the turning frequency of the outer ring minus the turning frequency of the bearings cage.

Also, the number of bearing elements have to be considered.

Important note:

There are bearings with one more rows of rolling elements. If this is the case, the following has to be considered:

If the damage is a kind of line/scratch or crack over all/multiple raceways on the inner ring or outer ring, the overall number of elements should be used for calculation. If the damage is just a point on one of the raceways, the elements number of one row should be used for the calculation.

Below you can see the legend for the used formula symbols.

The diameter of a bearing element can be calculated by subtracting the outer raceway diameter with the inner raceway diameter. 

The dimensions of a bearing cannot always be specified exactly. This is the case, for example, if the bearing has a compensating function and the elements can shift. Therefore, the results of the calculations only ever indicate a range in which the frequency can lie.
The next point to consider is that you never know which failure will happen in the future, therefore you can calculate all possible failure frequencies of the relevant bearings and watch the whole frequency range.

Some of the bearing manufacturer also have calculators, where the frequencies above can be calculated. This is a lot easier. The mentioned calculations are showing how it is done manually.