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## Section 7, Calculations for Bearing Defect Frequencies

Fig. 4 shows various formulas which can be used to calculate these frequencies. Unfortunately, much of the information required is not always readily available, so the use of the approximations given in Fig. 6 are recommended. The only information required to calculate these approximations is the machine's rpm and the number of balls. This information is usually available. Some bearing manufacturers now offer databases and computer programs to determine bearing frequencies. Another fact that assists in recognizing fundamental bearing frequencies is that they almost occur at non-integer multiples of operating speed (non-synchronous) such as 4.3 x rpm, 5.6 x rpm, 6.8 x rpm, etc. They do not occur at full integer (synchronous) multiples such as 2 x rpm, 6 x rpm, 8 x rpm and so on.

All bearing frequency calculations are made with the assumption that pure rolling contact is occurring. In practice, however, it is unlikely that this type of contact is occurring perfectly, which can lead to small frequency errors. Also, errors in accurately determining rpm, errors caused by FFT bandwidth, etc., require the acceptance of a certain amount of approximation.

As with the component natural frequencies, the amplitudes of these peaks are relatively small. As the bearing deteriorates further, 1 x rpm sidebands develop, especially around the inner race frequencies. This is due to amplitude modulation as the defect(s) passes in and out of the "load zone." They can occur at +/- 1 x rpm, +/- cage frequency, or +/- ball spin frequency, depending on the situation.

Stage Three:

Fig. 5 represents the velocity spectrum for the third stage of failure. IBF has reached a maximum. As the problem develops further, bearing defect frequencies that can be calculated appear. Multiples or harmonics of these frequencies are also common. The more harmonics of a bearing defect frequency, the greater the deterioration. However, rpm must also be considered. Low speed machines show considerably lower amplitudes, as well as less bearing defect harmonics, for the same deterioration as in higher speed machines.

Stage Four:

Fig. 6 represents the velocity spectrum for the fourth stage of failure. This is the final
detectable stage, and the IBF units have dropped. At this time, bearing defects start to become less distinct as the noise floor rises. Multiple sidebands occur around harmonics of fundamental bearing defect frequencies. Eventually the spectrum becomes erratic, and broadband noise occurs. Notice that the amplitudes of individual peaks have decreased. Due to the spread over a very large frequency range, and much broadband noise, this stage is often confused with the symptoms of cavitation. It is recommended, however, that when a significant increase in IBF units occurs or "haystack" activity is present on the velocity spectrum, then data collection time intervals should be considerably reduced.

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