## Practical Solutions to Machinery and Maintenance Vibration Problems## Chapter 8, Vibration in Bearings## Section 7, Calculations for Bearing Defect FrequenciesFig. 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.
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