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## Section 7, Evaluating Harmonics Due to Shaft-to-Shaft/Coupling Misalignment

As the understanding of harmonics is so necessary when analyzing for shaft/coupling misalignment, this section is included in the chapter on alignment as well as in the chapter that deals with all types of vibration harmonics. However, the last portions of this section also include other sources for harmonics. These are added so that the analyst is reminded of all the main possibilities and can better compare them with each other.

To determine a machine's source for excessive vibration, it helps to understand how to evaluate the amplitudes of the individual harmonics. As a reminder, a vibration harmonic is defined for our purposes, as a vibration with a frequency that is a multiple of the "fundamental" 1 x rpm vibration. Most often, analysts have focused on harmonics which were full integer multiples such as 2 x rpm, 3 x rpm, 4 x rpm, 5 x rpm and so on. However, harmonics do not have to be full integer multiples. For instance, there are sub-harmonics equal to fractional multiples such as 1/4 x rpm, 1/3 x rpm, ½ x rpm, 2/3 x rpm, 3/4 x rpm and so on. Other harmonics can be equal to 1 ½ x rpm, 2 ½ x rpm, 3 ½ x rpm, etc.

Too often, vibration guidelines are based on "overall" vibration amplitudes, with their highest contribution usually provided by vibration at 1 x rpm. As a result, the guidelines for unfiltered readings are now being used for the filtered vibration tuned to 1 x rpm. There is some danger in this, as the major source for the unfiltered reading may not originate from the more usual 1 x rpm, but instead from a "higher frequency" originating from such problems as produce gearmesh frequencies, rolling element bearing defect frequencies, and so on. Or the primary sources for unfiltered high amplitudes may be vibrations at frequencies below 1 x rpm, such as "slightly less than ½ x rpm" (oil whirl), "exactly ½ x rpm" (rub or something loose, such as the bearing in its housing) and so on.

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