Vibration Time wave form : Single Frequency With Harmonics .

A harmonic is some exact multiple of a discrete frequency. The discrete frequency,called the fundamental, is the first harmonic. The second frequency, which is two times the fundamental frequency, is the second harmonic. The second, third, fourth, etc., harmonics can be either in phase or out of phase with the fundamental. The phase relationships between the fundamental and the harmonics are valuable in diagnosing problems in rotating machines. Failure to understand and use the time signal and harmonic phase can result in diagnostic errors .

A single frequency without harmonics will have one positive-going peak per time period. The number of positive-going peaks in one time period of the fundamental frequency identifies the highest number of true harmonics. This is true for a single frequency with harmonics only, and is true regardless of the phase relationships between the fundamental and the harmonics. The amplitudes of the fundamental and the harmonics determine the amplitudes of the positive-going peaks. However, the phase relationships of the harmonics to the fundamental determine the locations of the positive going peaks in the signal.

Single Frequency with an In-Phase Harmonic.

Single Freq. with a 180 Degree Phase Shift and Harmonic.

Single Freq. with a 180 Degree out-of-Phase Harmonic.

However, both positive-going peaks are at the top of the signal. This can only occur if the second harmonic is 180 degrees out of phase with the fundamental.

These phase and amplitude relationships hold true for linear systems. However, most real applications contain nonlinearities,called distortion. The distortion can appear in the signal as a phase shift in one or more of the harmonics. Distortion of the signal can also generate additional harmonics in the frequency domain which are not true harmonics of the signal. Therefore, the number of peaks in the time signal must be checked for true harmonic content.

Continuing with phase relationships, the next step is to observe a phase shift of 90 degrees.

Single Freq. with 90 Degree Phase-Shifted Harmonic.

A good rule to remember is that if the source of the harmonic is tied to the source of the fundamental, such as a fixed, geared, or bolted coupling, the harmonic should be in phase. If the source of the harmonic is not tied to the source of the fundamental, the harmonic should be out of phase.

Single Frequency with a Lower Amplitude Harmonic.

After seeing the effect of changing amplitude , one can identify the effect of changing the amplitudes in other ways. Changing amplitude only affects the amplitude of the composite peak. It does not affect the number of peaks or the phase relationship of the composite.

Single Frequency with Two Harmonics.

The addition of a third harmonic will now be examined, along with the effects of changing the phase and amplitude. Changing the amplitude changes the amplitude of the individual peaks, as with two harmonics. Three positive peaks per cycle are present, indicating the three harmonics

Single Frequency with Only Third Harmonic.

Single Frequency with Two Harmonics.

Single Frequency with Two Phase-Shifted Harmonics.

The time domain signal is necessary to verify which harmonics are true and which harmonics are caused by distortion.