SINGLE FREQUENCY A single frequency is often referred to as a discrete frequency and is the simplest form of
frequency data. The time signalof a single frequencyand the resulting
frequency spectrum from the Signal Analysis Program. The time period for
each cycle is 0.01667 seconds and the signal is sinusoidal.
Sinusoidal simply means the signal follows the sine function. Mathematically, the time signal is:
The reason for using the cosine instead of the sine is because the
starting point at time zero of the fundamental is the highest point. The
cosine is the same as the sine, except for a 90 degree phase shift. In
the real world, the signal can start at any point between 0 and 360
degrees .
When the time signal is processed by the FFT, it is divided into the
amplitudes and phases of the individual cosine and sine functions. When a
spectrum is displayed, the plot is an amplitude plot of the
frequencies. If a complex FFT is performed, both the amplitude and phase
are available, but only the amplitude is displayed. In the
introduction, the frequency spectrum was said to lose the phase. In
actuality, it may not be lost. It is just not listed or is discarded.
Unless the phase is retained and viewed, the time domain signal must be
used to identify phase relationships.
To reconstruct the time signals from the frequency domain, a
starting point must be selected. When time equals zero, the cosine
starts at maximum amplitude and the sine starts at zero amplitude. It is
more consistent to start at the maximum amplitude of all signals, so
the signals add at a time equal to zero.
This is a cosine function with a 180 degree phase shift. In rotating
machinery, data taken from opposite sides of a motor should be the
same, except the phases of the fundamentals should be 180degrees apart.
This obeys all laws of physics.
Single Frequency 90 degrees phase shift
Single Frequency 180 degrees phase shift
Amplitudes of signals in rotating machinery will add or subtract, depending on their phase relationships.
Two Frequencies signals 180 degrees out of phase to each other .
Accurate diagnosis of problems in rotating machines requires a
thorough understanding of the time domain signal and the frequency
domain spectra. Following are some of the reasons:
1. The time signal is a plot of amplitude versus time. This
signal contains all frequencies, harmonics, and subharmonics. The phase
relationships of these frequencies are also contained in the signal.
Pulses, amplitude modulation, frequency modulation, truncation, and
distortion are also present.
2. The frequency spectra are plots of amplitude versus frequency.
These spectra contain frequency, harmonics, subharmonics, and sum and
difference frequencies. The FFT produces the frequency spectrum from the
time signal, based on electronic physics. However, during the process,
some information is lost. For example, phase, true amplitude of pulses,
nature of the pulses, bandwidth, and the various forms of modulation
are not easily identified in the frequency spectrum.
3. A mechanical machine may not generate a fundamental plus
harmonics in the same way as in the electronic world. However, a
rotating machine does generate relatively linear signals when a linear
problem exists, such as imbalance. A machine can generate a distorted
signal as a result of a nonlinear problem. This distorted signal is a
composite signal, as would be obtained after various frequencies and
harmonics are combined.
4. For the above reasons, various time signals can produce the
same frequency spectrum. This explains why the time signal must be
considered. Costly errors in diagnostics and loss of credibility could
occur if the time signal is not analyzed.
BASIC PHYSICS All things in the universe obey the
basic laws of physics. Vibration signals from rotating machinery must
obey these same basic laws of physics. This is why we can take data from
either side of a motor and receive the same results. (Some slight
variations can occur in nonlinear systems because of transfer
functions.) In a pure linear system, data taken in different directions
around a motor should be the same, except for phase.
a sine wave is the plot of a circle against time. All complete
circles contain 360 degrees and all complete sine waves contain 360
degrees. The phase of a signal can be anything from 0 to 360 degrees,
depending on the reference point .
Before analyzing the time signal, an understanding of how
frequencies add and subtract, and the effects of the phase relationships
is required. It may be helpful to remember that multiplication is a
series of additions, and division is a series of subtractions.
a signal taken from the horizontal direction with a signal taken from
the vertical direction, one signal should lag the other signal by 90
degrees. This is because the positions from horizontal to vertical are
90 degrees apart on the machine. This phase relationship should also
apply to other data taken at various points around the machine.
We can start taking data at any instant of time or location, and it
does not make any difference. The reason for this is the phase
relationship between the fundamental and other frequencies,or a
once-per-revolution marker, will remain constant.
These frequencies will add and subtract, depending on the phase
relationship. When the signals are in phase, the amplitudes will add.
This is why positive side bands occur on some frequencies. When the
signals are out of phase, they will subtract. This is why negative side
bands occur. This also explains how and why truncation occurs.
In rotating machines, several different problems can generate the
same frequency spectrum. For example, a machine that is loose can
generate a fundamental and the second harmonic. A machine that has a
bent shaft can also generate a fundamental and the second harmonic. The
only way to determine which problem exists is to determine the phase
relationship between the fundamental and the second harmonic. If these
two signals are in phase, the shaft is bent. If the two signals are out
of phase, the machine is loose. Currently, the only way to determine
this phase relationship is with the time signal.
