25-08-2017, 09:32 PM
Random Vibration
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Sinusoidal Vibration (Sine):
Strike a tuning fork or pluck a guitar string and the sound you hear is the result of
a single sinusoidal wave produced at a particular frequency (Figure 1). Simple musical
tones are sine waves (simple, repetitive, oscillating motion of the air) at a particular
frequency. More complicated musical sounds arise from overlaying a number of sine
waves of different frequencies at the same time. Sine waves are important in more areas
than music. Every substance vibrates and has particular frequencies (resonant
frequencies) in which it vibrates with the greatest amplitude. Therefore sine wave
vibration is important to help understand how any substance vibrates naturally.
Random Vibration:
Vibrations found in everyday life scenarios (vehicle on common roadway; rocket
in take-off, or an airplane wing in turbulent airflow) are not repetitive or predictable like
the sinusoidal wave. Consider the acceleration waveform for dashboard vibration found
in a vehicle traveling on Chicago Drive near Hudsonville, MI (Figure 2). Note that the
vibrations are by no means repetitive.
Random vs. Sine:
Sinusoidal vibration tests are not as helpful as random testing is, because a sine
test essentially consists of a single frequency in time. A random vibration test, on the
other hand, consists of all the frequencies in the defined spectrum being sent to the shaker
at any given time. Consider Tustin’s description of random vibration. “I’ve heard people
describe a continuous spectrum (random vibration, VRC), say 10-2000 Hz, as “1990 sine
waves 1 Hz apart”. No. That is close, but not quite correct. . . . (S)ine waves have
constant amplitude, cycle after cycle. . . . .Suppose that there were 1990 of them (constant
amplitude sine waves, VRC). Would the totality be random? No. For the totality to be
random, the amplitude of each slice would have to vary randomly, unpredictably. . . .
Unpredictable variations are what we mean by random. Broad-spectrum random
vibration contains not sinusoids but rather a continuum of vibrations (with different
amplitudes, VRC).”
Advantages of Random Vibration Testing:
One of the main goals or uses of random vibration testing in industry is to bring a
DUT to failure. For example, a company may desire to find out how a particular product
may fail because of various environmental vibrations it may be faced with. The company
will simulate those vibrations on a shaker and place their product under those conditions.
Testing the product to failure will teach the company many important things about their
product’s weaknesses and ways to improve the product. Random testing is the key
testing method for this kind of application.
Features of Random Vibration:
Power Spectrum Density (PSD):
In order to perform random testing, a random test spectrum must be developed.
Computer software collects real-time data over a time period and combines the data using
a spectrum averaging method to produce a statistical approximation of the vibration
spectrum. Generally the random vibration spectrum profile is displayed as a power
spectrum – a plot of acceleration spectral density (acceleration squared per Hertz) versus
frequency (Figure 3). A power spectrum essentially shows which frequencies contain the
data’s power.
Field-Data Replication (FDR):
Development in vibration research has resulted in newer methods that come
closer and closer to real-life data replication. Random testing is a great improvement on
sine testing but still does not perfectly represent what happens in real-life. In response to
this, vibration research companies developed “Sine-on-Random” testing which
overlapped sine spectra with random spectra. The goal of this testing is to include some
“peaks” that occur in real-life scenarios into the random spectra. This method has been
somewhat successful in bringing tests closer to reality.
More recent development has included a method of recording real-life data and
turning it directly into a spectrum to be used in lab. This method, called field-data
replication (FDR), is very helpful in accurately representing in a test setting what is
happening on the field. This is like “shaped” random in a way, because the spectrum is
the same as seen in the real application. This method is good, but also has its
shortcomings. It is difficult to find a representative waveform, especially in aerospace
applications. When one is obtained, it is representative of a particular situation of the
product. Unfortunately, it is probably not representative of the entire life of the product.
Gaussian Distribution vs. Kurtosis Distribution:
One final helpful distinction is that relating to the probability distributions of a
DUT’s vibratory accelerations. As mentioned earlier, a probability distribution shows the
reader how the data points compare with the average data point. Most of the data points
will center near the average with a number of outliers. Generally, as more data points are
collected the probability distribution forms a nice smooth bell-shaped curve.
Gaussian distribution is the normal probability distribution of random data. The
probability distribution curve takes on the classic “smooth bell-shaped curve”. Consider
the Probability Density Function (PDF) graph shown below for a set of data with
Gaussian distribution.