|
Trends in Vibration Test
by Tom Lecklider, Senior Technical Editor
Random vibration testing provides energy simultaneously at all frequencies.
Vibration testing can help ensure that your new design will survive its intended
environment. The problem is knowing how much and what type of vibration to apply.
The power spectral density (PSD) of random test vibration is defined by an
overall envelope divided into narrow frequency bands. Power is measured by
averaging several fast Fourier transform (FFT) results within each band. This
process allows a shaker controller to deliver the desired average (rms) PSD
profile but does nothing to address extreme peaks.
Because bumps in the time domain are short-lived transients, they tend not to
appear in the averaged spectrum produced by the controller. You may be able to
test to a prescribed PSD shape, but you also need to control the distribution of
the energy within each frequency band to more closely simulate environments with
transient bump events.
Courtesy of LDS-Dactron |
One alternative is to abandon random testing completely and instead test by
rerunning actual recorded vibration test data. For example, rather than use a
predefined standard transportation harshness test profile, why not subject the
DUT to actual truck-bed acceleration data recorded while driving over a variety
of typical road surfaces? Because real vibration data includes the odd
infrequent large bump, it may more realistically represent the actual
environment than an averaged, artificial PSD.
A trend toward this type of testing was noted by Thomas Reilly, product
marketing manager of vibration test systems at Data Physics. “We are seeing more
demand for time replication in both single- and multi-shaker test setups. Time
replication is being used to simulate more complex vibration environments like
gunfire using field-measured data.”
Thermotron’s Doug Mahn, a senior vibration application engineer, added, “The
automotive industry has fully adopted the practice of monitoring and measuring
the dynamic environments experienced by vehicles in actual use and abuse
conditions. This real-life data is recorded at the test track and then played
back at levels realistically encountered at various locations in the vehicle.
These vibration energy profiles can be run at increasing stress levels in an
attempt to induce failure more quickly and reduce test time.”
Actual test data may not correspond closely to random test levels defined in
existing standards. There are exceptions, such as the NEBS VERTQII seismic test
signal defined in the time domain. However, much testing today remains bounded
by average PSD envelopes.
Kurtosis
On the other hand, a prescribed PSD need not be seen as a severe restriction.
You can achieve the required G2/Hz levels in an infinite variety of ways by
varying the nature of the random distribution. The relationship of the amount of
power at the center of a probability distribution function (PDF) to that in the
tails is described by the kurtosis function.
More precisely, kurtosis is defined as a “normalized form of the fourth central
moment of a distribution.”1
where: s = standard deviation
N = number of data points
t0 = mean value
ti = typical data point
It often is convenient to work with the kurtosis excess, that is, the kurtosis
of a distribution in excess of the value 3.0 associated with a normal
distribution. In practice, kurtosis may be normalized by subtracting 3.0 so that
a normal distribution has value zero. Unfortunately, some kurtosis definitions
include the -3.0 and actually define kurtosis excess. This article uses the
nonnormalized form found in Maplesoft’s Maple 10 mathematics software
application.
In an effort to see some of the effects of a distribution’s kurtosis, the
equation for the probability distribution function (PDF) of a normal
distribution was altered. The usual form of the equation is
where: σ = standard deviation
Setting σ = 1 and t0 = 0 and adding a new variable ν to modify the power of the
exponent give
With these values for σ and t0, when ν equals 1.0, the PDF is identical to that
for a normal distribution. This condition is shown by the heavy blue curve in
Figure 1 together with four other curves representing values of ν greater and
less than 1.0. Peaked distributions resulting from ν<1 have kurtosis values
greater than 3.0 and are called leptokurtic. Those with flattened, narrow
probability distribution functions corresponding to ν>1 are termed platykurtic.
|
Figure 1. A Family of PDFs Based on the Normal Distribution |
Many distributions besides these four have kurtosis values other than 3.0. A
modified normal distribution is used here because it provides a simple means of
varying kurtosis within a normalized and familiar distribution. Regardless of
the PDF that is used, a higher kurtosis value corresponds to a more frequent
occurrence of large values.
Conversely, from Figure 1, it’s easy to see that a high ν value virtually cuts
off any random values greater than about 1.6. The familiar tails of the Gaussian
or normal distribution have almost entirely disappeared.
In Figure 2, the standard deviation and the kurtosis for this family of PDFs are
plotted vs. the value of ν. The green vertical line divides the graph between
those distributions having wider, higher tails than the normal distribution and
those with small, almost nonexistent tails.
|
Figure 2. Kurtosis and Standard Deviation for a Family of Modified
Normal Distribution PDFs as Functions of the Variable ν |
If your application requires an additional amount of large transients above
those provided by a shaker producing normally distributed excitation, increased
kurtosis might be an answer.
Vibration Research recently introduced random vibration control based on a
variable kurtosis distribution. As John Van Baren, the company president,
stated, “A newly developed kurtosis control distributes the random data at
higher kurtosis levels while maintaining the same testing profile and spectrum
attributes. Adjusting the kurtosis level will allow the product to be tested to
real-life data and result in faster product testing.”
Further Trends
Multiaxis
Real-world environments also are being better approximated by simultaneously
shaking the DUT in all three directions. Historically, products have been tested
first in one axis, then in another, and finally in the third. In many cases,
only when vibration is applied in all three directions at once can field
failures be repeated, for example.
Wayne Tustin, president of Equipment Reliability Institute, commented,
“Gradually, we are shifting from one-axis-at-a-time shaking to multiple-axis
simultaneous shaking. We see this in seismic simulation and road test
simulation. Multiaxis vibration testing is very slowly making inroads into
shipboard and flight simulation as well.
 “Certainly, there’s a bigger up-front investment needed in multiple actuators
with multiple control channels,” he continued. “But, note that one test instead
of several will save test time. More importantly, the increased capability to
find weaknesses limits field failures and reduces warranty expense. Most
automobile manufacturers, possibly all of them, have used multiaxis road
simulators for years.”
Mr. Tustin added that multiaxis vibration also is being used by manufacturers of
commercial and personal electronics products, often in the form of so-called
six-degree-of-freedom (6 DOF) highly accelerated life testing/highly accelerated
stress screening (HALT/HASS) vibration chambers. “Most of these shakers use six
or eight inexpensive pneumatic repetitive shock (RS) devices mounted with
different compass headings. They drive upward into softly sprung platforms on
which the test specimens are mounted. For HALT and HASS applications, these
platforms form the bottom of fast-ramping thermal stress chambers,” he
explained. “Although RS-based platforms are effective and inexpensive, little
spectrum control is possible.”
While this restriction has existed in past systems, Qualmark’s Chief Technical
Officer Ralph Poplawsky described a recent advance in 6 DOF shakers. “One of the
basic requirements of the HALT/HASS process is to simultaneously excite all of
the fundamental resonant modes of a product or assembly. These modes can include
everything from case and PCB to connectors, hold-downs, and individual
components from relatively large transformers to small surface-mounted
capacitors. If the testing is successful, the weak points will be rapidly
identified.
“To accomplish this, we excite a product with random vibration in which not only
the frequency and amplitude, but also direction, including rotation, varies
randomly,” he continued. “Some companies attempt this with electrodynamic (ED)
shakers, but that method generally is less effective. Still, HALT/HASS vibration
spectra often fall short of ED shaker spectra in the lower frequency range. To
address this, Qualmark has developed new XLF Vibration Systems that more closely
match ED shaker performance.”
Comprehensive Control
A trend among LDS-Dactron customers toward automation of the entire
environmental testing process from a single PC screen was discussed by the
company’s Director of Marketing Dave Galyardt. “Automation is achieved by
integrating operation of the ED vibration controller with the shaker amplifier
and thermal chamber. From one PC console running one software application, the
operator can select a test setup, switch on a remote amplifier, and control and
monitor vibration and climatic chamber conditions. Besides reducing the total
test time required, this approach also helps to prevent errors.”
For 6 DOF testing, test chambers manufactured by Chart Industries use a
PLC-based control system. Jim Weiler, a product manager for the company,
explained, “One unique feature is the capability to simultaneously ramp thermal
and vibration levels. It enables customers to accelerate product failures,
leading to earlier identification and correction of design and production
weaknesses.”
The benefit of applying both thermal and vibration stresses at the same time
goes beyond convenience. As Gregg Hobbs, Ph.D., president of Hobbs Engineering
and HALT&HASS Systems, detailed in a recent article, “…you can find a given
weakness using vibration in HALT whereas, in the real world, temperature would
cause the same failures to occur. This crossover effect is one of the reasons
for reacting to weaknesses found by stresses other than those naturally
occurring…. Combined stresses are even better as stresses generally add up to a
higher stress but not necessarily linearly-only in a Mohr’s circle sense.”2
Under the hood, controllers themselves have progressed considerably. For
example, the Data Physics modular Abacus Controller provides up to 32 input
channels, eight output channels, and eight tachometer channels in a single
chassis. Multiple chassis can be connected to create a system with up to 1,024
input channels.
 For smaller applications, the company’s Quattro Data Acquisition System offers
up to four input channels, two output channels, and a tachometer in a small,
USB-powered device. Both analyzers and controllers have standard sampling rates
of >100 kS/s with rates >200 kHz optionally available. New hardware platforms
based on 24-b ADCs and DACs provide from 120 to 150 dB of dynamic range.
Expanded Operating Modes
“A pocket PC used with a wireless network allows remote operation of an
LDS-Dactron vibration controller,” according to Mr. Galyardt. “The operator can
control and monitor tests while at the shaker. Monitoring capabilities include
parameters such as run time, status, frequency, and level. Changing test
conditions while at the shaker makes it possible to visually and audibly
correlate test-article dynamic responses with the test excitation.”
The company also has considered safety. “Test monitoring includes the provision
for automatic abort based on changes to the test system’s transfer function,”
Mr. Galyardt explained. “This feature protects the test article from damage by
detecting changes to its structural response characteristics due to material
fatigue. A controller will attempt to make the output vibration match the
desired profile, but monitoring the system’s transfer function ensures that
nothing has broken, for example, to significantly change the test conditions.”
Some Data Physics products allow distribution of measurement chassis over wide
areas in a test environment. Mr. Reilly said, “This capability is very useful in
testing large satellite structures and aircraft such as the Airbus 380. Special
clock synchronization between distributed chassis allows for precise phase
matching even with long cables.”
Summary
Vibration test products are sufficiently flexible that a number of equally
effective test solutions may be possible for a given application. For example, a
random-on-random vibration specification may be equivalent to a random
excitation with a carefully designed kurtosis. Either of these approaches could
be equivalent to excitation resulting from time replication of an appropriate
real-life signal.
Today’s test methods are changing as the technical limitations that historically
restricted the control and application of vibration for reliability testing
disappear. If test is unavoidable, it should at least pay for itself by reducing
field return costs through improved product reliability. For that reason, the
correlation between a product’s actual operating environment and the tests
performed upon it has come under scrutiny. The increased use of multiaxis
excitation, time replication, and HALT/HASS methods is the result.
References
1. mathworld.wolfram.com/Kurtosis.html
2. Hobbs, G., “Reflections on HALT and HASS,” EE-Evaluation Engineering,
December 2005, pp. 38-41. |
