Trends in Vibration Test

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.

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
           t_i = 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

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.

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.

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.

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.