Random Vibration & Mechanical Shock Excite All Resonances

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RAC is a DoD Information Analysis Center Sponsored by the Defense Technical Information Center INSIDE T h e J o u r n a l o f t h e 5 RAC Supports Development of New R&M Distance Learning Module 6 Improving Mission Performance & Reducing Total Ownership Cost 12 PRISM Column 13 New Special Interest Area on Reliability and Maintainability at DAU Acquisition Community Connection Web Site 14 RAC Product News 17 RMSQ Headlines 19 Alion Science and Technology Initiates Program to Provide Free Facility Maintenance Surveys 21 Future Events 22 From the Editor Reliability Analysis Center Fourth Quarter - 2004 Abstract Whereas a "swept sine" vibration test sequential- ly excites a product's many resonances, a "broad band random" vibration test simultaneously excites those same resonances, often with greater chance of failure, more like much "real world" vibration. Whereas much single-axis-at-a-time vibration testing is still performed, more realistic multiple axes testing and screening identifies more failure modes. Vibration 101 Recall from mechanical engineering the classical single degree of freedom (SdoF) model of Figure 1. We learned that shaking the model at a specif- ic forcing frequency ff (one matching the "natu- ral frequency" fn of that model) creates a condi- tion called resonance. The response T can be much greater than the input, per the equation. Note that the equation ignores any damping or friction that may be present. Figure 1. Classical Single Degree of Freedom (SdoF) System Your Equipment is Vulnerable Each component of each subassembly of each assembly of each deck of each rack of your equip- ment is more complex than Figure 1. Each has numerous vulnerabilities, numerous sensitive nat- ural frequencies fn. Some resonant responses can result in temporary or permanent misoperation (damage). Better for this to happen at the test lab (where we can observe what happens and correct the design or manufacture) than in service. Sine Vibration Testing We mount our product on a shaker (same operat- ing principle as an electrodynamic loudspeaker see Figures 13, 14, and 15), which we then pro- gram to single-frequency-at-a-time vibrate, sweeping from perhaps 10 to 2,000 Hz. We ask the shaker to maintain a sinusoidal waveform, as in Figure 2 (upper). In the frequency domain (lower) we see that all vibratory energy is at that single frequency. We ask for a constant peak acceleration of perhaps 1g (32.2 ft/sec2 or 9.8 m/s2). This has the effect of stimulating our prod- uct's various resonances sequentially. Figure 2. Sinusoidal Waveform By: Wayne Tustin, Equipment Reliability Institute (315) 337-0900 General Information (888) RAC-USER General Information (315) 337-9932 Facsimile (315) 337-9933 Technical Inquiries rac@alionscience.com via e-mail http://rac.alionscience.com Visit RAC on the Web Random Vibration & Mechanical Shock Excite All Resonances 2 n f f f - 1 1 T = Mass M or Weight W K C f Frequency Ener gy Acceleration T h e J o u r n a l o f t h e R e l i a b i l i t y A n a l y s i s C e n t e r F o u r t h Q u a r t e r - 2 0 0 4 2 If we were to hold the mechanical spectrum analyzer of Figure 3 against the vibrating armature of our shaker, one of its reeds would respond. As the shaker frequency increased, that reed's motion would die away and the next reed would respond. If instead we attach a product to our shaker and perform a swept- sine vibration test, we will observe the product's various reso- nances being excited sequentially. This may damage the product. Figure 3. Mechanical Spectrum Analyzer Random Vibration Testing But suppose that instead of sweeping with sine, we program our shaker to vibrate randomly, with a motion resembling Figures 4 (time domain) and 5 (frequency domain, a possible Fourier trans- form of Figure 4). Figure 4. Random Vibration Time History Figure 5. Continuous Spectrum We are asking for all frequencies perhaps 10 to 2,000 Hz to be applied simultaneously. If now we hold the mechanical spectrum analyzer of Figure 3 against the vibrating armature of our shak- er, all of its reeds will respond simultaneously. (If you don't have a shaker, rap the analyzer with your knuckle to see all the reeds respond simultaneously.) If instead we attach a product to our shaker and perform a ran- dom vibration test, we will stimulate our product's various reso- nances simultaneously. This approach often finds failure modes not observed with sine excitation. Simultaneously? Should you conduct testing with frequencies, perhaps 10 to 2,000 Hz, occurring simultaneously? Yes. Recall from high school or college physics the optical demonstration shown in Figure 6. Recall the concept that all frequencies, all wavelengths in the visible (and somewhat beyond) spectrum, were present. Adapt, that concept to mechanical engineering. Figure 6. Visible Light Spectrum In a similar fashion, visualize all the possible resonances in your hardware being excited simultaneously. Perhaps you have evi- dence that in flight, adjacent circuit cards in your card cage (Figure 7) have been colliding. Yet in the lab, with sinusoidal, one-frequency-at-a-time excitation perpendicular to the cards, only individual cards have responded. Each has responded at its own natural frequency fn, yet they have not collided. Try testing with random vibration containing all forcing frequencies ff. Now it is quite likely that adjacent cards will respond simultaneously, and some will collide with adjacent cards. Figure 7. Card Cage Assembly (Courtesy C. Felkins) Flight and Road Vibrations The foregoing is just one example of broad-spectrum vibration finding product weaknesses not found by sine vibration testing. Flight vibrations, particularly at rocket launch (Figure 8) are strongly random. So are road inputs to automobiles (Figure 9). Figure 10 (upper) shows three time histories experienced by lat- eral, longitudinal and vertical accelerometers mounted on a sus- pension. Figure 10 (lower) shows their Fourier transforms into the frequency domain. Note that all frequencies 1 to perhaps 200 Hz were present. A suitable automotive component vibration test specification might call for a similar (but probably somewhat Sp ectr alDensity Frequency T h e J o u r n a l o f t h e R e l i a b i l i t y A n a l y s i s C e n t e r F o u r t h Q u a r t e r - 2 0 0 4 3 increased in intensity) random vibration to be delivered by a shaker. To meet such a specification, you might employ a shak- er resembling Figures 13, 14, and 15, suitably programmed. Figure 8. Lift off of an Early Rocket Figure 9. Terrain Inputs are Random Figure 10. An Analysis of Automotive Vibration Time Domain Our focus has been on the frequency domain, but we should also consider the time domain, illustrated in Figure 11. Both are need- ed to fully describe random vibration. Figure 11 shows a wide- spectrum random time history on an oscilloscope. Recall how a oscilloscope sweeps relatively slowly left-to-right, then "jumps" left and repeats. Here each sweep traced out a different time histo- ry (rather than endlessly repeating a non-changing time history, as in Figure 2). Figure 11. Oscilloscope (Time Domain) Display of Random Vibration, With Amplitude Probability Density Overlay The bell-shaped overlay, called an amplitude probability density (APD) graph, in Figure 11 tells us how much time is spent at dif- ferent intensities, different scaling levels. It quantifies our own automobile driving experience and what our eyes reveal in Figure 11: most time is spent at small accelerations. Probability P is large. Large accelerations rarely occur. Probability P is small. Scaling factor to an electrical engineer is the root mean square (RMS) value; statisticians generally call the standard deviation. Seismic Events Consider the response (upper graph, Figure 12) of internal com- ponents of a rack of telecom or other floor-supported equipment in a building. The center graph describes the floor response to earth input (lower graph) during an earthquake. The floor responds fairly strongly to certain frequencies of ground motion, transmitted through the building structure. Unfortunately, the rack further magnifies floor vibration. Design or installation people have failed to follow Rule #1 of successful dynamic design: THOU SHALT NOT STACK THY RESONANCES. Figure 12. Horizontal Seismic Input and Responses T h e J o u r n a l o f t h e R e l i a b i l i t y A n a l y s i s C e n t e r F o u r t h Q u a r t e r - 2 0 0 4 4 The possibility of damage to such racks has necessitated a class of relatively low frequency, long stroke random vibration testing called NEBS (Network Equipment Building Standards). Automobile designers respect Rule #1. The instrument cluster designer asks about (and avoids) instrument panel resonances. The instrument panel designer asks about (and avoids) body res- onances. The body designer asks about (and avoids) suspension resonances. Shakers Relatively low frequency, long stroke EH or electrohydraulic (servohydraulic) shakers (not shown) are used for most seismic testing and much automotive testing, but here let's consider more common ED or electrodynamic shakers. See Figure 13, in which a product is clamped to an ED shaker. Figure 13. Product Clamped to ED Shaker Armature Such shakers operate on exactly the same principle as does an electrodynamic loudspeaker; with the latter, the moving coil drives a paper cone; with the former, the moving coil drives an aluminum or magnesium armature which in turn drives the prod- uct under test via some kind of attachment fixture. Vibration Test Fixtures The fixture that we see in Figure 14 (driving a cranking motor destined for a diesel truck engine) was quite probably designed for very high stiffness. Figure 14. Cranking Motor Driven by ED Shaker Of all fixtures, cubes similar to Figure 15 are the most common shape. Products can be bolted to the several sides of such a cube and be successively excited in their X, then Y, and then Z direc- tions. Figure 15. Cube Fixture on ED Shaker Multi-axis Shaking A valid criticism of the tests shown in Figures 13, 14, and 15 is that excitation is single axis at a time, whereas we all know that "real world" excitation is multi-axis. A very few test labs simul- taneously shake products with three or more EH or ED shakers, and have reproduced field failures that single-axis-at-a-time test- ing could not reproduce. Costly? Yes, indeed. Multiple shak- ers, multiple power amplifiers and multiple channels of control. Is there a cheaper approach? Repetitive Shock (RS) Testing for HALT, ESS, and HASS A much less expensive (although less controllable) approach to multi-axis vibration testing and screening is the use of pneumatic hammers. See in Figure 16 how several shop-air-driven vibrators slope upward to give a vertical force component to a softly-sprung table or platform. Note that "thumpers" act on different compass headings. Unsynchronized, they give the platform three linear and three angular motions, six degrees of freedom, 6DoF for short. In most stress screening applications, the platform forms the bottom of a thermal chamber. Conditioned air, alternating hot with cold, thermally stresses (perhaps 100°C change, perhaps 50°C per minute) table top-mounted products. Concurrently, multi-axis random vibration mechanically stresses the products. Figure 16. Pneumatic Vibrators on "Rigid" Table (Courtesy QualMark) T h e J o u r n a l o f t h e R e l i a b i l i t y A n a l y s i s C e n t e r F o u r t h Q u a r t e r - 2 0 0 4 5 Shock Testing While some mechanical shock tests can be performed on ED shakers such as those in Figures 13, 14, and 15, most shock testing is done on "falling carriage" machines resembling the one in Figure 17. The product is successively orient- ed with various sides pointing down. The actual test occurs when the carriage is physically stopped by, for instance, penetrat- ing a rubber bumper. That shock (remember what you learned by striking the analyzer of Figure 3) simultaneously excites all the product's natural frequencies fn. Summary A "broad band random" vibration test that simultaneously excites a product's many resonances is more realistic than a "swept sine" vibration test that sequentially excites each resonance. The for- mer is more likely to precipitate failures that will occur under "real world" vibration conditions. Although at one time more prevalent and less expensive, single-axis-at-a-time vibration test- ing is much less effective than multiple axis testing and screen- ing in identifying failure modes. For Further Reading 1. Barra, Ralph J., Geo-Metric Vibration Analysis, 1977, RMS Publishing. 2. Broch, Jens Trampe, Mechanical Vibration and Shock Measurements, Bruel & Kjaer Measurement Systems (Denmark), 2nd Edition, 1979. Ask B&K about other hand- books. 3. O'Connor, P.D.T., Practical Reliability Engineering, Heyden, 1981. 4. O'Connor, P.D.T., Test Engineering, 2001, John Wiley, ISBN 0-471-49882-3. 5. Petroski, Henry, To Engineer is Human, the role of failure in successful design, 1985, St. Martin's Press, ISBN 0-312- 806809. 6. Seippel, Robert G., Transducers, Sensors and Detectors, Reston Publishing, 1983. 7. Steinberg, Dave S., Vibration Analysis for Electronic Equipment, John Wiley and Sons, 1988, ISBN 0-471-63301. 8. Thomson, William T., Theory of Vibration with Applications, Prentice-Hall, 1981. 9. Tustin, Wayne, Random Vibration in Perspective, 1984, Tustin Institute of Technology, ISBN 0-918247-00-4. 10. Wright, Charles P., Applied Measurement Engineering -- How to Design Effective Mechanical Measurement Systems, 1995, Prentice Hall. About the Author Wayne Tustin is founder and president of Equipment Reliability Institute, ERI, a specialized engineering school (focus on reliabil- ity of equipment), located at Santa Barbara, California. Wayne's short course teaching (USA and abroad) emphasizes testing, leav- ing reliability theory to others. His autobiography is posted at . A soon-to- be-published text, "Random Vibration and Shock Testing" is described at . Figure 17. Drop-Carriage Shock Test Machine RAC Supports Development of New R&M Distance Learning Module The Defense Acquisition University (DAU) recently added a new distance learning module (DLM) to their continuous learn- ing curriculum. The new module is on reliability and maintain- ability (R&M). DAU provides a full range of basic, intermediate, and advanced certification training, assignment-specific training, performance support, job-relevant applied research, and continuous learning opportunities for members of the DoD Acquisition, Technology, and Logistics (AT&L) community. To achieve their vision as a premier corporate university serving the DoD AT&L workforce, DAU has shifted from the traditional classroom of the 20th cen- tury to the total learning environment of the 21st century. Integral parts of the total learning environment include continu- ous learning, knowledge sharing, and communities of practice. The new R&M DLM is an important addition to the continuous learning portion of the total learning environment. The effort to develop the R&M DLM was funded by the System Engineering Office of OUSD/AT&L and managed from that office by Yvonne Jackson. It was developed by a team made up of Ann Marie Choephel representing the System Engineering Office, Robert Faulk of DAU, and two contractors: the Reliability Analysis Center (RAC) and Team CSC. The Reliability Analysis Center served as the Subject Matter Experts (SMEs) for the effort. Peter Tabbagh was the principal engineer for the project and was supported by Andrew Foote, Norman Fuqua, and Ned Criscimagna. The RAC engineers: · Developed Learning Objectives. · Prepared module outline. · Gathered and harvested subject-specific information related to the development of module content. · Organized module content relative to the outline in a practical and relevant content package. · Provided support to Instructional Systems Design (ISDs) during development of storyboards/programmed lessons. · Submitted and reviewed content package with ISD devel- oper. · Worked with Team CSC to review and integrate appro- priate module material and references. · Provided simple, realistic examples. (Continued on page 19)