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Pareto-optimal target definition for multi-axis random vibration testing

In random vibration testing with multiple control channels, existing control laws require specification of a complete spectral density matrix at each control frequency. Spectral density matrices include autospectral densities on the diagonal and cross-spectral densities on the off-diagonal. In practice, the off-diagonal terms are often unknown, and recent vibration testing research has focused on fixing the diagonal and specifying the off-diagonal to minimize the required control energy, subject to a constraint that the target matrix is positive semidefinite. This paper shows that, even with a fixed diagonal, off-diagonal terms strongly affect control residuals. This overlooked effect occurs in both square and rectangular systems. By jointly considering input energy and control residuals, open-loop inputs are derived directly from the diagonal without specifying the off-diagonal terms. Vibration targets that can be used in closed-loop control are then derived using the optimal inputs, with positive semidefinite constraints applied during the derivation. The result is a set of Pareto-optimal control solutions. For each solution in the set, any other possible solution produces greater control error, greater input energy, or both. A balanced solution is selected automatically, though others can be chosen based on test needs. Simulations and experiments show that the proposed method outperforms state-of-the-art energy-minimizing approaches, achieving significant reductions in both control error and input energy.

Autospectral density↗

Shape-constrained Input Estimation for Efficient Multi-shaker Vibration Testing

Multi-shaker vibration testing is gaining interest from structural dynamics test engineers as it can provide a much more accurate match to complicated field vibration responses than traditional single-axis shaker tests. However, the force capabilities of the small modal shakers typically used in multi-shaker vibration tests has limited the achievable response levels. To date, most multi-shaker vibration tests have been performed using a variety of standard, commercially-available control systems. While these control systems are adequate for a wide range of multiple-input/multiple-output tests, their control algorithms have not been tailored for the specific problem of multi-shaker vibration tests: efficiently coordinating the various shakers to work together to achieve a desired response. Here, a new input estimation algorithm is developed and demonstrated using simulations and actual test data. This algorithm, dubbed shape-constrained input estimation, is shown to effectively coordinate multiple shakers using a set of constraint vectors based on the deflection shapes of the test structure. This is accomplished by using the singular vector shapes of the system frequency response matrix, which allows the constraint vectors to automatically change as a function of frequency. Simulation and test results indicate a significant reduction in the input forces required to achieve a desired response. Finally, the results indicate that shape-constrained input estimation is an effective method to achieve higher response levels from limited shaker forces which will enable higher level multi-shaker vibration tests to be performed.

42 ENGINEERING↗

A simulation study of test fixture attachment points for vibration test optimization (MEEN 5440 Final Project)

The aerospace industry uses vibration shaker tables to perform component durability testing. These dynamic environments tests often have a hard time replicating the service environment of a component due to a mismatch in the applied force or the boundary condition. Figure 1 shows the desired outcome of a dynamic environments test. The measured responses in a lab test, ideally, should match the measured response of the service environment field test. One way to address the mismatch between field environment and lab environment is with test fixture design. The test fixture attaches the component under test to the shaker table. Single-axis shakers are the industry standard type of shaker table, and, therefore, test fixtures are often rigid in order to minimize cross-axis responses.

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Rapid, Approximate Multi-Axis Vibration Testing [Thesis]

The aerospace industry uses vibration shaker tables to perform component durability testing. In these tests a component, piece of equipment, or entire system is attached to a shaker table where it is subjected to dynamic excitation. The goal is to understand how the article under test will perform in its service environment without having to run it through its entire service life via field testing. In a vibration test, an aerospace system or component is qualified if it is shown to survive a test meant to replicate its lifetime service conditions. The test is designed based on recorded field data. To develop a test, a system is taken through all of its intended environments, e.g., transportation, launch, and reentry. Acceleration data measured from these environments is then brought back to the lab and imported into a shaker table controller. The controller then drives a vibration test intended to mimic the acceleration conditions experienced by the system or specific components of the system in the field. However, it is often difficult to match the measured field response in a lab test. This is largely due to the test’s boundary conditions and excitation methods. In a lab test, a shaker table is the excitation source. The two most common shaker table types, differentiated by their number of independent degrees of freedom, are single-axis and multi-axis shaker tables. Multi-axis shakers have the ability to reproduce service environments more realistically, as real accelerations inevitably produce multiple degrees of freedom of excitation simultaneously. Figure 1 depicts a generic multi-axis testing setup on a three-axis shaker table. Often multi-axis tests use six-degree-of-freedom (6DOF) shaker tables. Yet multi-axis shakers are not yet common in the aerospace industry due in part to their high cost and the difficulty for shaker controllers to handle the added complexity. Single-axis shaker tables are much more common. They are not as expensive to purchase and have a wide range of control software options.

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Detection of Damage Inducing Impact Events in Vibration Test Fixtures Using Holder Exponents

The Shock and Vibration team within the Test Engineering group at Los Alamos National Laboratory (LANL) aids in the development and qualification of weapon systems for the United States Department of Energy (DOE). Performing tests that replicate shock and vibration environments representative of a weapon’s lifetime is critical in ensuring safety, survivability, and reliability. A key factor in shock and vibration testing is accurate representation of the weapon’s boundary conditions in its end use configuration. The boundary conditions representative of a reentry body in flight are particularly difficult to replicate on an electrodynamic shaker. When executing shock and vibration tests on a reentry body, two system axes are tested with the system in a cantilevered configuration. This cantilevered testing configuration results in a moment load being applied to the system while undergoing vibration environments. A special fixture, known as the Flex-Web, was developed to decouple this moment load from the reentry body in order to more accurately represent real world boundary conditions while replicating flight environments.

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Rapid, Approximate Multi-Axis Vibration Testing [Slides]

Sequential single-axis testing provides a poor approximation of service environments. Multi-axis vibration tests are not yet standard practice. How good do multi-axis tests need to be to replace single-axis testing in practice? Is the simplest possible multi-axis test close to single-axis testing in test quality? Can single-axis testing techniques provide a sufficient rapid approximation to a multi-axis test? How much can we improve multi-axis test quality by optimizing passive test fixture hardware instead of adding active excitation sources?

42 ENGINEERING↗

Improving convergence of the Matrix Power Control Algorithm for random vibration testing

Herein, this paper describes modifications to the Matrix Power Control Algorithm (MPCA) to improve convergence for Random Vibration Control (RVC) testing. In particular, this paper presents Multiple-Input Multiple-Output (MIMO) implementations of MPCA in simulation and experiment. An Euler–Bernoulli beam model was simulated with applied base excitations and the Box Assembly with Removable Component (BARC) was used in experiment to validate results. The Bayesian optimization package Dragonfly was used to optimize control parameters. Additionally, a moving-average was employed and optimized to improve the measured response feedback for MPCA, reduce the number of averages needed to be taken between control updates, and further improve convergence. The key results of this paper show that the performance of MPCA can be improved by tuning the control parameters and by applying an optimized moving-average. Furthermore, it is demonstrated that convergence can be achieved within 12 drive-frames, which greatly enhances vibration control capability.

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Window Cooling Studies and Disk Vibration Testing on a Subset of Mo-100 Disks

Production of metastable Technetium-99 (Tc-99m), a radioactive tracer that emits gamma rays, is vital to the medical imaging community. Tc-99m is extracted from the decay of Molybdenum-99 (Mo-99) which has a half-life of about 2-3 days. The work presented in this report is part of the NNSA’s mission to produce Mo-99 commercially, within the US, without the use of highly enriched uranium (HEU) in support of nonproliferation and global security. Los Alamos National Laboratory (LANL) is working with NorthStar Medical Radioisotopes (NMR) on their efforts to produce Mo-99 through the irradiation of Mo-100 targets using an electron beam. The NMR target comprises a stack of approximately 60-70 Mo-100 disks with diameter 24 mm and thickness 0.74 mm held in stainless steel laminations, each separated using 0.25 mm thick stainless-steel spacers. The symmetric target stack is housed in an Inconel vessel with two Inconel windows on either side. Two electron accelerators are used to produce 40 MeV, 3.16 µA electron beams each that penetrate the Inconel windows and irradiate the Mo-100 disks. Approximately 90% of the total 250 kW beam power is deposited in the NMR target during the irradiation process, with a smaller percentage adding up to 2.2 kW of heat deposited on the Inconel window. During irradiation, pressurized helium gas flows through thin gaps between the disks cooling the beam window, target disks, disk laminations and spacers. Both NMR and LANL have found during cold testing of the target system (no heat deposition) that the Mo 100 disks undergo significant mass loss and disk breakage due to vibrations induced by the flowing helium gas. The mass loss is not only undesirable due to monetary loss from reduced final quantities of Mo-99, but also due to the hazards associated with radioactive material trapped in the cooling lines and particle filters. The effect of flow rate and target geometry on the flow induced vibrations need to be quantified, and recommendations provided to minimize this mass loss. LANL has previously also tested NMR’s Inconel beam window by heating the window, while flowing pressurized helium, using the average heat deposited on the window. However, the NMR beam is pulsed with a duty cycle of 12.5%, which introduces oscillation in temperature around the nominal 600 °C steady state value with each pulse. Available fatigue curves for Inconel are few, established for room temperature, and they are based on mechanical strain cycles not thermally induced strain as in the NMR target. The effect of pulsed beam heating on the Inconel window therefore needs to be quantified. This report details the experiments conducted to assess the factors that lead to mass loss in the NMR target disks as well as to understand the effect of a pulsed beam on NMR’s Inconel window. This work describes LANL’s experimental characterization of the flow induced vibrations and disk mass loss in a reduced scale set-up containing 5 to 10 Mo-100 disks. We use high speed imaging, displacement measurements and microphone measurements combined with signal processing to estimate the vibration frequency of each disk. The effect of disk thickness, target fit and duration of testing on the mass loss is described. We find that in the current configuration of NMR targets, the vibrations and mass loss on the first disk are minimized, while those in the adjacent disks are highest. The microphone and high-speed image data show that increased flow rates and increased duration of testing increases vibration frequency and mass loss. The mass loss is due to both disk rotation and back and forth motion. There are visible wear marks on the disks with the highest mass loss. We also note that the current NMR window gap reduces flow induced vibrations compared to the previous smaller gaps. Improved target holders significantly reduce disk mass loss to almost negligible quantities. This work finds that the larger window to first disk gap and improved target holder geometry should allow NMR to successfully conduct irradiations with minimal mass loss. The window tests were conducted to understand the effect of a pulsed beam on both the window longevity and to estimate the window temperature and displacement during pulsing. The experiments presented here were performed at significantly low power, due to the limitations of the induction heating system. The window temperature rose to approximately 73 °C with a significantly reduced power of 45 W without beam pulsing. With a 5 Hz pulse rate, 12.5% duty cycle, the window temperature remained constant at 26 °C. These experiments will be repeated with improved coil geometry and reported in upcoming journal papers.

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Vortex Induced Vibration Test of the WITT Device in a Tidal Channel

Fluid flow around a bluff body causes vibrations as the boundary layer separates and vortices are shed. This phenomenon, called vortex induced vibration (VIV), is minimized in most engineering applications, but can be utilized for power generation. Vortex induced vibration has potential for energy harvesting in low velocity water flows and therefore could open many locations to marine renewable energy. Here we present the results of a field test of a device that utilizes VIV to harvest energy from flow in a tidal channel. The pendulum-type device has been designed to generate electricity from motion around and along three axes. It is named the Whatever Input to Torsion Transfer (WITT) energy device and in this test is mounted on top of a pipe. During the field test, the WITT generated electricity at flow velocities from 0.27 to 2.82 m/s. The field test has proven that the WITT can utilize VIV to produce electricity and charge a battery in tidal flows with velocities as low as 0.27 m/s. In the future, the electricity could be used to charge a battery for ocean observation instruments such as temperature and nitrate sensors. In-situ power generation by the WITT would extend deployment times and increase the frequency of measurements.

Branch, Ruth A.↗