Using Modal Projection Error to Predict Success of a Six Degree of Freedom Shaker Test.
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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.
Currently, spent nuclear fuel (SNF) is stored in onsite independent spent fuel storage facilities (ISFSIs), which is a dry storage facility, at 55 nuclear power plant sites. The majority of SNF in dry storage is in welded metal canisters (2,917 canisters at the end of 2019). The canisters are loaded for storage in storage overpacks (vertical casks or horizontal storage modules) and placed on outdoor concrete pads. Because the SNF will be stored at ISFSIs for an extended period of time, there is growing concern with regards to the behavior of the SNF within these dry storage systems during earthquakes. To address these concerns, the SFWST program is considering conducting an earthquake shaker table test. The goal of this test is to determine the strains and accelerations on fuel assembly hardware and cladding during earthquakes of different magnitudes to better quantify the potential damage an earthquake could inflict on spent nuclear fuel rods. The seismic integrity of the storage system has been addressed in the past by the US Nuclear Regulatory Commission and is not the focus of this potential test. Instead the DOE would benefit from knowing the condition of the fuel cladding from storage, transportation, to disposal so that it can ascertain repository performance for the fuel and packaging in its final state. A seismic event is part of the possible loading events that the fuel could experience in its lifetime. This report proposes several earthquake shaker table tests with different degrees of complexity. Alternative 1 was defined in the FY20 work scope. Alternatives 2 and 3 were recently developed to take advantage of the NUHOMS 32PTH dry storage canister that may be available in FY21 for this test at a minimum cost to the project. The selection of the alternative(s) will depend on the available budget and the SFWST program priorities for the near future.
The process of characterizing a damper involves both experimental techniques and model simulation. Experiments characterize dynamic behavior of a system through empirical modal analysis using impact and shaker testing. The layout of the test setup is crucial for a low-mass, nonlinear system. Physical arrangement, orientation of the system, and instrumentation affect the results that are discussed in this paper. These results can be used to validate a numerical simulation of the same system. With a validated model, important physical input parameters and modeling techniques can be determined and implemented in future designs. In other words, this modeling can be used with confidence to design alternative dampers that may be difficult, costly, and time-consuming to characterize experimentally.
Los Alamos National Laboratory (LANL) is an important fixture in the United States Department of Energy’s (DOE) National Nuclear Security Agency (NNSA) complex. LANL is one of the largest national laboratories in the country, and the laboratory’s primary mission is to support the nation’s nuclear stockpile. The lab functions as a design agencies for the NNSA and performs extensive testing on weapons as part of that mission. The shock and vibration test team at LANL utilizes electrodynamic shaker systems for important qualification testing in support of the laboratory’s mission. Modern engineering relies heavily on bolted joints to connect two objects. During these shaker tests, engineers depend on bolted joints to secure the test article to a fixture and the fixture to the table. The test article may be hazardous and contain high explosives which could create a safety issue if a bolted joint failed. A loss of preload in a bolt will affect the way energy is input to the system and may introduce nonlinearities as the joint opens and closes. The loss of preload can create challenges controlling the test and make acquired signals useless. Being able to monitor preload within bolted joints during testing can improve the quality of the data and keep workers safe.
Abstract not provided.
Shaker excitation is a popular technique in experimental modal analysis because it gives the practitioner a high level of control and repeatability in the excitation. However, the dynamics of the shaker and test article can fundamentally limit the excitation bandwidth when a voltage-mode amplifier is used to power the shaker. Further, multiple shakers can couple to one-another through the test article and correlate the forces during a multiple-input / multiple-output modal test, potentially impa
One concept in smart dynamic testing is to match the impedance that a component experiences between test and the environment of interest, but this begs the question: how much of an impedance match is needed and could there be too much? In a prior work, the authors performed MIMO testing with a small component connected to various assemblies, each of which had a differing degree of similarity to the actual flight boundary conditions. The results showed that the fidelity of the response at locations away from the control accelerometers was highly sensitive to the impedance. This work presents further case studies to explore these ideas. Subsequent tests are presented for an assembly that presumably matched the impedance even better, and which was also much more flexible, and the results obtained are even worse than when no attention was given to the impedance. Hence, the work presented here suggests that one should seek a balance between 1.) matching the impedance and 2.) improving the controllability of the component of interest. The concepts are explored using both test data of a benchmark component, for which the environment of interest was recorded as the component flew on a sounding rocket.
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Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. Finally, the results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system’s dynamics.
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.
Bifurcations are commonly encountered during force controlled swept and stepped sine testing of nonlinear structures, which generally leads to the so-called jump-down or jump-up phenomena between stable solutions. There are various experimental closed-loop control algorithms, such as control-based continuation and phase-locked loop, to stabilize dynamical systems through these bifurcations, but they generally rely on specialized control algorithms that are not readily available with many commercial data acquisition software packages. A recent method was developed to experimentally apply sequential continuation using the shaker voltage that can be readily deployed using commercially available software. By utilizing the stabilizing effects of electrodynamic shakers and the force dropout phenomena in fixed frequency voltage control sine tests, this approach has been demonstrated to stabilize the unstable branch of a nonlinear system with three branches, allowing for three multivalued solutions to be identified within a specific frequency bandwidth near resonance. Recent testing on a strongly nonlinear system with vibro-impact nonlinearity has revealed jumping behavior when performing sequential continuation along the voltage parameter, like the jump phenomena seen during more traditional force controlled swept and stepped sine testing. Here, this paper investigates the stabilizing effects of an electrodynamic shaker on strongly nonlinear structures in fixed frequency voltage control tests using both numerical and experimental methods. The harmonic balance method is applied to the coupled shaker-structure system with an electromechanical model to simulate the fixed voltage control tests and predict the stabilization for different parameters of the model. The simulated results are leveraged to inform the design of a set of experiments to demonstrate the stabilization characteristics on a fixture-pylon assembly with a vibro-impact nonlinearity. Through numerical simulation and experimental testing on two different strongly nonlinear systems, the various parameters that influence the stability of the coupled shaker-structure are revealed to better understand the performance of fixed frequency voltage control tests.
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.
Impedance Matched Multi-Axis Tests (IMMATs) can replicate in-service vibration induced stress more accurately than single axis shaker table tests as they can better match a part’s operational boundary conditions and excite it in multiple degrees of freedom simultaneously. Here, the shakers used in IMMATs are less powerful than shaker tables, so shaker force limits can be exceeded during tests if they are not placed adequately for the desired environment. The ability to predict shaker voltage and force before performing a test is, therefore, helpful in selecting shaker locations so that their limits are not exceeded. In this study, electrodynamic shakers were modeled as discrete electromechanical systems, and the shaker parameters were chosen to match experimentally obtained acceleration/voltage frequency response functions (FRFs). These models were coupled to a finite element model of the device under test (DUT) via dynamic substructuring, and the substructured model was demonstrated to accurately predict shaker voltage as well as the error in reproducing the environment at multiple accelerometer locations. A simple method called the FRF Multiplication method, in which the FRF of the substructured system is approximated as the product of two separate FRFs of the shaker and DUT respectively, was proposed and applied to the same system, yielding similar voltage and error predictions to those obtained using substructuring. Simple case studies were presented to explore the applicability of the proposed method, and it was demonstrated to have similar accuracy to the substructuring method in a range of cases. Additionally, we showed that while it was not possible to derive a unique model of the shakers from acceleration/voltage FRFs alone, the models that could be obtained were sufficient to predict test error almost perfectly and shaker voltage with less than 40 percent error.
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