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Balancing Impedance and Controllability in Response Reconstruction with TS-IMMAT

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Abstract

In a prior work the authors proposed a variant on the Impedance Matched Multi-Axis Test (IMMAT) in which a fixture is defined, called the Transmission Simulator (TS), and the desired environment is matched at a set of sensors on the TS. If the motion of the TS is matched then the response of the rest of the component will also match, provided that the attached component has the same dynamics as it did when the environment was measured. Hence, one would like the TS to be flexible so that it reproduces the boundary conditions that the component of interest experiences during flight, but the more flexible the TS, the more shakers might be needed to control its response. This work presents a derivation that gives expressions for these two potential error sources in TS-IMMAT. Then, various case studies are presented, both on simulated and real hardware, to understand the importance of each error term in practical testing. The theory explains the phenomena that were observed when using measurements from a component that flew on a sounding rocket. The environmental response was measured and then various fixtures were attached, each comprising more of the next assembly, or the hardware to which the component was attached in flight. MIMO testing was repeated with each fixture and the results were compared to seek to understand the role of the impedance match in this type of testing. The results show that the number of modes that are active in the transmission simulator is also very important, and so the best solution balances these two considerations. An improved method of simulating the MIMO test is then proposed, so simulations can be used to predict what fixture, or transmission simulator, will give the best results in a TS-IMMAT test.

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Data Availability

The flight data presented in this paper is available by request from the authors, pending clearance from the research sponsor. The simulation data from the simple spring mass systems can be shared upon request.

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Acknowledgements

The authors gratefully acknowledge the Department of Energy’s Kansas City National Security Campus, operated by Honeywell Federal Manufacturing & Technologies LLC, for funding this work under contract number DE-NA0002839.

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Authors and Affiliations

  1. Department of Engineering Physics, UW-Madison, Madison, WI, USA

    M. J. Tuman

  2. Mechanical Engineering Department, Brigham Young University, Provo, UT, USA

    M. Behling & M. S. Allen

  3. Honeywell Federal, Manufacturing & Technologies, Kansas City, MO, USA

    W. J. DeLima & J. Hower

  4. Mayes Consulting, Albuquerque, NM, USA

    R. L. Mayes

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Appendix: Shaker Selection Algorithm

Appendix: Shaker Selection Algorithm

Prior to performing any test, it is helpful to have a means of ensuring that the shaker locations used are adequate. The theory just presented shows how the spectra obtained in a MIMO test are related to the FRFs of the system of interest. Those FRFs can be created from a finite element model or measured experimentally; in this work we take the latter approach as detailed later.

The iterative shaker placement algorithm from [26] was adapted to find the shakers locations used in this work. First, the average dB difference of two ASDs for all relevant accelerometer channels at a frequency line is computed using Eq. (14). After computing an error value for each frequency line, a final metric is computed using Eq. (15). This final error number represents the average dB error across all accelerometers and frequency line. A low error metric communicates a successful reconstruction test and will be used moving forward to compare various tests. With the error metric defined, the shaker location algorithm used in this work is as follows:

  1. 1)

    Start with a pool of all possible forcing input locations from the roving hammer test of the component

  2. 2)

    Simulate the MIMO response for each forcing input location in the remaining pool (controlling to the eight plate accelerometers)

  3. 3)

    Identify the forcing input location that produces the lowest error on the controlled DOF (plate accelerometers). Add that input location to the set of chosen forcing locations and remove from the pool of possible locations.

  4. 4)

    Repeat steps 2–4 with the kept forcing input location/s from the previous iterations plus each candidate location and again keep the best candidate location until the number of desired shakers is reached.

The optimization was terminated once it determined the six best shaker locations. The error metric in Eq. (15) was also used in the results that follow to provide a measure of how successful a particular test was in recreating the desired environment.

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Tuman, M.J., Behling, M., Allen, M.S. et al. Balancing Impedance and Controllability in Response Reconstruction with TS-IMMAT. Exp Tech 48, 51–68 (2024). https://doi.org/10.1007/s40799-023-00645-1

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