Chapter 8 Using Modal Projection Error to Predict Success of a Six Degree of Freedom Shaker Test Tyler F. Schoenherr, Janelle K. Lee, and Justin Porter Abstract Six degree of freedom shaker tests are becoming more popular as they save testing time because they test a component in multiple directions in one test rather than executing multiple tests in one direction at a time. However, there are several difficulties in conducting a component six degree of freedom shaker test in a way that adequately replicates the component field stress. One difficulty is knowing if a classical rigid test fixture will produce component modes that span the displacement space of the component in the field environment. If the modes of the component while attached to a rigid fixture do not span the space of the component in the field environment, then the test will be unable to replicate that motion and corresponding stresses. This paper will examine the motion of the Removable Component of the BARC hardware in an field assembly and calculate the modal projection error expected by executing a six degree of freedom shaker test on a rigid fixture. The paper will conclude by examining the data and comparing it to the pre-test predictions of error calculated by the modal projection error. Keywords Modal projection error · 6 DOF Shaker · Boundary condition · Testing · BARC 8.1 Introduction The frequency and use cases for multi-axis shaker testing is growing. Multi-axis shaker tests reduce test time testing all axes simultaneously. Multi-axis tests also can increase the fidelity of the result by providing a more realistic stress state [1] for the unit under test. Like all dynamic environment tests, the test fixture and the shaker table need to represent the boundary condition impedance of the unit under test in the field to realize the benefits of the multi-axis shaker test. If the boundary condition of the shaker configuration is different from the field configuration, the unit under test can have a different set of mode shapes or even a different basis set. If the basis set of mode shapes differ between field and test, the stress profile of the unit under test cannot be matched. Quantifying the effect of the test fixture in a dynamic environment test is difficult due to the response of the unit under test being a product of the input forces and the system transfer functions. The modal projection error (MPE) is a newly developed parameter that tests two sets of shapes to determine if one set spans the space of another [3]. In relation to test fixture development, this error determines the lower limit that the test response will exhibit to reproduce the field response. Because the MPE is an examination of the mode shape space, a parameter of the system transfer functions, it is an appropriate method of quantifying the effectiveness of the test fixture. The purpose of this paper is to determine if the MPE is a good predictor of success for a multi-axis shaker test. In order to determine if the MPE can predict multi-axis shaker success, this paper will present two case studies. The first case study uses Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE- NA-0003525. T. F. Schoenherr ( ) · J. K. Lee Sandia National Laboratories, Albuquerque, NM, USA e-mail: tfschoe@sandia.gov J. Porter Rice University, Houston, TX, USA © The Society for Experimental Mechanics, Inc. 2021 A. Linderholt et al. (eds.), Dynamic Substructures, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47630-4_8 93
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