6 Reproducing a Component Field Environment on a Six Degree-of-Freedom Shaker 75 Fig. 6.2 RC attached to Team Tensor 900 instrumented with 13 triaxial accelerometers test data. The MATV ASDs were sampled at a 1.25 Hz resolution and truncated from 50 Hz to 2000 Hz to accommodate the Spectral Dynamics requirements. The measured ASD responses from the 6 DOF shaker test (red) and the target MATV acoustic responses (blue) are shown in Fig. 6.3. Note, here we are trying to match all 12 responses on the 4 triaxial gauges using a multi-axis base excitation. The measured (red) and target (blue) ASD responses match well over most of the control bandwidth (50–2000 Hz). There are two consistent frequencies where the fit is less precise: 1140 Hz and 1900 Hz. The first discrepancy (1140 Hz) is only in the X direction of the four nodes and corresponds to the third fixed base mode where the RC component lunges side to side in the X-direction [5]. Mathematically, this fixed base mode is controllable, but the Spectral Dynamics control system did not have enough dynamic range to notch the inputs low enough to remove this fixed base resonant response. The second mismatch is near 1900 Hz and can be observed in all 4 nodes in the X, Y and Z direction. This corresponds to a twist mode of the 6 DOF [5] shaker and fixture plate which was not controllable in this experimental set-up with the Team-Tensor 900. We provide these curves as evidence that a controlled 6-DOF test can simulate a field response for a base mounted component. The second test of interest with this configuration was to understand how well one could match the RC response using a single degree of motion test. To do this, first a simple buzz test was conducted using base control. The base accelerometers were used to produce flat broadband spectrum in all three translations (X, Y, Z), and all three rotation (Rx, Ry, and Rz). The six base acceleration inputs were uncorrelated. The responses of nodes 1–4 were measured and a transmissibility matrix was calculated to the six base inputs to understand the dynamic response of the RC on the 6-DOF shaker. The input for this single degree of motion test is an ASD for the X-direction only; this was directly measured on the MATV component plate approximately 4 inches away from the RC. Here the Y-direction and Z-direction translation motions and all three rotations (Rx, Ry and Rz) are ignored, this drastically affects the response. The results of this test are shown in Fig. 6.4. The measured ASD responses from the 1DOF shaker test (red) and the target MATV acoustic responses (blue) is a poor recreation of the field responses. Using a controlled measured X input from the field as the target specification yields a different RC response when Y, Z, Rx, Ry, and Rz are constrained. For the frequency range 50 Hz to 1100 Hz, the measured response and target response match well for all 4 nodes in the X-direction only. However the overall amplitude and response structure for the constrained Y, Z, Rx, Ry, and Rz does not match. MIMO testing can be complex, and this test series presented a few challenges that can be explored in future works to minimize the error between the target and measured ASD responses. Firstly, the reference response matrix must be a positive definite matrix. It is important to note that when using the Spectral Dynamic MIMO random controller, the software truncates all terms to 6 significant digits past the decimal point and this truncation can cause a positive definite system to become nonpositive definite or the coherence to be greater than 1, which is physically impossible. One solution is to truncate the matrix in MATLAB prior to testing while ensuring positive definiteness or multiplying the coherence by 0.9999 (until it is less than 1) which is undesirable. Another important coefficient is the condition number of the matrix. With the current control scheme all 12 response were treated with equal importance and if the condition number is too high then the controller struggles to control to the target, sometimes even aborting prior to reaching steady state at low levels. This single degree of motion test is also related to the dynamic range of the controller software. If the target references span too many decades the drives of the servos will not have enough dynamic range to control and overcome dynamic response and unwanted resonances. For these series of tests, a condition number of 1000 was used, and the matrices were truncated in MATLAB while ensuring positive definiteness. Because there was insufficient dynamic range, the 1140 Hz mode could not be notched enough. If a higher condition number was used, the controller could not run the environment.
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