37 Next-Generation Random Vibration Tests 401 0 10−8 10−6 10−4 10−2 100 500 1000 Frequency (Hz) Acceleration PSD (g2/Hz) 1500 PSD 1X PSD 1Y PSD 1Z 2000 Fig. 37.7 Example PSDs obtained during wind tunnel testing Fig. 37.8 Twin-shaker single-axis vibration test Prior to carrying out the vibration test, it was necessary to generate a test specification. As the vibration test involved two shakers (Fig. 37.8), the test specification must be suitable for MIMO random control. It order to replicate current practice, two response positions (2 and 5) were selected to control the test and were situated close to the two excitation locations (Fig. 37.8). The test specification consisted of two PSDs and one cross spectral density (CSD). The PSDs and CSD in the test specification were obtained directly from the wind tunnel environment at the control accelerometer positions and are shown in Fig. 37.9. It should be noted that harmonics, beginning at 307 Hz, can clearly be seen in the spectral density curves in Fig. 37.9. These harmonics are from the wind tunnel fan and excite the missile via the roof of the wind tunnel. They have been included in this case study to simulate the vibration that a missile might experience from its parent structure, e.g. the vibration induced by the engine through the aircraft wing. The two electrodynamic shakers were rigidly connected to the missile via fixtures. This fixturing arrangement is typical of current practice and significantly alters the dynamics of the missile by stiffening and mass loading the local region, preventing it from bending freely and restricting cross-axis excitation. The shakers provided random excitation to the missile for 50 seconds with the test being controlled and recorded using the Leuven Measurement Systems (LMS) MIMO Random Control software and the Supervisory Control and Data Acquisition System (SCADAS) hardware. The control curves from the twin-shaker test are shown in Fig. 37.10 and indicate good agreement between the test specification and the vibration test. This demonstrates that at the two control positions the vibration test is providing a good simulation of the aerodynamic environment from the wind tunnel. In addition, there is good agreement between the CSD from the wind tunnel and that of the twin-shaker test and of particular importance is the relative phase between the two control positions. The twin-shaker vibration test was able to go some way to replicating the harmonics of the wind tunnel fan, but it could not achieve the amplitude of the peaks. As with the wind tunnel measurements, all thirteen accelerometers were used to measure the vibration in the twin-shaker test. Of these, two were control accelerometers used to control the vibration test with the remaining eleven being uncontrolled response measurements. The PSDs from the twin-shaker test are shown in the appendices (Fig. 37.13), with only twelve of the thirteen shown for convenience. The plots show that the vibration at the uncontrolled positions is a relatively poor simulation of the complete aerodynamic environment. In particular, there is evidence of considerable overtesting, undertesting and crossaxis overtesting (Fig. 37.13). Similar results were observed for the CSDs from the twin-shaker test (Fig. 37.14). There were
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