The Virtual Shaker Testing (VST) approach and its application to a Spacecraft

Into the design and verification framework of a S/C, a fundamental milestone is provided by the qualification and acceptance tests during which the capability of the platform to withstand the mechanical environment, reproduced by proper devices with suitable load values, is observed. Focusing on sinusoidal vibration tests, also called sine sweep, the aim is to impose low frequency loads on three axes, between 5÷100 Hz, through a shaker placed at the base of the S/C. Mechanical proper interfaces connect the slip table to the S/C. Typically, the curves acquired during the test are different with respect to the ones predicted in the classical numerical sine test prediction. In general, the anomalies unforeseen in the numerical sine test prediction can imply test aborts and schedule issues to complete the test campaign. The detailed study of these anomalies, between the sine test numerical predictions and the corresponding test acquisitions, shows that differences are mainly attributable to an inconsistent imposition of the boundary conditions (BCs) into the numerical model, “Hard mounted” (HM), where translations and rotations are constrained to the base of the S/C. Moreover, the transient phenomena neglected in the Frequency Response Analysis (FRA) are an additional source of discrepancy. Precisely, the geometrical and mechanical characteristics of the shaker as mass, inertia, elasticity and constructive elements (seismic mass, struts, and supports), are completely omitted into the classical approach. It follows the inability to model and study the phenomenon observed during the test phase as dynamic couplings (“rockling”, “saddle”, “bending”) between shaker and S/C, the dynamic effect of the seismic mass and “Cross-talks”. In addition, the “sweep rate”, the rate of climb of the forcing frequency during the test, increases the gap between model and reality, separating the stationary predictions based on FRA, compared to the extracted transient. As result, the natural frequencies observed during the vibration test are distorted through a frequency shift. A low sweep rate is critical for the S/C because forces it to oscillate subjected to a forcing function with a frequency close to the natural one of the S/C itself. For these reasons, the classical approach based on FRA with HM conditions is inconsistent due to an incomplete modelling of the problem. In this framework, the innovative transient approach called “Virtual Shaker Testing” (VST), extends the BCs beyond shaker, modelling the complex shaker –S/C. It allows to perform the sine test prediction anticipating the dynamic transient behaviours, sweep rate effects and coupling issues between S/C and shaker-assembly that are impossible to recognize though the steady state approach. From the applicative point of view, a MATLAB/Simulink© model, called Vibration controls, provided by SIEMENS®, has been used. These routines are able to automatically integrate the Notching criteria, i.e. the reduction of the forcing amplitude when dedicated acceleration thresholds are exceeded, into the computational loop of a transient analysis. For this reason, the preparation of a computational framework capable to setup and carry out the VST with dynamic structural models, in a state-space form using condensed models in Craig-Bampton formulation, is possible. In this way, the real transient prediction is performed for two satellites with a comparison between numerical and experimental possible results.