Vibration mitigation in spacecraft components using Stewart platform and particle impact damping

Abstract

A spacecraft encounters two regimes of vibrations: launch loads and on-orbit loads. Both these loads propagate through the spacecraft structure, which is primarily made up of honeycomb sandwich. The launch loads that are high amplitude and low frequency are critical to subsystems mounted on honeycomb sandwich panels that further amplify it owing to low inherent damping and local resonance. The damping behavior of the panels can be improved, and amplification at resonances can be reduced by inserting damping particles in the empty cells of the honeycomb core. Another way of reducing the vibration is to use a multi-axis isolator between source and target. This scenario is particularly useful for on-board extremely low amplitude vibrations called micro-vibration. In this work, both approaches have been addressed. First, a multi-axis vibration isolator design based on a Stewart-Gough platform (SGP) and a modified Stewart-Gough Platform (MSGP) is considered. We propose a design where the first six modal frequencies are close to each other for a predefined payload, thus enabling effective vibration isolation for all six primary modes. The equations of dynamics of the 6-6 semi-regular SGP was obtained in terms of five geometric variable and position of the mass center of the combined top platform and the payload. A gradient-based optimization was used to obtain the dimensions of an SGP such that the first six modal frequencies are close to each other – the ratio of the maximum to the minimum natural frequency (also termed as dynamic isotropy index) was obtained as 1.70 and 1.31 when the torsional mode was excluded, respectively. A detailed analysis, including the effects of a typical payload and leg inertia, was performed. Based on the obtained design, a prototype Stewart-Gough vibration isolator was fabricated. The experiments with the prototype show that the observed ratio of the maximum to the minimum natural frequency, excluding the torsional mode, was 1.50. To obtain a better dynamic isotropy index, a modified version of the semi-regular SGP is considered. The main modification considered is that the attachment points on each platform are not in a circle but two circles. This modification leads to a configuration where all six frequencies are the same even after incorporating a cross-blade flexural joint and metallic bellow to provide the required stiffness to legs. The detailed finite element model used for modal analysis and steady-state dynamic analysis is performed. The transfer functions show the isolation of 33dB/oct is achievable. A numerical study to assess the performance of a fully isotropic MSGP with the top platform made up of honeycomb embedded with damping particles is also carried out. In the second approach to improve the damping characteristics of the honeycomb panel, damping particles (DPs) are filled in the core of the honeycomb sandwich at strategically selected locations. The locations are chosen based on the targeted frequency band and mode shapes of the host structure. We present a mathematical model governing the motion of the cell-walls, DPs, and honeycomb plate/beam. The coupled dynamics of damping particle and honeycomb plate/beam is modeled using the discrete element method (DEM) combined with the finite element method (FEM). The DEM used to model the dynamics of the DPs is based on Newton's Laws, and the particle-particle and particle-cell walls interaction are modeled using modified nonlinear dissipative Hertz contact theory in conjunction with Coulomb friction. The coupled equations of motion of DPs, cell-walls, and host structure were solved using a numerical method. The interactions of damping particles with the walls of the cells and its overall effect on the frequency response function (FRF) and the damping of the structure were obtained. In two cases: a beam and a plate are considered for numerical and experimental studies. In the honeycomb cantilever beam, contiguous blocks of cells near the tip of the cantilever beam were filled with the damping particles, and the beam was excited with a random signal near the fixed end. The damping and transfer functions were obtained and compared with the mathematical model, and they were found to match very well. Further, the model was used to study the effect of fill fraction, mass ratio, and excitation signal level on the transfer function. Significant reduction of vibration level was observed with respect to mass ratio and fill fraction. In another study, a honeycomb plate was partially filled at selected locations with damping particles. All the four edges were excited by a swept sine signal. The damping ratios and resonance peaks of the lower four modes of the HC plate, excited up to 1000 Hz, were obtained experimentally from the FRF measurements and numerically from the DEM model. They also compare very well. The damping ratios, response at resonances, and the FRF profiles are also similar. Significant improvement in damping ratios and attenuation of vibration level has been observed in the experiments.