Analytical Method and Experimental Verification of Coupled Micro-Vibration for Spacecraft Based on Mechanical Impedance Theory

Abstract Micro-vibrations exert detrimental effects on spacecraft that requires extreme precision performance. Dynamic mass method (DMM) is a component-level grounded micro-vibration measurement method, which is widely used in the analysis of coupled interplay between micro-vibration sources and spacecraft. However, this study reveals that all existing research involving DMM contains a fundamental error during its theoretical derivation. In light of this, the root cause of the error is investigated based on the mechanical impedance theory. Building upon this, a modified dynamic mass method (MDMM) is further proposed, and corresponding solution steps are also given, with emphasis on the treatment of gyroscopic effects of reaction wheels (RWs). To validate this analytical method, a grounded micro-vibration measurement system for RWs is designed and established. Micro-vibrations of an RW are measured under both the rigid-mounted and isolated conditions, respectively. Leveraging the physical parameters of the isolator, MDMM is applied to process the micro-vibration data measured under a rigid-mounted condition, which predicts the transmitted data under an isolated condition. The analytical data produced by MDMM agrees well with the measured results, which partially validates the feasibility and effectiveness of the proposed MDMM. This analytical method proposed in this work can serve as a theoretical tool for both measurement and analysis of the coupled micro-vibrations of sources and spacecraft.