Random Vibration Evaluation and Optimization of a Flexible Positioning Platform Considering Power Spectral Density

The flexible positioning platform is a critical structural component in the ultra-high acceleration macro-micro motion platform, enabling precise positioning across multiple scales. However, under high-frequency start-stop cycles and prolonged multi-condition operation, it is prone to fatigue damage induced by random vibrations, which poses a threat to system reliability. This study proposes a method for evaluating and optimizing the platform's performance under random vibration based on power spectral density (PSD) analysis. In accordance with the IEC 60068-2-64 standard, representative load spectra from Tables A.8 and A.6 were selected as excitation inputs. Frequency-domain analyses of stress, strain, and displacement were conducted using ANSYS Workbench 2022R1 in conjunction with the nCode platform, incorporating the Gaussian three-sigma probability interval. The results reveal that stress and deformation are highly concentrated in the hinge region, indicating a structural vulnerability. Fatigue life predictions were carried out using the Dirlik method and Miner's linear damage rule under various PSD loading conditions. The findings demonstrate that hinge stiffness is a key factor influencing vibration resistance and service life. This research provides theoretical support for the design optimization of flexible structures operating in complex random vibration environments.