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

## TL;DR

This paper evaluates and optimizes a flexible positioning platform's performance under random vibrations using power spectral density analysis to improve its reliability and lifespan.

## Contribution

A novel method for evaluating and optimizing flexible positioning platforms using PSD analysis and fatigue life prediction under random vibrations.

## Key findings

- Stress and deformation are highly concentrated in the hinge region, indicating a structural vulnerability.
- Hinge stiffness significantly influences the platform's vibration resistance and service life.
- Fatigue life predictions using the Dirlik method and Miner’s rule show the impact of various PSD loading conditions.

## Abstract

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.