# Displacement Transmissibility Analysis of Stewart Platform Based SINS’s Bumper Under Base Vibration Excitation

## TL;DR

This paper introduces a new method to analyze how well a Stewart platform bumper reduces vibrations in navigation systems.

## Contribution

A novel displacement transmissibility analysis method for a Stewart platform bumper under base vibration is proposed.

## Key findings

- A lumped parameter model with stiffness, damping, and mass matrices was developed for the bumper.
- The proposed method achieved a maximum 3.6% gap between theoretical and experimental results.
- A calculation flowchart was introduced to evaluate vibration isolation performance effectively.

## Abstract

The Stewart platform based bumper is essential for the strap-down inertial navigation system (SINS) to attenuate the vibration excitation from base to SINS. Displacement transmissibility is the most important performance indicator to quantify the vibration isolation effectiveness of the bumper. In this paper, considering the structural complexity and dynamic coupling of the bumper in parallel mechanism shape, a novel method of displacement transmissibility analysis for the bumper under base vibration excitation is proposed. Firstly, a lumped parameter model is established for the bumper by defining dynamic matrices, which includes stiffness matrix, damping matrix and mass matrix. Secondly, coupled dynamic equations of the bumper under base vibration excitation are derived based on the proposed model, and the coupled dynamic equations are transferred to decoupled dynamic equations by decoupling method. Thirdly, a calculation flowchart of the vibration isolation performance for the bumper is proposed based on the deduced decoupled dynamic equations, and theoretical results for displacement transmissibility are obtained by the calculation flowchart. Finally, the proposed analysis approach of displacement transmissibility for the bumper is validated by vibration experiments as the maximum quantitative gap between theoretical and experimental results is 3.6%.