諧振半球殼質量補償模擬與分析

Abstract

本文首先採用了Niordson的半圓球薄殼理論與Kirchhoff-Love的薄殼假設。利用Lord Rayleigh的半圓球殼假設及漢彌爾頓原理獲得理想狀態的半圓球殼振動陀螺儀的運動方程式。 目前文獻中已有許多不同的物理模型與數學模型假設來建立分析、設計與控制各種形式之振動陀螺儀的基礎。且進一步推導誤差模型與模態調校以及控制方程式以作為半圓球殼陀螺儀設計分析、製造與校正之依據。 本研究所獲得半圓球殼陀螺儀之誤差模型與其對應質量微調之對應步驟與去質量型式與多寡，達成半圓球殼陀螺儀在最低頻模態下兩正交運動方程式之頻率失諧與進動誤差，減少日後在控制訊號精度上之提升。

There are a lot of references which contain hypothesis of physical and mathematical model to analysis and design varies form of gyroscope. Under this condition, there may be the accordance to derive the error model, mismatch tuning and control. Firstly, this article use the Niordson’s semi-spherical shell theory and Kirchhoff-Love’s assumption. Using hemi-spherical shell assumption proposed by Lord Rayleigh and Hamilton principle obtain the motion equation. This research simulates the hemi-sphere shell’s error model and mass compensation to tune mismatch and promote the precession of control.