微小環型諧振式陀螺儀的分析與設計

Abstract

在本篇論文□，我們利用電腦輔助軟體ANSYS5.3來分析整個環型諧振式陀螺儀，這些分析主要分成三種分析，即模態分析、靜態分析與熱分析。在模態分析中，我們得到了此陀螺儀的兩個二階振動的模態形狀和其工作頻率，並經由所得到的結果證實了這兩個n=2的模態是完全一樣的，也證實了此兩模態的振動主軸是相差45度的。在靜態分析中，我們得到了各種參數和陀螺儀零敏度的關係，這些參數包括中心環的寬度與半徑、彈簧的寬度與半徑與整體結構的厚度。除此之外，我們也得到此陀螺儀的應力分佈與位移量在各方向的比例關係。在熱分析方面，我們發現由於熱膨脹所引起的位移量大約是靜電力所產生的位移量的一千倍。為了解決此問題，我們設計了一機制並改變尺寸以減少因熱膨脹所引起的位移量。經由這些分析，進而設計出整個環型陀螺儀的尺寸，並且改變陀螺儀中心環與彈簧接點的形狀，以達到分析結果的要求。

In this thesis, we analyzed this vibrating ring gyroscope using the finite element program ANSYS 5.3. The analyses we performed were divided mainly into three categories, the modal analysis, the static analysis and the thermal analysis. In the modal analysis, we obtained the two vibration flexural mode shapes, which is n=2, of this structure. We also obtained the frequencies of these two flexural modes. In the static analysis, we established the relations between the sensitivity of the structure and the geometry parameters including the width, the radius and the thickness. Besides, we also obtained the stress distribution of this structure and the ratio between the displacement along z-axis and the one along x or y-axis. In the thermal analysis, we discovered that the displacement of the structure due to thermal expansion is thousand times the one due to electrostatic force. To solve this problem, we designed a mechanism and changed the dimensions of the structure to decrease the displacement of the structure due to thermal expansion. Through these analyses, we designed the dimensions of this structure and changed the shape of the connection points between the ring and the spring to accomplish the demand of the analytical results.