| 摘要: | 本論文旨在針對漸開線與切線雙圓弧兩種齒形進行諧波齒輪(Harmonic drive，HD)減速機之特性分析。首先利用齒輪原理，分別以各自之刀具建立二維柔輪齒齒面數學模式，並根據諧波齒輪的運動模型與包絡法推導和柔輪齒形互相共軛的二維剛輪齒齒面數學模式。除此之外，以二維柔輪齒齒面數學模式為基礎，發展自動化網格分割程式進行柔輪齒的網格劃分，並透過二維諧波齒輪之有限元素分析，成功模擬出全齒負載下諧波齒輪的傳動比、運動軌跡、嚙合區間、扭轉剛性及齒根和齒面週期應力。本研究串聯有限元素軟體、c++程式與最佳化軟體進行二維的齒形最佳化分析，獲得應力滿足疲勞限且不干涉條件下，扭轉剛性最佳的齒形。最後加入軸向的參數，包含筒長、齒寬等等，進行初步的三維諧波齒輪有限元素分析，成功模擬出全齒負載下諧波齒輪的扭轉剛性與嚙合區間，除了探討柔輪有、無導程修整的模擬結果比較以外，也對二維與三維諧波齒輪模擬之差異進行比較與討論。本研究所提出的方法將為未來三維諧波齒輪有限元素分析和三維諧波齒輪最佳化分析之研究鋪路。
;The purpose of this study is to analyze the meshing characteristics of harmonic drives (HD) with involute profile and double-circular-arc profile. Firstly, the 2-D mathematical model of flexsplines (FS) with involute tooth profile and double-circular-arc profile were developed by using respective rack cutter based on the theory of gearing. Then the engaging circular spline (CS) with conjugate tooth profile of FS was derived based on the enveloping theory and kinematic model of HD. Additionally, a mesh generation program was developed to discretize the FS based on the 2-D mathematical model. Furthermore, 2-D FEA was conducted to explore the engagement movement of the FS, the torsional stiffness, transmission ratio, fillet stress and contact stress of the FS during meshing process and the engaged area of teeth of the HD under various conditions. In this study, an optimization method was adopted in the parametric design of 2-D tooth profile. The optimization aims to achieve the maximum torsional stiffness, and the constraints are that the stress is smaller than the fatigue limit of the FS material and no interference between the teeth of FS and CS is presented. An 2-D tooth profile optimization processing combining c++, finite element analysis and optimization algorithm was successfully performed. Moreover, a preliminary 3-D FEA was conducted to explore the torsional stiffness and the engaged area of teeth of the HD under two conditions, such as HD with lead crowning or HD without lead crowning by adding in axial parameters, including cup length, tooth width and so on. Finaly, The results from 2-D FEA and 3-D FEA were compared and discussed. The proposed methodology in this study paved the way for future investigations of 3-D FEA and 3-D optimization.
keywords：harmonic drive, torsional stiffness, engaged area of teeth, involute tooth profile, double-circular-arc profile, finite element analysis, optimization |
