具多段弧斷面新型鍵的幾何設計與加工

本論文提出具多段弧斷面新型鍵的幾何設計步驟，首先利用座標轉換提出了多段弧構型的計算機構圖法，推導出其通用數學模式，可產生具等寬度的任意奇數邊多段弧圖形，拓展了目前邊數為三的多段弧鍵在設計上的受限。在該模型下，已求出其面積、面積慣性矩、面積極慣性矩等基本特性，可供進一步的應力分析之用。本文為瞭解多段弧新型鍵的特性，將在相同胚料尺寸下與邊數為三的多段弧鍵作接觸應力比較，除了求出不同設計參數下新型鍵接觸點的位置之外，也針對不同設計參數下之新型鍵產生的應力做相關的分析，除供評比外也可供實際選用的依據，也證實多段弧鍵的優越性。在多段弧斷面新型鍵的數控加工方面，由於圓弧差補的優點，具有可單節程式產生圓弧的優點，基於圓弧差補所需的參數之數控加工模型已建立，排除了 CAM 專用軟體的依賴；針對隨著多段弧的段數增加而使程式變得龐大且容易出錯，本文編寫了巨集指令，解決了此方面的困擾，除了使程式簡化且具效率外，也使除錯工作變的更簡單。為了方便應用，本文分別提出了具等寬性和非等寬性的多段弧構型，除了程序化的構圖外，對等寬性也做了證明，同時也透過輪廓檢驗，驗證了數控加工模型的正確性。為顧及完整性，本文對具多段弧斷面所對應之螺旋面的生成和曲面方程式作了描述和推導，並針對所伴生的加工路徑斜率、曲率不連續性，利用微分幾何作了探討，並提出便於使用的設計參數臨界判別式，可供業界設計與實際加工此類新型動力螺桿的參考。

關鍵字

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並列摘要

A geometric design process of the new type key with multilobe polygonal section is proposed in this study. First of all, by using coordinate transformation a calculator composition of the multilobe polygonal construction is presented, and inquired into its general mathematic model, which can develop any odd number multilobe polygonal figure with equal width. Thus, the limitation in the existing trilobe polygon key design is broken through. Those basic characters known from this model, such as its areas, area moments of inertia, and ares polar moments of inertia, can be used in the further stress analysis. In order to understand characters of the multilobe polygonal new type key, this study composed contact stress with those of the existing trilobe polygon key. Not only compute of the multilobe polygonal new type key contact point with different design parameter, also analyze stress of the multilobe polygonal new type key with different design parameter. Besides comparison and reference as practical decision, the results also confirm the superiority of the multilobe polygonal key. In the aspect of NC Machine, the advantage of circular interpolation is that the block code could produce the arcs. Because of the NC machining model of parameters, which circular interpolation called for, has been established, there if no more depending on CAM purpose software. Along with the increase of edges, the programs become enormous and one may easily make mistakes. This article composes macro commands to solve these problems. They make the programs more simplistic and efficient, while the task of eliminating errors become easier. For the purpose of utilization, multilobe polygonal constructions with either constant-breadth or no constant-breadth are proposed in this article. Their procedural compositions are established, and the constant-breadth has been comfirmed later. Also, through the contours inspection, the correctness of NC machining model has been verified. For the sake of completeness, the generation of helicoid surface and the curved face equation corresponding to multilobe polygonal section are described and derived. Based on differential geometry the discontinuity of slope or curvature of the cutting path followed if discussed. In the end, an usable design parameter equation is referred to the industrial field for designing and practical machining this kind of new type mechanical helicoid screw.

並列關鍵字

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參考文獻

42. H. -Y. Lai, C. -K. Chen and D. -S. Wu, "A High-Precision Circular

43. D. -S. Wu, H. -Y Lai, and C. -K. Chen, "Mathematical modeling of

39. Uffe Hindhede, John R. Zimmerman, R. Bruce Hopkins, Ralph J. Ersman,

104-109, 1976.

and Metal Forming, vol. 44, n 5, May, pp.201-204. 1977.

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具多段弧斷面新型鍵的幾何設計與加工

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