齒形過切在刀具設計與製造之應用

Application of Tooth Undercutting on the Cutting Tool Design and Manufacture

曾煌棊(Huang-Chi Tseng)

國立虎尾科技大學/工程學院/動力機械工程研究所/碩士(2005年)

摘要

本研究透過特殊滾齒刀的設計及完全過切概念，發展出可在一次的滾
齒加工過程中，快速創成出刀具全部之切削角、刀具容屑槽及主體外形之
滾齒刀。
本文之刀具創成設計方法主要是由齒輪嚙合原理及微分方程理論所架
構而成，亦利用漸開線理論及齒輪原理計算出刀具在不同轉位量時之切削
角 (正徑向斜角、離隙角、餘隙角) 及齒頂寬度變化情形，並針對刀具外
形所需之完全過切條件提出分析研究。在文中推導出直齒狀、螺旋狀、塑
膠切粒刀具之數學模式，提供刀具設計者參考，並藉由 CATIA 繪圖軟體建
構出刀具實體模型。
本文亦針對所設計出的刀具外形，進行 ANSYS 有限元素分析，透過不
同之元素類型及負載設定，分析模擬刀具二維簡化模型及三維模型下之實
際加工情形，並觀察其應力分佈趨勢。而後利用兩種不同之最佳化設計方
法，來求得符合目標函數、圓柱狀刀具設計限制及滾齒刀幾何限制條件下
之刀具最佳化參數設計值，讓設計者能快速取得最佳之設計參數。此外吾
人經由先前的程式基礎，整合撰寫成刀具設計軟體介面，讓設計分析流程
更為順暢有效率。以上研究流程將使本文之創新刀具設計方法，不論在刀
具參數還用、刀具特性分析、設計效率及實際適用性上達到最佳化之整體
性設計概念。

並列摘要

In this thesis, by the special design of hob cutter and undercutting
phenomenon, an effective generation method is developed to form the
multi-cutting angles, chip flue, and main body of the cutting tools in a single
hobbing process.
The approach is based on the principle of coordinate transformation, the
theory of differential geometry, and the theory of gearing. In addition, the
cutting angles (radial rake angle, relief angle, and clearance angle), the condition
of full undercutting, and the width of the top land of the cutter with difference
shifted amount were also studied. In this thesis, the mathematical models of the
spur-typed, helical, and plastic rotary knife cutting tools are derived, and CATIA
solid model software is used to construct the solid model of the cutting tools.
This research is beneficial as design guidance for tool designers.
The stress analysis are studied for the spur-typed, helical, and plastic rotary
knife cutting tools by the FEM. By applying the mathematical model of the
cutting tools proposed, the solid model is then transformed into the FEM model
file (ANSYS) for the 2D and 3D-stress analysis with different load, element type,
and material property Two different methods of optimization design, i.e., global
search method and optimum subroutine with MATLAB programming, are
applied to determine the optimum parameters of cutting tool satisfying the
objective function and the geometry constraint of rack cutter.
The results and concepts proposed in the paper would be beneficial for tool
designers to choose proper cutting tool parameters, and improve the design and
manufacturing efficiency of cutting tools.

參考文獻

15. C. Y. Wang, "The errors analysis for helical gears with double circular arc

3. B. W. Bair, "Computerized tooth profile generation of elliptical gears

4. S. L. Chang, and C. B. Tsay, "Computerized tooth profile generation and

undercut analysis of noncircular gears manufactured with shaper cutters,"

5. C. F. Chen, H. T. Lin, and C. B. Tsay "Mathematical model and undercutting