A Mathematical Model for Manufacturing Truncated-Cone Toroidal Cutters with Constant Pitch Helical Grooves

具等螺距螺旋溝槽之錐形圓鼻迴轉銑刀之製造模式

吳昌祚(Chang-Tzuoh Wu)

《高雄師大學報：自然科學與科技類》 28期 (2010/06) Pp. 1-24

https://doi.org/10.7060/KNUJST.201006.0001

摘要

數學理論的發展是推動現代刀具設計與製造技術進步的主要關鍵，亦是應用電腦輔助設計技術解決實際問題之重要橋樑。因此，本研究針對具有等螺距螺旋溝槽之錐形圓鼻迴轉銑刀進行探討，呈現了系統化的製造數學建模。藉由微分幾何原理與嚙合原理，推導出刃口曲線與螺旋溝槽之相關數學模式。基於包絡情況，本研究建構了刀具設計與製造模式等，歸類於複雜曲面加工的包絡反問題求解方法與程序。大部分迴轉銑刀之製造問題，諸如刃口曲線之設計、砂輪與螺旋溝槽之包絡反問題求解方法與程序，在本研究中均已提出討論。透過數值模擬結果，驗證了本研究結論是可行且有效的。

關鍵字

螺旋溝槽 ； 刃口曲線 ； 迴轉銑刀 ； 砂輪 ； 反問題

並列摘要

This paper presents a systematic method for design and manufacture of a toroidal type revolving cutter. By using the principles of differential geometry and kinematics, the correlative models of the cutting-edge and helical groove are presented. Based on the envelope condition, CAD approaches for solving the direct and inverse problems related to the manufacturing models are also presented. By modifying the feeding speeds of the grinding wheel, undercut and destruction during the grinding processes can be avoided. The deviation of the cutting edge and residual material caused by the proposed feeding speeds are simulated and discussed. According to the simulation results, post-process remedies are also introduced.

並列關鍵字

helical groove ； cutting edge ； rotating cutter ； grinding wheel ； inverse problem