孔於長刀桿切削下不規則輪廓成形之理論

Abstract

從過去的文獻中，我們發現幾乎沒有較嚴格的運動公式描述在長刀桿的切削狀況下，不規則孔形的成形原因。建立在一些理論的分析，這篇論文架構了一個統御方程式為了探求在深孔鑽中多邊孔形的形成原因。藉由模擬統御方程式，我們展現出整個的切削過程發現多邊孔形形成的原因與夾頭(chuck)上的爪數有關，也就是說，多邊孔形的邊數等於夾頭上的爪數。這個現象應該是由被富里葉級數（Fourier series）展開後簡諧徑向切削力所導致。這個結果不同於較早的一些究研只有觀察被加工工件的某單一截面而較不具上述結果的說服力，也因此沒有被歸納成結論。另一個重要的結果是系統共振的發生只有當轉述接近其各階自然頻率的1/n，此處，n代表爪數，且當轉速越接近自然頻率，多邊孔形越明顯。這個結果在可接受的公差內對不同長度刀桿作切削速度選擇最佳化。

Literatures investigation revealed that there is no rigorous dynamic equation for making a description of formation of irregular profile in a machined hole with a long tool shaft. Based on some theoretical analysis, this paper constructed a governing equation to search for the formation of irregular profile in hole making. By simulating the governing equation, the entire cutting processes are shown to interpret the number of multi-cornered shape is related to the number of jaws on the chuck, i.e., n-cornered shape is caused by n-jaw chuck. The phenomenon can be resulted from the harmonic radial cutting force expanded as Fourier series. This result is different from some earlier researches just observing a certain cross-section in a cylindrical machined workpiece. Another important outcome is resonance occur only if the spindle speed approaches the 1/n of natural frequencies, where n is the number of jaws on the chuck. And the multi-cornered shape get more prominent when the spindle is closer to the 1/n of natural frequencies, therefore, we can optimize the cutting speed within an acceptable tolerance for various length of tool shaft.