本文係根據齒輪原理(Theory of Gearing)與微分幾何(Differential Geometry)進而提出一種新的單一刀具切削戟齒輪設計流程。在過去,小輪切削刀具參數是分別在大輪驅動面與非驅動面的計算點上藉由局部共軛理論推導而成,然而推導出的內刀與外刀的刀半徑差異過大,以至於無法安裝在同一個刀盤上,所以小輪的驅動面與非驅動面通常是由不同的刀盤切削而成。為了使小輪的內刀與外刀可以安裝在同一個刀盤上,本文提出一種創新的戟齒輪設計流程-單一刀具法。藉由改變內刀與外刀的壓力角來調整刀具計算點曲率半徑,使得大輪與小輪的刀具面能夠在節面上重合,且內刀與外刀刀半徑必須控制在合理的範圍之內。因此利用單一刀具法,小輪的兩側齒面可以在同一切削循環內由同一台CNC戟齒輪創成機切削而成。
Based on the theory of gearing and differential geometry, a novel uni-tool manufacturing process for hypoid gear set is developed. In the past, the cutter geometry for pinion cutting is derived according to the local synthesis data at the calculation point on the driving and coast gear tooth surfaces. The point radius difference between the inside blade (I.B.) and outside blade (O.B.) of the pinion cutter might be too big to fit in the same head cutter. Therefore, the driving and driven sides of pinion are usually cut in the different hypoid generator with different head cutter. In order to make sure the I.B. and O.B. of pinion can be installed on the same cutter head, a novel hypoid gear uni-tool design process is developed by modifying the I.B. and O.B. pressure angle to adjust the point radius difference and making the pinion and gear cutter cone surface coincides with each other in the pitch plane. The point radius difference of I.B. and O.B. is controlled within the allowable range to fit in the same cutter head. With this uni-tool feature, both side of tooth surface of pinion can be cut in the same CNC hypoid generator in the same cutting cycle.