根據齒輪原理與微分幾何觀念，本論文推導出泛用滾刀磨銳機之滾刀刃口面數學模式。此數學模式可以做為逆推砂輪軸向廓形的基礎，並能模擬砂輪磨銳滾刀刃口面的運動。此加工法為成形砂輪磨法，當輪磨不同螺旋角的滾刀刃口面所需之砂輪廓形並不相同，本論文主要目的為探討是否能使用相同的砂輪廓形，磨銳一定範圍螺旋角的滾刀刃口面。另外一個目的則是建立現有CNC滾刀磨銳機之滾刀刃口面數學模式，及其製造誤差修正的方法。首先根據陸聯精密公司CNC滾刀磨銳機之機台結構配置，建立六軸CNC滾刀磨銳機座標轉換矩陣，再利用泛用滾刀磨銳機和六軸CNC滾刀磨銳機之磨削運動必需相同的關係，可由已知泛用滾刀磨銳機機械設定推導出六軸滾刀磨銳機之機械設定，進而得到此機器磨削之滾刀刃口面數學模式。依據此滾刀刃口面數學模式，可建立機器各軸之於磨削面的敏感度矩陣，再加上已知之滾刀刃口面之誤差量，使用線性回歸的方法計算出機械設定修正量，最後使用修正後機械設定磨削工件，以達成降低機械製造誤差的目的。本論文只做到數學模式建立和推導，所有誤差和修正結果皆使用電腦程式模擬。

Based on the theory of gearing and differential geometry, we develop a mathematical model for the cutting face of hob based on the universal-type hob sharpening machine. Apply the proposed mathematical model, the axial profile of the grinding wheel can be derived, and it also can simulate the motion for the grinding wheel sharpening the cutting face of hob.
This manufacturing process is the profile grinding method. It is well-known that the axial profiles of wheels for grinding different helical angles of hob flutes are not the same in this process. Therefore, the main purpose of the thesis is to investigate whether the same wheel profile can be use to sharpen the cutting faces with a range of helical angles to satisfy the demand of hob precision or not. Another purpose is to establish the mathematical model for the cutting face of hobs based on the six-axis CNC hob sharpening machine and its correction method for reducing the manufacturing errors.
Based on the structure of CNC hob sharpening machine of Luren Precision Co., Ltd, the coordinate systems of the six-axis CNC hob sharpening machine are established at first. The six-axis movement for resharpening the cutting face of hob can be obtained by way of the conversion from a universal machine to a six-axis machine. And then, the mathematical model for the cutting face of hob is derived based on the six-axis CNC hob sharpening machine.
Based on the mathematical model of the hob cutting face, the sensitivity matrix of six-axis machine settings is established. According to this sensitivity matrix and the given flank errors of hob cutting face, the corrections for six-axis machine settings can be calculated by the linear regression. The corrections of machine settings can be applied to regrind the work-piece for reducing the manufacturing errors. In this thesis, all results are obtained by the computer simulation.

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