中文摘要
本研究針對非軸對稱光學曲面，發展一套簡易的CAM系統，建構的自動平滑化加工製程，進行平滑化製程對於形狀誤差與表面形貌的探討。首先在CAD環境，依非球面公式所繪製的曲線，利用邊界混合的指令，建構出以NURBS表示的自由曲面，再與設計的光學曲面比對，建構出參數式的光學曲面。接下來以Borland C++ 6開發一套簡易的電腦輔助製造程式，探討路徑建構與形狀誤差。路徑建構是結合往復式、碎形路徑與參數式刀具(Automated Grinding Tools Planning)，依法線向量或是Minkowski Addition方法進行刀具路徑補償。再將所建構的路徑依Z-Map模式作為加工切削模擬，求出殘留的軸向形狀誤差。實驗方面主要是以20x20 mm的雙圓弧曲面(Bi-spherical surface)進行加工，驗證程式所模擬形狀誤差與磨拋製程，與針對平滑化加工所造成的形狀誤差與表面形貌改變。量測方面是將雙圓弧曲面利用表面輪廓儀Mitutoyo CV-1000取得通過軸心的個斷面進行分析，將取到的點資料以曲線近似法進行擬合，估算出形狀誤差。由實驗結果得知，以銑刀加工的形狀誤差與模擬結果誤差約為23.4%以下。平滑化加工針對球銑刀、鑽石磨棒與帶柄砂輪進行加工，其造成均方根(RMS)形狀誤差分別為2.2、4.6與3.6μm，波峰至波谷(PV)值分別為12.1、27.8與18.7μm。本研究針對精密曲面分析平滑化加工製程所造成的形狀誤差之探討，使未來的曲面自動磨拋系統可達到鑽石切削加工所需的形狀精度與表面粗糙度要求。

Abstract
This research is to investigate the form error and surface roughness of non-axial symmetrical optical surface in an automated surface smoothing system with a developed Easy CAM software. First, 3D curve is designed according to the aspherical function and utilized the boundary blending to construct a free form surface by Non-Uniform Rational B-Spline (NURBS) representation and the parametric optical surface constructed after comparing with designed optical surface. Then an computer-aided manufacturing program, Easy CAM has been developed to generate the toolpath and estimate the form error using Borland C++ 6. ZigZag and Fractal toolpaths are considered with automated Grinding Tools Planning (AGTP) parametric tools. Toolpath compensation methods by the normal vector or the Minkowski operations have been developed and investigated. The constructed toolpahts are displayed by the Z-map model and also the axial residual form error can be estimated. Experiments were performed to verify the simulated form error from the developed Easy CAM program, surface smoothing processes on a 20x20 mm bi-spherical surface were performed by a CNC machining center attached with a grinding that were tested for different setup and toolpaths. For measurement, the profile data through the center of cross-feed direction of the bi-spherical surface is acquired from a Mitutoyo CV-1000 profilometer and then the form error is estimated by curve fitting method. Experimental results of ballend mills cutting show that the error difference between the simulated and the measured date is low than 23.4%. The root-mean-square (RMS) of form error and Peak-to-Valley (PV) are 2.2 and 12.1 μm with ballend mills, there are 4.6 and 27.8 μm with mounted diamond tool grinding, and there are 3.6 and 18.7 μm with mounted grinding tool in smoothing process. In the future, the Easy CAM for surface smoothing process would continue to evolve into an automated finishing system to achieve fine form accuracy and surface roughness for diamond machining process of optical surfaces.

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