目前工業界在二維路徑補償可透過CNC 控制器做內建磨耗補正、手動偏移NC 加工路徑，甚至使用外部程式運算來達到更精確之加工尺寸。但在三維曲面補償，現階段一般CNC 控制器是無法做尺寸補正，隨著曲面應用越來越廣泛，尺寸精度的要求也隨之提升。本研究之目的為開發一自動化補償系統，透過線上量測設備並藉由NX Open API 以及Visual Studio C#撰寫NX 二次開發程式，以改善CNC 銑床加工的尺寸誤差、尺寸歪斜，以及可預期之誤差來源等問題。實驗所使用之加工設備為五軸數控銑床，並使用RENISHAW OMP400 進行線上檢測，所使用之軟體包含NX CAD/CAM 以及Visual Studio C#程式語言，並開發自動曲面誤差補償演算法，以補償銑床加工產生之尺寸偏差。
NX 二次開發程式包含量測工法之佈點功能、鏡射補償方法與向量修正理論、曲線及曲面擬合方法和CAD 模型重建功能。透過程式讀取線上量測後之量測報表，取得量測點之X、Y、Z 座標值並建點於NX CAD 模型上，自動計算並透過向量修正理論取得實際曲面之補償點，再將所有補償點劃分區塊並擬合最佳階數曲線。藉由擬合曲線並透過NURBS 理論以擬合曲面，最後自動重建CAD 模型，以生成精加工路徑，即為補償路徑。
本研究提出一向量修正理論，認為理想量測點與實際量測點將受曲面複雜度、探頭真實直徑、機台幾何誤差及量測誤差等影響，導致兩量測點並非於相同量測向量上，實際測試其在五軸工法上有顯著的誤差影響，其含有0.001 mm 至0.007 mm 之誤差，可透過此方法修正。
三維曲面自動化誤差補償實驗，分別進行三種曲面模型加工測試，其一為由二次曲線組成之曲面，其二為曲面由兩條二次曲線一凹一凸掃掠成形，最後為曲面由兩條二次曲線以及兩條導引曲線組成。比較三種曲面模型之中加工量測結果與補償後數據，其誤差百分比平均下降分別為87.30 %、92.12 %、89.89 %，代表補償後之準確度有明顯地提升。而根據其標準差平均分別下降4.8 μm 、2.5
μm 、1. 9 μm ，代表此誤差補償方法可確實改善工件尺寸歪斜之問題，並提升工件尺寸之精密度。
使用不同控制器之機台進行驗證自動化誤差補償系統，由第一個曲面模型進行測試，其4 個曲面誤差百分比分別下降85.84 %、85.27 %、28.55 %、82.74 %，而母體標準差分別下降1.9 μm 、2.1 μm 、1.6 μm 、1.7 μm ，結果證明其自動化系統可應用於不同之機台。
本研究結合CAD/CAM 二次開發達成自動化，而習知技術所使用佈點演算法，需倚靠CAIP(Computer-Aided Inspection Planning)或其它軟體，無法將加工、量測、補償一併整合於同一系統上，對自動化來說將造成許多不必要之麻煩。故本研究進行開發並將功能統一於同一軟體上，即在CAD/CAM 上實現全自動加工、量測及補償，將前述工作時間由幾小時降至約1 分鐘，且可避免不同操作人之人為疏失。

Currently, the industry can compensate errors by using the compensation function
in a CNC controller to achieve better accuracy in 2D dimensions. However, most of
CNC controller cannot compensate errors effectively for free-form surfaces. As the applications of the free-form surfaces are getting popular, the requirements for dimensional accuracy increase. We use Visual Studio C# and NX Open API to write the secondary development program of NX. The objective of this research was to enhance the accuracy and precision of parts made by CNC machines by compensating the errors. A five-axis CNC milling machine was used in the experiments, and on-line probe used in the experiments was RENISHAW OMP400. It follows that an automatic surface error compensation algorithm was developed to compensate the errors caused by milling.
NX secondary development includes the function of distributing measuring points,
compensation of error-mirroring method, the theory of revising compensating vector,the curve-fitting method, and the CAD model reconstruction. First, the measurement results were read, then the measured points were created in NX CAD, and the the compensation points were figured out by the error-mirroring method. After obtaining compensated points, we will do curve-fitting by using optimal fitting parameters algorithm. From the fitted curves, fit surface can be automatically reconstructed by using NURBS (Non-Uniform Rational B-Spline) theory. Finally, Reconstruct CAD model automatically to generate finishing cutting tool path, which is the path of compensation.
We also proposed the vector correction theory, as we found that the ideal
measurement points and actual measurement points are not always on the same normal vector, which can be affected by the complexity of the measurement surface, the diameter of probe, the geometrical errors of the machine, and the measurement errors, etc. The measurement can be corrected by the vector correction theory.
In this research, there are three different types of surfaces, and they are a convex surface, a half-concave half-convex surface and a surface sweep by the concave and convex surface. The absolute errors of surface models were reduced by 96.65 %, 91.89 %, and 89.89 %, respectively. Moreover, the standard deviations were reduced by 4.8 μm 、2.5 μm and 1.9 μm , respectively, which mean that this error compensation method can solve the problem of uneven errors effectively, and also can enhance precision of dimension.
To verify that the automatic error compensation method can be used on different
machines, a model was tested that has four surface. The absolute errors of surface models were reduced by 85.84 %、85.27 %、28.55 %、82.74 %, and the standard deviations were reduced by 1.9 μm 、2.1 μm 、1.6 μm and 1.7 μm , respectively. The results turned out that automatic error compensation system can be applied to different machines.
This research was implemented by using NX CAD/CAM secondary development program to achieve automation. We combined machining, measuring, and compensating into one one software package, which not only can avoid the communication among different software packages, but also save time and prevent human from making errors.

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