本論文利用觸發式測頭與精密校正球作為量測媒介，建立了一套完整的旋轉軸幾何誤差量測系統，以百德機械的MF400U五軸工具機作為實驗載體，該機台為業界常見的中小型搖籃式工具機，此量測系統的優點為安裝方便，價格便宜，並可應用在不同的構型上，達成建立快速線上誤差量測系統的目的，符合實際需求。根據國際標準規範，幾何誤差分為安裝誤差與運動誤差，兩者的定義與成因皆不同，安裝誤差為工具機各零件安裝時的位置沒有對準或沒有裝配密合所產生，而運動誤差則為工具機各零件在生產製造時有瑕疵所產生，安裝誤差一般存在於旋轉軸的任何誤差，且誤差值皆相同，運動誤差值會隨著轉動角度做變化，在不同角度有不同的誤差值，依據這次特性去區分兩者。在先前研究往往會忽略安裝誤差求且運動誤差，反之亦然，但兩者會同時存在於旋轉軸上，並對工具機定位精度造成影響，因此本論文目的為同步量測求解旋轉軸安裝誤差與運動誤差，改善因為旋轉軸定位精度不佳而造成的刀尖點相對於工件的體積誤差。
經由對工具機的幾何結構進行分析，利用齊次座標轉換矩陣建立工具機的正逆向運動學，觀察各個運動軸之間的座標轉換關係，推導出校正球在不同旋轉軸角度下的理想位置，並與實際量測到的校正球實際位置之間做相扣，建立出包含幾何誤差的方程式，最後透過最小平方法同時解出旋轉軸的安裝誤差與運動誤差。將解出的幾何誤差帶入工具機進行補償後，發現補償前後體積誤差明顯降低，在不同的量測角度下，體積誤差平均下降了80.7%，證明此方法的可行性，本論文提出了一套能夠同步量測與解析五軸工具機旋轉軸幾何誤差的量測系統，並能進行機上自動定時量測，發展出自動化、智能化的量測儀器。

This paper proposes a synchronous measurement system of four position-independent geometric errors (PIGEs) and six position-dependent geometric errors (PDGEs) for the rotary axis in five-axis machine tools. This study takes the five-axis machine tools MF400U produced by Quaser Machine tools Inc. Machinery as the research vehicle. Previous studies on identifying geometric errors of rotating axes usually cannot solve PIGEs and PDGEs simultaneously, so the key points of this paper is synchronous measurement and calculation of PIGEs and PDGEs (axial and angular positioning errors) through only one measuring process. Compared to commercially measuring instruments, the advantages of this measurement system are easy to install, inexpensive, and can be applied to different types of five-axis machine tools which can achieve the purpose of establishing a fast on-machine error measurement system. First step of this process is according to the type of machine tool, establish the mathematical model and calculate the geometric error equations. Then find out the difference between the ideal and real center positions of the calibration sphere by touch-triggering probe when the machine’s rotary table is at different angles. Finally, we can get the geometric errors of the rotary table by putting the experimental data into the mathematical algorithm.
After the experiment, the geometric errors calculated by this method are compensated in the controller. The feasibility of this method is checked by measuring the volumetric error of the machine tool before and after compensation. The results show that the deviation of the volumetric error of the machine tool is significantly reduced to 2.31 µm from 11.97 µm after compensation. It is expected that this method can be used for simultaneous measurement of the geometric error of the machine tool’s rotary axis and for different type and situation.

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