本論文針對臥式五軸工具機的雙旋轉軸提出一套幾何誤差包含四項安裝誤差與六項運動誤差批次量測系統，以東台精機開發出的HTT-500臥式五軸工具機作為實驗載體，此系統使用之量測儀器為單點觸發式測頭並搭配三顆標準校正球，利用校正球之幾何特徵回算出工具機誤差。根據國際標準規範，ISO 230定義旋轉軸的幾何誤差可以分為安裝誤差與運動誤差，安裝誤差是由於工具機零件在安裝過程中未能精確對齊理想位置所導致，此數值在旋轉軸的任何角度均保持一致；而運動誤差則源自於工具機零件在生產製造過程中出現的缺陷所導致，此數值會隨旋轉角度改變，在不同角度下產生不同的誤差值。過去的研究往往僅考慮安裝誤差或運動誤差其中之一，忽略了兩者同時存在於旋轉軸上的情況，然而這對工具機的定位精度會產生顯著影響。因此，本論文的目的是同步量測並解析雙旋轉軸的安裝誤差與運動誤差。
首先執行觸發式測頭的校正程序，之後進行三顆校正球的初始定位。利用已編寫的自動量測 G-code 程式，在設計好的特定角度下量測三顆校正球於不同角度下的座標值。透過分析工具機幾何結構，利用齊次座標轉換矩陣建立正逆向運動學誤差模型，推導標準校正球在不同旋轉角度下的理想位置，並與實際量測位置比較，建立幾何誤差的方程式，先計算安裝誤差並補償後，再計算運動誤差，以批次解析的方式提升計算結果的準確性，避免最小平方法在擬合誤差實失準。透過OP CUA通訊協定，系統實現了各量測階段的智慧串接，無論是初始定位、數據擷取、資料剖析、誤差計算、VCS補償表填寫，還是最終的補償驗證，都可以通過單一操作指令完成。將解出的幾何誤差數值輸入工具機Siemens控制器的 VCS 補償表中。結果顯示，補償前後體積誤差明顯降低，其中在不同量測角度下，A軸體積誤差平均降低 78.7%，B軸體積誤差平均降低 70.7%。這些結果充分證明了所提出方法的可行性與有效性。

This paper proposes a batch measurement system for identifying the geometric errors of the dual rotary axes in a horizontal five-axis machine tool. The system focuses on four location errors and six component errors, using the HTT-500 machine developed by Tongtai Machine & Tool Co. as the experimental platform. A touch trigger probe and three standard calibration spheres are used, and the geometric characteristics of the spheres are utilized to back-calculate the machine tool errors. According to ISO 230, location errors result from misalignment during assembly and remain constant at all rotation angles, while component errors are caused by manufacturing imperfections and vary with the rotation angle. Previous studies often considered only one type of error, neglecting the simultaneous presence of both, which significantly affects positioning accuracy. Therefore, this research aims to simultaneously measure and analyze both types of errors in the dual rotary axes.
The experiment begins with probe calibration and initial positioning of the calibration spheres. Using a self-developed automatic G-code program, the coordinates of the three spheres are measured at various predefined angles. A geometric error model is built based on homogeneous transformation matrices and kinematic analysis to derive the theoretical positions of the calibration spheres. These are compared with the actual measurements to construct error equations. To enhance computational accuracy and avoid overfitting in the least squares method, location errors are solved and compensated first, followed by the calculation of component errors through a structured batch analysis. The entire measurement process, including initialization, data acquisition, error calculation, compensation table generation, and final validation, is fully integrated via the OPC UA communication protocol. Experimental results show that volumetric errors were significantly reduced, with average reductions of 78.7 percent for the A-axis and 70.7 percent for the B-axis, verifying the feasibility and effectiveness of the proposed method.

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