因應競爭日益激烈之國際工業市場，五軸工具機已成為工業市場中最不可或缺之一。影響五軸工具機精度有以下重要因素: 幾何誤差、熱變形、結構誤差、靜態誤差等，其中，幾何誤差為最具影響之誤差源。通常，補償幾何誤差之方法為透過修改誤差補償控制器來提升工具機之精確度。但是，在本研究中我們無法修改五軸工具機之控制器。因此，本研究對工件進行多次之切削試驗，並且量測工件上之切削路徑，進一步估算與補償五軸工具機之幾何誤差。
五軸工具機幾何誤差的測量方法有三次元量床(CMM)及雙球桿(DBB)及雷射干涉測量儀，但是大多數的方法並沒有考慮切削力對於五軸工具機的影響。本研究提出了一種對工件進行實際切削的方法，用於校驗及估算五軸工具機上各軸之幾何誤差。使用齊次座標轉換矩陣法考慮及分析幾何誤差，在五軸工具機上設計並實際進行一系列切削試驗，透過CMM量測切削結果，比較CMM和CAD模型的測量數據，可以計算切削結果的誤差。
從第一次切削實驗中可獲得切削誤差，進一步用於補償及重新設計CAD模型，可以從新的CAD模型中獲得切削路徑，於同一個五軸工具機上重新進行切削工件之實驗，再透過第二次比較CMM的測量數據和原始CAD模型，可以獲得第二次切削實驗的誤差。齊次座標轉換矩陣(HTM)用於建立幾何誤差分析模型，進一步估測每個實驗之幾何誤差。將獲得之誤差數據進行分析與優化，其中僅使用最有效之因子來代表工具機之誤差。本研究將最佳化理論應用於幾何誤差之計算，並透過線性規劃與拉格朗日乘數法作為誤差估測模型。
在本研究的實驗中使用五軸DMU 70 eVolutilon工具機，包括X軸、Y軸、Z軸、B軸及C軸，而透過PH10T CMM三軸量床測量切削結果數據，本研究中工具機之B軸及C軸為非正交且成45度相交，將本研究提出的補償算法應用於新的刀具切削路徑生成之後，而實驗結果顯示，切削之誤差有效降低，切削之精度顯著提高。

Responding with an increasingly competitive international industrial market, the five-axis machine tools has become the most commonly used one in the industrial market. The important factors affect the accuracy of the five axis machine tool: geometric errors, thermal deformation, structural error, static error and so on. Among them, geometric errors are the most effective one in the error sources. Generally, to improve accuracy of a machine tool can be achieved by modifying the error compensation parameters in the controller. However, most of the methods do not consider the effects of cutting forces on the five-axis machine tool. This study proposes a workpiece real cutting method to identify and estimate the geometry errors of each axis on the five-axis machine tool. The geometric errors are considered and analyzed by using homogeneous coordinate transformation matrix method. A series of cutting tests were designed and performed on a five-axis machine tool. The cut results were measured by CMM. The errors of cutting results can be calculated or estimated by comparing the measured data from CMM and workpiece CAD model.
The obtained cutting errors from first cutting test are then further used as compensate data to redesign the CAD model. A new cutting path can be obtained from the new CAD model and then used to re-cut the workpiece on the same five-axis machine tool. The errors of second time cutting tests can be obtained again by comparing the measured data from CMM and the original workpiece CAD model. The homogeneous coordinate transformation matrix (HTM) is used to establish the geometric error analysis model for estimating the geometric errors on each experiment. The obtained error data will be analyzed and optimized and only the most effective factors are used to represent the errors of the machine tool. We apply the optimization theory for geometric errors computation. The Linear program and Lagrange multiplier methods are used as the error estimating models in this research.
A five-axis DMU 70 eVolutilon machine tool, including X-, Y-, Z-, B- and C-axis, is used during the experiments in this research. A PH10T CMM machine is used to measure the cutting result data. It is worth to mention that B-axis and C-axis of the machine tool in are non-orthogonal and they intersect at 450 situation. After applying the compensation algorithm addressed in this research into the new tool cutting path generated, the experimental results show that the cutting errors are effectively reduced and the cutting precision is significantly improved.

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