A Study on Improving the Spatial Precision of A Three-Axis Machine Tool by Scraping Based on Straightness

機台的空間精度是其性能的重要指標，為提高機台空間精度，鏟配修整是普遍的做法，然而鏟配向來以人工憑經驗加工，未見有系統地分析或探討其鏟配順序及位置與修整量對於空間精度的影響，本研究針對上述課題，以三軸工具機為載具，藉由量測各運動軸的直線度數據分析機器運動之空間誤差，並進一步依據此數據分析鏟配位置、順序與修整量，提高該機器運動精度至設定目標，以有效改善機台的空間精度。 研究主要成果有三部分：(1)經由量測各進給軸直線度的數據，並依據三軸工具機構型與尺寸參數，計算工具機在空間各點的空間誤差，此結果與海德漢控制器中的誤差補償進行比較，其結果顯示兩者平均差異小於0.3%；(2)經由量測進給平台的兩導軌直線度與平行度數據以及機台的幾何尺度，分析平台在導軌上的移動，藉此計算工具機在空間各點的誤差；(3)進一步依照空間誤差規格的需求，計算鏟配修整之位置與修整量，可迅速有效地達成目標規格。以本研究之三軸工具機為例，由其真直度估算空間1311點中誤差超過20μm的有87個點，經連續三次修整後，其空間誤差超過20μm的點逐步降為41點、15點與3點，修配四次後所有點之空間誤差皆小於20μm，顯示本研究所發展方法的有效性。本研究結果除可提供機械產業組配人員迅速有效地修整機台軌道以達成所需之精度外，亦可提供機台快速精度調整之依據。Spatial precision is the most important index for precision machinery. Manual scraping is the most commonly employed method to improve the spatial precision of a machine. While scraping is conducted manually, there is an urgent need to develop a method for improving the spatial precision on scraping sequence, location and amount. This investigation is aimed on the above issues to investigate a systematic methodology to analyze the spatial precision of a three-axis machine tool and to improve its spatial precision based on its straightness. Major contributions of this research achieved are as the following. (i) Developed a methodology to calculate volumetric errors (VEs), a major index of spatial precision, based on straightness of each feeding axis and geometric dimensions of the machine tool. The results were compared with the results by the Heidenhain iTNC530 controller and showed the average different is less than 0.1m/0.3%. (ii) Developed a methodology to calculate VEs based on straightness and parallelism of the guideways. (iii) Developed a methodology to calculate the location, sequence and amount of guideway scraping to reduce the VEs of the machine tool. As an illustrating example, a 3-axis machine tool with 87 points, among 1131 spatial points, with VE higher than 20μm. After three consecutive scraping, the points with VE higher than 20μm are rapidly reduced to 41 points, 15 points and 3 points respectively. The VEs of all 1131 points are reduced to less than 20μm at the fourth scraping. This result shows the effectiveness of the developed methodology in this study.致謝 i 摘要 ii ABSTRACT iii 目錄 iv 圖目錄 vi 表目錄 viii 符號表 ix 第一章 緒論 1 1.1研究動機與目標 1 1.2研究方法與步驟 2 1.3本文架構 2 第二章 理論與文獻回顧 4 2.1鏟配相關的研究回顧 4 2.2剛體運動學 6 2.3三軸工具機之座標轉換 9 2.4實驗量測設備與方法 13 第三章 進給軸直線度對機台空間誤差之影響分析 15 3.1空間誤差之定義 15 3.2 工件之空間誤差計算 16 3.3 刀具之空間誤差計算 20 3.4進給軸誤差對空間誤差影響分析軟體結果 24 3.5誤差分析之驗證 25 第四章 導軌誤差對空間誤差影響分析 32 4.1導軌基本假設 32 4.2導軌水平方向誤差計算 34 4.3導軌垂直方向誤差計算 35 4.3導軌誤差對空間誤差影響分析軟體結果 37 第五章 導軌修配分析 40 5.1空間誤差的敏感度與貢獻度分析 40 5.2 導軌修配準則 47 5.3導軌修配計算 48 5.3.1導軌修配水平角度誤差計算 48 5.3.2導軌修配垂直角度誤差計算 49 5.3.3導軌單點修配結果 49 5.3.4導軌單點修配後對整體誤差之影響 52 5.4導軌空間誤差修配分析結果 58 第六章結論與未來展望 60 6.1研究結論 60 6.2未來展望 60 參考文獻 61 附錄：本研究不同空間點之誤差分析結果與海德漢虛擬控制器計算之誤差補償比較 6