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系統識別號 U0026-2607201011432400
論文名稱(中文) 以形狀創成函數探討五軸工具機組裝誤差對體積誤差之效應
論文名稱(英文) Investigation on Effect of Assembly Error of Five-axis Machine Tool on Volumetric Error Using Form-Shaping Function
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 98
學期 2
出版年 99
研究生(中文) 陳冠安
研究生(英文) Kuan-An Chen
學號 n1697158
學位類別 碩士
語文別 中文
論文頁數 91頁
口試委員 指導教授-李榮顯
口試委員-佘振華
口試委員-林昌進
中文關鍵字 五軸工具機  形狀創成函數  裝配誤差  體積誤差  敏感度分析  蒙地卡羅模擬 
英文關鍵字 Five-axis machine tool  Form-shaping function  Assembly error  Volumetric error  Sensitivity analysis  Monte Carlo simulation 
學科別分類
中文摘要 五軸工具機廣泛應用在加工自由曲面上,而加工精度為工具機製造者及使用者共同關注的焦點之一。而刀具位置誤差主要來自工具機幾何誤差,因此許多研究建立了數學模型欲分析工具機誤差,以便在設計階段做誤差配置或量測後做誤差補償,但對於誤差項的效應往往沒有清楚地推導及證明。然而不管是誤差配置或誤差補償,推導誤差項的效應都是不可或缺的步驟。本研究之目的在於提出一套數學分析方法,以形狀創成函數為基礎,分析工具機之各線性誤差項及旋轉誤差項對刀尖點中心位置誤差的影響。此數學模式更容易了解其物理意義,藉由齊次座標矩陣的運算性質能判斷出可以直接補償之誤差項。將數值代入誤差項中做敏感度分析,可比較各誤差項對體積誤差之貢獻度,並應用蒙地卡羅方法模擬區間之數值。最後以工具機組裝誤差為實例,應用本文所提出的分析流程並以人機介面實作,提供工具機設計或製造者一套分析的系統,依照不同的加工件可以對不同的工具機構形加以分析,建議出刀尖點中心位置誤差最小之工具機構形,可成為工具機在組裝公差設計時的分析工具。
英文摘要 Five-axis machine tool is widely used in machining freeform surfaces. Accuracy of machine tool becomes one of the most critical considerations for both manufacturer and user. The geometric errors of machine tool contribute to the major part of tool position error. Many previous works have established mathematical models for analyzing the errors of machine tool, in order to allocating errors in design stage or to compensating errors after measurement. However, the effect of error terms in the model was seldom studied and clearly derived. It plays an important role in either error allocation or error compensation. Therefore, the purpose of this paper is to present a mathematical analysis method for investigating on the effect of each translational and angular error terms on the tool center point error of the machine tool based on form-shaping function. This model not only is clear in physical meaning but also easy to identify the errors which can be compensated directly from the property of matrix. Numerical values are substituted for error terms to perform the sensitivity analysis. The contribution of each error term to the volumetric error has been compared. Monte Carlo method is used to simulate the interval values. Finally, a case study is given for analyzing geometric errors due to assembly errors of machine tool using the presented methodology. An evaluation interface for machine tool designer or user has been developed. It provides for the system user to analyze the different configuration of machine tool and suggest the one with minimum error of tool center point position. It can be used as a tool in assembly tolerance design of machine tool according to a given workpiece.
論文目次 摘要 I
英文摘要 II
誌謝 III
總目錄 IV
表目錄 VII
圖目錄 VIII
符號說明 X
第一章 前言 1
1-1 概述 1
1-2 文獻回顧 2
1-3 研究目的與範疇 7
第二章 理論背景 11
2-1 座標轉換矩陣 11
2-2 工具機構碼與形狀創成函數 12
2-3 矩陣運算性質 16
2-4 工具機加工誤差 17
2-4-1 幾何誤差 17
2-4-2 運動誤差 19
2-4-3 外在環境造成之誤差 20
2-4-4 加工誤差 20
2-5 組裝公差 21
2-6 蒙地卡羅模擬於組裝公差分析 22
第三章 系統核心理論 23
3-1 誤差矩陣 23
3-2 考慮誤差之形狀創成函數 27
3-3 誤差項對刀尖點中心位置之效應 29
3-4 可直接補償之誤差項 38
3-5 考慮偏置量之座標析統 40
3-6 分析結果之應用 41
第四章 工具機組裝誤差分析 43
4-1 建立組裝誤差之數學模型 43
4-2 組裝誤差分析系統之規劃與流程 54
4-2-1 情境分析 54
4-2-2 程式介面規劃 55
4-3 系統演算法 61
4-3-1 系統計算體積誤差最小之工具機 61
4-3-2 誤差敏感度分析 62
4-3-3 刀具中心誤差 63
4-4 系統實作 65
4-5 結果與討論 67
4-5-1 蒙地卡羅穩健性與區間模擬 68
4-5-2 敏感度分析與公差分配之比較 69
4-5-3 呈現體積誤差分佈 72
4-6 商用軟體驗證 80
第五章 結論與建議 85
5-1 結論 85
5-2 建議 86
參考文獻 88
自述 91
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