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研究生:朱昆磊
研究生(外文):Kun-Lei Chu
論文名稱:以幾何誤差模型與切削誤差模型提升銑削加工精度
論文名稱(外文):Using Geometric and Cutting Error Models to Enhance the Milling Precision
指導教授:王郁仁
指導教授(外文):Wang,Yu-Jen
學位類別:碩士
校院名稱:國立中山大學
系所名稱:機械與機電工程學系研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2023
畢業學年度:112
語文別:中文
論文頁數:123
中文關鍵詞:幾何誤差最小平方法切削力比切削力剛度模型
外文關鍵詞:Geometric ErrorLeast Squares MethodCutting ForceSpecific Cutting ForceStiffness Model
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在五軸工具機的搖籃型(AC)設計中,誤差來源組合在一起時,形成了位置相依性幾何誤差(Position-Dependent Geometric Errors, PDGEs),主要成分涵蓋了定位、真直度和旋轉等誤差。為獲得這些誤差數據,採用了雷射干涉儀進行量測,使用不同的鏡組對各種幾何誤差進行測量,利用CARTO軟件來進行數據分析。
幾何誤差的預測方面,使用雷射干涉儀進行量測,利用最小平方法(Least Squares Method, LSM)來建立一個與座標相關的模型,預測特定座標的幾何誤差。通過運動學誤差模型校正機台精度,計算出各個誤差項造成的整體誤差,並確定主要的誤差來源,找到與機台定位誤差相關的主要誤差項,使用CAD/CAM軟體(MasterCAM)來規劃刀具的路徑。再使用雷射干涉儀(Laser Interferometer)進行空間點坐標的採集,提供三維空間的精確坐標值。
銑削過程中三個分力可以通過向量分解為三個主要方向的力:切削方向力(Main Cutting Force,以F_c表示)、進給方向力(Feed Force,以F_f表示)、和軸向方向力(Axial Force,以F_a表示)。
本研究建立的切削力模型是基於Victor和Kienzle理論,考慮受力材料面積和比切削力乘積組合進行分析。在比切削力部分,考慮特定切削力,即切削橫截面積A=1 mm∙1 mm=1 mm^2時,材料常數會決定切削過程中的力量大小和方向。另考慮刀具前角、刀具在切削過程中的變形現象、切割速度及磨損係數等因素,建立修正因子,根據加工過程中刀具和工件的特性修正加工力量,使模型更加完善。
另採用最小平方法和運動學誤差模型,分析X360、X280和X200線段補償前後精度變化,結果X和Y方向補償後精度明顯提升。由於Z方向初始誤差低,且重力影響顯著,故不進行Z方向補償。利用TC50 3D測頭和剛度模型驗證,預測主切削向切削力(F_c),在不同切削深度和進給速率下精度提升至98%。然而,刀具軸向剛度與顫振問題導致軸向量測不準確。
In the cradle type (AC) design of five-axis machine tools, when error sources are combined, they form Position-Dependent Geometric errors (PDGEs). These primarily encompass errors related to positioning, straightness, and rotation. To precisely acquire this error data, a laser interferometer was employed for measurements. Different mirror assemblies were used to measure various geometric errors, and the CARTO software was applied for data analysis.
For geometric error prediction, the laser interferometer was again used for measurements. The Least Squares Method (LSM) was utilized to establish a model related to coordinates, predicting the geometric errors of specific coordinates. The kinematic error model was adopted to correct machine accuracy, calculating the overall error caused by various error terms. The primary error sources were identified, particularly those related to machine positioning errors. The CAD/CAM software (MasterCAM) was employed to plan the tool path. Furthermore, the laser interferometer was utilized to collect spatial point coordinates, providing accurate coordinate values in three-dimensional space.
In the milling process, the three partitioned forces can be vector-decomposed into three primary directional forces: the Main Cutting Force (F_c), the Feed Force (F_f), and the Axial Force (F_a).
The cutting force model established in this study is based on the theories of Victor and Kienzle. It considers the force-receiving material area and the combination of specific cutting force products for analysis. In terms of specific cutting force, when considering a cutting cross-sectional area of A=1 mm∙1 mm=1〖 mm〗^2, the material constant determines the magnitude and direction of the force during cutting. Factors such as the tool''s rake angle, deformation of the tool during cutting, cutting speed, and wear coefficient were also considered to establish correction factors. This allowed for adjustments in the machining force based on the characteristics of the tool and workpiece during the process, refining the model.
The study adopted the least squares method and a kinematic error model to analyze the accuracy changes before and after compensation for the X360, X280, and X200 line segments. The results showed that the accuracy in the X and Y directions significantly improved after compensation. As the initial error in the Z direction was low and the impact of gravity was significant, no compensation was carried out in the Z direction. Using the TC50 3D probe and a stiffness model for verification, the predicted main cutting direction cutting force (F_c) achieved an accuracy improvement up to 98% under various cutting depths and feed rates. However, the axial stiffness of the tool and issues with chatter led to inaccuracies in axial measurement.
論文審定書 i
誌謝 ii
摘要 iii
ABSTRACT iv
目錄 vi
圖次 viii
表次 x
符號說明 xi
第一章 緒論 1
1.1前言 1
1.2研究動機與目的 2
1.3文獻回顧 2
1.3.1銑削加工精度 3
1.3.2幾何誤差模型 6
1.3.3體積移除率及切削力誤差模型 14
1.4本文架構 24
第二章 幾何誤差校正 25
2.1幾何誤差量測 25
2.2幾何誤差項預測 27
2.3主要誤差項估計模型 28
2.4誤差靈敏度辨別 33
2.5刀具路徑規劃 35
第三章 切削力誤差校正 36
3.1切削力 37
3.2切削力模型建立 38
3.2.1切削力模型 40
3.2.2受力材料面積 41
3.2.3比切削力 44
3.3剛度模型 47
第四章 後處理程式建立 50
4.1幾何誤差後處理程式建立 50
4.1.1誤差關係式輸入 51
4.1.2座標轉換 51
4.1.3 G-Code讀取 53
4.1.4幾何誤差G-Code轉換結果顯示 54
4.2切削誤差後處理程式建立 55
4.2.1切削參數輸入 55
4.2.2刀具路徑輸入 57
4.2.3切削誤差結果輸出 58
第五章 實驗與驗證 60
5.1幾何誤差實驗 60
5.1.1實驗裝置 60
5.1.2幾何誤差量測 63
5.1.3幾何誤差項刪減差異 67
5.1.4幾何誤差補償結果 72
5.2銑削誤差實驗 77
5.2.1實驗裝置 78
5.2.2銑削誤差實驗 81
5.2.3實驗結果 89
第六章 結論與未來展望 101
6.1結論 101
6.2未來展望 102
參考文獻 104
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