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研究生： 吳秉芳
Wu, Ping-Fang
論文名稱： 包含偏心效應之球銑刀銑削力解析模式及線上偏心幾何判別
An analytical Model of Milling Force in Ball-end Milling with Runout and Its Application to On-Line Identification of Cutter Runou
指導教授： 王俊志
Wang, J-J Junz
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2002
畢業學年度： 90
語文別： 中文
論文頁數： 80
中文關鍵詞： 球銑刀 、偏心 、切屑負載 、銑削力 、偏心幾何判別
外文關鍵詞： milling forces, identification of runout geometry, Ball-end milling, chip load, runout
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    • 摘要
    　　本文主要針對球銑刀在受到偏心影響時，推導其切屑厚度受偏心影響的表示式，並且探討因切屑負載變化而導致的切削區域變動以及始進角與終切角變化，發現偏心值對於每刃進給量比值的大小直接影響到切削區域的變化。再以推導的切屑厚度為基礎，進而推導球銑刀受偏心影響的銑削力解析模式，發現偏心會導致在主軸轉速頻率上產生一銑削力，並針對偏心幾何參數，即偏心量r及偏心角度l的變化及各種加工條件探討其銑削力變化情形。

    　　在偏心幾何判別應用方面，應用銑削力解析模式，可以由實驗銑削力逆求偏心幾何。利用兩次切削實驗的平均力或是一次實驗第一諧合力來判別切削常數，並以判別的切削常數為基礎，透過因為偏心而在主軸頻率所產生的銑削力來判別動態的偏心幾何。最後再透過各種不同進給的槽銑實驗來驗證模式，而得到一致性的判別結果。

    Abstract

    　This thesis presents an analytical model for the chip load variation and milling forces in ball-end milling with cutter runout. The cutting region and chip load variation is first discussed and an analytical expression for the chip thickness is discussed in this paper. Based on the chip thickness expression, the force model of ball-end milling with cutter runout is established. The force model shows the that the presence of cutter runout causes a significant change in the cutting force at the spindle frequency. The variation of milling force is shown to vary with the change of runout geometry, the runout magnitude, r, and the angular position, l.
    　Method for identification of cutting costants and runout geometry are presented. Two methods are presented to identify these cutting constans. The first method uses only the first harmonic components of the milling forces, and the second methods utilizes the average forces with two feeds per tooth. Based on the identified cutting constants, the identification of runout geometry is developed by using runout component cutting forces. Finally,the milling force model and the identification of runout geometry is verified through milling experiments.

    總目錄 中文摘要……………………………………………………………………I 英文摘要……………………………………………………………………II 致謝…………………………………………………………………………III 總目錄……………………………………………………………………IV 圖目錄……………………………………………………………………II 表目錄……………………………………………………………………XI 符號說明…………………………………………………………………XII 第一章 序論…………………………………………………………………1 1.1 研究動機…………………………………………………………1 1.2文獻回顧………………………………………………………2 1.2.1關於偏心效應……………………………………………2 1.2.2 關於銑削力模式……………………………………………3 1.3 研究範疇及論文架構……………………………………………6 第二章 球銑刀幾何及切屑分佈分析………………………………………7 2.0 前言…………………………………………………………………7 2.1 座標幾何及刀具幾何………………………………………………7 2.2 包含偏心效應的切屑厚度變化…………………………...………9 2.3 切削區域變化與切屑負載………………………………….……13 2.4 偏心造成的切削窗變化…………………………………………24 2.5 結語………………………………………………………………28 第三章 包含徑向偏心之銑削力…………………………………………...29 3.0 前言………………………………………………………………29 3.1 局部銑削力………………………………………………………30 3.2 基本切削函數與座標轉換函數…………………………………33 3.3 總銑削力模式……………………………………………………35 3.4 銑削力模擬………………………………………………………41 3.5 結語………………………………………………………………49 第四章 偏心幾何之線上識別……………………………………………...50 4.0 前言………………………………………………………………50 4.1 切削參數之識別…………………………………………………51 4.1.1 運用平均力判別切削常數……………………………….51 4.1.2 運用第一諧合力判別切削常數………………………….54 4.2 運用第一及第二諧合力判別相位角……………………………55 4.3 偏心幾何識別……………………………………………………59 4.4 結語………………………………………………………………62 第五章 球銑刀偏心幾何判別實驗………………………………………...63 5.1 實驗目的…………………………………………………………63 5.2 實驗設備…………………………………………………………63 5.3 實驗刀具及工件材料……………………………………………64 5.4實驗步驟與實驗結果……………………………………………..64 5.4.1 動態判別結果……………………………………………...64 5.4.2 靜態量測結果……………………………………………...65 5.4.3 銑削力模擬結果…………………………………………...66 5.4.4 不同轉速偏心比較結果結果……………………………...69 5.5 結語………………………………………………………………74 第六章 結論與建議………………………………………………………...75 6.1 結論………………………………………………………………75 6.2 建議………………………………………………………………77 參考文獻…………………………………………………………………….78 自述………………………………………………………………………….80 圖目錄 圖2.1 球銑刀座標…………………………………………………8 圖2.2 球銑刀之工件座標與刀具座標………………………….9 圖2.3 四刃球銑刀切削路徑示意圖-沒有偏心………………………….10 圖2.4(a) 切屑厚度示意圖……………………………………………….12 圖2.4(b) 切屑厚度示意圖……………………………………………….12 圖2.5(a)半徑變化示意圖…………………………………………13 圖2.5(b)半徑變化示圖…………………………………………..13 圖2.6(a) 球銑刀逆銑徑向切削區域圖………………………………….14 圖2.6(b) 球銑刀順銑徑向切削區域圖………………………………….14 圖2.6(c) 球銑刀步徑銑削逆銑徑向切削區域放大圖………………….15 圖2.7 球銑刀逆銑軸向切削區域放大圖 N=4…………………………..15 圖2.8 球銑刀切削區域 N=4………………………………………………15 圖2.9(a) 未受偏心影響之球銑刀正規化切屑負載分佈圖……………….16 圖2.9(b) 未受偏心影響之球銑刀正規化切屑負載分佈圖-球形區域……16 圖2.10(a)受偏心影響之切屑厚度變化-ho=0.1…………………………….20 圖2.10(b) 受偏心影響之切屑厚度變化-球形區域-ho=0.1……………….20 圖2.10(c)受偏心影響之切屑厚度變化-ho=0.3…………………………….20 圖2.10(d) 受偏心影響之切屑厚度變化-ho=0.5….…20 圖2.10(e)受偏心影響之切屑厚度變化-ho=0.8…………………………….20 圖2.10(f) 受偏心影響之切屑厚度變化-球形區域-ho=0.8...……………...20 圖2.11(a) 切削區域變化圖-N=2…………………………………………...21 圖2.11(b) 切削區域變化圖-N=3…………………………………………...21 圖2.11(c) 切削區域變化圖-N=4…………………………………………...21 圖2.11(d) 切削區域變化圖-N=8…………………………………………...21 圖2.12(a) 切屑厚度負載分佈……………………………………………22 圖2.12(b) 切屑厚度負載分佈-球形區域……………………………….22 圖2.13(a)切屑厚度誤差分佈-ho=0.1……………………………………22 圖2.13(b) 切屑厚度誤差分佈-球形區域ho=0.1……………………….22 圖2.14(a) 切屑厚度誤差分佈-ho=0.3………………………………….23 圖2.14(b) 切屑厚度誤差分佈-球形區域ho=0.3……………………….23 圖2.15(a)切屑厚度誤差分佈-ho=0.5…………………………………..23 圖2.15(b) 切屑厚度誤差分佈-球形區域ho=0.5……………………….23 圖2.16(a) 受偏心影響之半徑變化-球形區域………………………….24 圖2.16(b) 受偏心影響之半徑變化-非球形區域……………………….24 圖2.17 偏心項所造成的額外切屑厚度變化…………………………….24 圖2.18 ηo對始進/終切角的影響………………………………………….26 圖2.19 λ對始進/終切角的影響…………………………………………..27 圖2.20 步徑銑削逆銑真實切削區域………………………………………27 圖3.1 犁切力示意圖………………………………………………….30 圖3.2 切刃長度(ds)示意圖……………………………………………….32 圖3.3 切屑寬度(db)示意圖………………………………………………32 圖3.4(a) 刀具序列函數ts1………………………………………38 圖3.4(b) 刀具序列函數ts2………………………………………38 圖3.5(a) 球銑刀X軸槽銑銑削力, N=4……………………………………41 圖3.5(b) 球銑刀Y軸槽銑銑削力, N=4……………………………………41 圖3.5(c) 球銑刀Z軸槽銑銑削力, N=4…………………………………….42 圖3.6球銑刀三軸頻譜圖, N=4……………………………………………..43 圖3.7球銑刀含偏心與不含偏心銑削力頻域比較圖,N=4………………...43 圖3.8 球銑刀槽銑剪切力, N=4…………………………………………….44 圖3.9(a) fo之X軸銑削力……………………………………………………45 圖3.9(b) fo之Y軸銑削力……………………………………………………45 圖3.9(c) fo之Z軸銑削力……………………………………………………45 圖3.9(d) fn之X軸銑削力…………………………………………...………45 圖3.9(e) fn之Y軸銑削力……………………………………………………45 圖3.9(f) fn之Z軸銑削力……………………………………………………45 圖3.10(a) f(f)之X軸銑削力.………………………………………………..46 圖3.10(b) f(f)之Y軸銑削力………………………………………………...46 圖3.10(c) f(f)之Z軸銑削力………………………………………………...46 圖3.10(d) X銑削力軸頻譜………………………………………………….46 圖3.10(e) Y銑削力軸頻譜…………………………………………………..46 圖3.10(f) Z銑削力軸頻譜…………………………………………………..46 圖3.11 三軸銑削力隨ho變化圖……………………………………………47 圖3.12 三軸銑削力隨l變化圖…………………………………………….48 圖4.1 偏心幾何識別流程圖……………………………………………….50 圖4.2（a）銑削力相位差圖…………………………………………58 圖4.2（b）相位差判別圖……………………………………………59 圖5.1 實驗儀器配置………………………………………………….64 圖5.2 偏心幾何靜態量測方法…………………………………………..66 圖5.3 (a) 球銑刀模擬與實驗銑削力之比較 da =9 mm tx=0.075mm…….70 圖5.3(b) 球銑刀模擬與實驗銑削力之比較 da =8 mm tx=0.075mm…….70 圖5.3(c) 球銑刀模擬與實驗銑削力之比較 da =7 mm tx=0.075mm……..71 圖5.4(a) 球銑刀模擬與實驗銑削力之比較 da =9 mm tx=0.0875mm…....71 圖5.4(b) 球銑刀模擬與實驗銑削力之比較 da =9 mm tx=0.075mm……..72 圖5.4(c) 球銑刀模擬與實驗銑削力之比較 da =9 mm tx=0.0625mm……72 圖5.5實驗頻譜圖da=7mm tx=0.075……………………………………….73 表目錄 表6.1 四刃球銑刀槽銑實驗配置表………………………………….68 表6.2 切削常數判別結果……………………………………………...68 表6.3 偏心幾何靜態量測結果………………………………………...69 表6.4 不同轉速下偏心量之比較……………………………………...69

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