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研究生:魏嘉生
研究生(外文):Jia-Sheng Wei
論文名稱:高精度擺線齒輪誤差檢測之探討
論文名稱(外文):Study on Inspection of High Precision Cycloid Gears
指導教授:蔡錫錚
指導教授(外文):Shyi-Jeng Tsai
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
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:2019
畢業學年度:108
語文別:中文
論文頁數:106
中文關鍵詞:擺線齒廓迭代最近點演算法偏心誤差節距誤差輪廓誤差
外文關鍵詞:Cycloidal profileiterative closest point algorithmeccentricity errorpitch errortooth profile error
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因應工業4.0的發展,擺線齒輪需求量大增,精密加工方法也越來越普及,因此隨著擺線齒輪精度的上升,對於擺線齒輪精度檢測的重要性也隨之上升。因此本論文的研究目的即在建立擺線齒輪加工輪廓的精度評估方法,透過比對擺線量測輪廓與擺線理想輪廓,評估分析出彼此之間的偏差量,求得擺線齒廓偏心誤差、節距誤差以及輪廓度等三種誤差。
本論文在分析比對量測輪廓與理想輪廓所使用演算法係以「迭代最近點演算法」為基礎。此一所開發之演算法以同時比對量測輪廓與理想輪廓的三個齒廓,提高收斂速度,藉由旋轉、平移量測輪廓的方式使與理想輪廓可以有最接近的貼合位置,最後可得到此三個齒廓的整體平移量、個別齒廓旋轉量以及量測輪廓與理想輪廓間的誤差量。所得到的計算結果可進一步轉換成輪廓偏心誤差、各齒節距誤差以及各齒輪廓度,以做為誤差評估以及提供加工改善之參考。
在將實際案例使用開發之演算法計算之前,在研究中先用測試數據對此開發演算法進行驗證。透過預設不同偏心量、節距與輪廓度偏差等三種誤差量,自理想齒廓產生測試數據。驗證的結果顯示計算所得到之誤差與預設誤差值之差值皆小於1 m,證明此演算法可以有效對具誤差的擺線輪廓進行評估。
本論文中分析的實際案例分為 “CYCLO”以及 “RV”兩種擺線盤。案例中所使用的輪廓資料皆是由HEXAGON 三次元量測儀量測而得,原始資料皆為全齒廓數據。透過不同加工條件的案例比較,分別結果具有分辨性,也證明了本論文所開發之演算法可以正確的對擺線輪廓進行分析計算。
由本論文所進行之研究可以確認所開發之演算法可以有效對擺線輪廓進行誤差評估,評估的結果有助於對加工精度狀況的判斷以及後續加工的控管與改進。
In response to the development of Industry 4.0, the demand for cycloid gears has increased significantly. On the other hand, precision machining methods are also popular today, the inspection of cycloid gears becomes therefore more important, as the precision of the cycloid gear increases. The aim of this thesis is to propose a precision evaluation method for machined profiles of cycloid gears. With comparison of the measured contour and the ideal cycloid contour, three errors can be evaluated, namely the eccentricity error of the cycloid profile, the pitch error and the profile error.
The algorithm proposed in this paper I developed based on the "Iterative closest point" method. Three tooth profiles of the measured contour are simultaneously moved and oriented to minimize the difference with the ideal contour. The center position deviation and the orientation angle of each individual tooth profile can be thus obtained. The convergence speed is also increased. The calculated results can be further converted into profile eccentricity error, tooth pitch error, and tooth profile error to evaluate the manufacturing errors and to improve manufacturing process of cycloid disc.
Before analysis of the actual cases using the proposed algorithm, the algorithm is at first verified with test data. Test data is generated from the ideal tooth profile by presetting different error sets of eccentricity, pitch and profile errors. The verification results show that the difference between the calculated error and the preset error is less than 1 m, which proves that this algorithm can effectively evaluate the measured contour of the cycloid with error.
The actual cases analyzed in this thesis are divided into two types of cycloidal discs, namely “CYCLO” and “RV”. The contour data used in the case study were measured by the HEXAGON coordinate measuring machine. The original data were all entire profile data of the cycloid disc. Through the comparison of different machining conditions, the results are distinguishable, and it is also proved that the algorithm proposed in this thesis can correctly analyzed the cycloidal contour.
The research results conducted in this thesis can confirm that the proposed algorithm can effectively evaluate the errors of the cycloidal contour. The evaluation results are helpful to judge the precision situation of manufacturing process and to control and to improve afterwards.
摘要 I
ABSTRACT II
謝誌 IV
目錄 V
圖目錄 IX
表目錄 XIII
符號說明 XV
第 1 章 前言 1
1.1 研究背景 1
1.2 文獻回顧 5
1.2.1 擺線齒輪修形齒廓 5
1.2.2 擺線齒廓量測相關文獻 5
1.2.3 數值分析工具相關文獻 6
1.3 研究目標 7
1.4 論文架構 7
第 2 章 擺線曲線幾何及數值分析方法 9
2.1 擺線齒輪輪廓設計參數及方程式 9
2.1.1 齒廓修整方法 10
2.1.2 自由修整之修形量函式 11
2.2 迭代最近點演算法推導與發展之演算法推導 16
2.2.1 迭代最近點演算法基本流程 16
2.2.2 點至點(Point-to-Point) 17
2.2.3 點至面(Point-to-Plane) 20
第 3 章 誤差評估 24
3.1 迭代最近點演算法為基礎發展之演算法 24
3.2 偏心誤差 29
3.3 節距誤差 30
3.4 輪廓度 32
第 4 章 演算法驗證 33
4.1 測試案例 33
4.1.1 擺線盤設計參數 33
4.1.2 測試數據規劃 34
4.2 程式驗證:測試案例一 43
4.2.1 偏心量 43
4.2.2 節距誤差 44
4.2.3 輪廓度 45
4.3 程式驗證:測試案例二 47
4.3.1 偏心量 47
4.3.2 節距誤差 47
4.3.3 輪廓度 49
4.4 程式驗證:測試案例三 50
4.4.1 偏心量 50
4.4.2 節距誤差 51
4.4.3 輪廓度 52
4.5 小結 54
第 5 章 分析案例 55
5.1 輪廓量測方法 55
5.2 案例 56
5.2.1 RV 56
5.2.2 CYCLO 57
第 6 章 分析結果 60
6.1 RV案例一 60
6.1.1 偏心量 60
6.1.2 節距誤差 61
6.1.3 輪廓度 64
6.2 RV案例二 64
6.2.1 偏心量 65
6.2.2 節距誤差 66
6.2.3 輪廓度 68
6.3 CYCLO案例一 70
6.3.1 偏心量 70
6.3.2 節距誤差 71
6.3.3 輪廓度 73
6.4 CYCLO案例二 75
6.4.1 偏心量 75
6.4.2 節距誤差 76
6.4.3 輪廓度 78
6.5 小結 79
第 7 章 結論與未來展望 81
7.1 結論 81
7.2 未來展望 82
參考文獻 83
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