臺灣博碩士論文加值系統

由於為了滿足圓柱齒輪的組裝精度與運轉順暢的需求，因此齒輪精加工中常使用齒面修整來調整齒輪咬合位置。磨齒方法則是目前齒輪精加工中最為穩定且高效率的方法。本文研究以蝸桿式創成磨齒機中，加入蝸桿砂輪修砂變化來計算加工齒輪修整齒面的方法。由於目前的創成磨齒機多配有數控式修砂器，可藉由規劃修砂動作來調整蝸桿砂輪的三維齒面，再藉由此蝸桿砂輪磨齒時輔助加工齒輪的修整齒面。本文提出使用多項式方法設定多軸同動方式的修砂動作，包括修砂時的徑向、切向，與軸向三方向進給規劃，擇一進給加工三維修整的蝸桿砂輪，如使用修砂軸向進給規劃可以形成雙導程或變導程蝸桿砂輪，使用修砂徑向進給時則可加工變半徑的蝸桿砂輪，以此修整砂輪進行磨齒，配合磨齒時對角進給的同動動作來執行磨齒加工。磨齒同動以控制器中電子齒輪箱(Electronic Gear Box EGB )的動態輔助修整功能為基礎，研究由修砂與磨齒兩道流程所創成的修整齒輪齒面。並由反置敏感度矩陣方法(Sensitivity matrix and SVD method)，以欲修整齒面拓樸圖為輸入，計算本文設定在兩道加工過程中的加工參數與同動多項式之係數，再由此係數結果模擬磨齒機加工齒輪之齒面。由數值範例得知，加入多軸修砂動作後的隆齒修整齒面，在可以大幅抑制傳統徑向進給修整方法造成的扭曲誤差(Twisted Error)。並且本文提出的加入多軸修砂方法，更能加以控制其扭轉誤差的方向與大小，使其變成咬合齒印走向的調整參數，數值範例用齒面接觸分析探討隆齒的扭轉誤差方向對咬合齒印的分布，發現抑制扭轉並不是所有隆齒齒面的解決誤差方法，如能控制其扭轉程度與方向，可以控制其接觸路徑與咬合齒印的走向，進而設計更適合齒輪的修整形式。

Tooth modified a ground helical gear is usually done on the modern gear finishing machine since the demand for assembly precision and smooth working. And using generated grinding machine is the most stable and efficient method. Modern gear grinding machine equipped with CNC dresser. In this paper, study on the modified gear tooth surface grinding by gear grinding machine and its dressing disk. Hence, we propose a tooth flank modified method for helical gears that uses a diagonal (combined tangential and axial) feed on a grinding machine with a variable grinding worm obtained by adjusting the axial, radial, and tangent feed of the dressing disk with respect to the rotating angle of the grinding worm. Since all the required corrective motions for the proposed multi-axis dressing method are existing CNC controlled axes on modern gear grinding machines, it can easily be implemented without extra cost to modify the grinder hardware. By setting the polynomial of multi-axis dressing grinding worm, polynomial of dresser profile, and polynomial of grinding feed. Then solve the coefficients of these polynomial with sensitivity analysis and singular value decomposition method are proposed and supplemented to modified work gear. This multi-axis dressing method not just correcting common twisted error in gear crowned tooth flank, more to control direction and magnitude of the twisted error. The three numerical examples used to validate the proposed method clearly show its ability to reduce or control tooth flank twisted error in crowned helical gear. We found that the gear pair have a better performance from the control of their twisted error.

論文口試委員審定書 i
致謝 ii
摘要 iii
ABSTRACT iv
目 錄 v
圖目次 viii
表目次 x
第一章 緒論 1
1-1、 前言與背景 1
1-2、 動機與目的 3
1-3、 文獻回顧 4
1-4、 論文架構 7
第二章 蝸桿砂輪與磨齒加工齒輪數學式 8
2-1、 立式齒輪磨齒機與掛載之修砂器 8
2-2、 具多軸修砂的蝸桿砂輪數學模式 10
2-3、 齒輪磨齒機的各軸進給方式 22
2-3-1 磨齒對角進給 22
2-3-2 磨齒徑向進給與常見齒面修整 24
2-4、 齒輪磨齒加工數學式 27
2-4-1. 控制器的動態輔助修整運動 27
2-4-2. 磨齒修整齒輪齒面數學式 29
第三章 標準齒輪、砂輪與修砂器數學式 36
3-1、 磨齒加工的齒胚簡介 36
3-2、 標準漸開線齒型 38
3-3、 加工範圍輪廓起始徑與輪廓終止徑的計算 42
3-4、 標準蝸桿砂輪與標準修砂盤 44
3-4-1. 標準蝸桿砂輪數學式 44
3-4-2. 標準修砂盤數學式 46
第四章 齒面拓樸與敏感度矩陣 48
4-1、 加工齒輪齒面差異量拓樸圖 48
4-2、 建立反置敏感度矩陣 50
4-3、 加入多軸修砂方法修整齒輪範例 59
4-3-1. 傳統徑向進給方法之隆齒範例 59
4-3-2. 變導程蝸桿砂輪方法之隆齒修整範例 62
4-3-3. 變半徑蝸桿砂輪方法之隆齒修整範例 65
4-3-4. 變切向修砂蝸桿砂輪方法之隆齒修整範例 67
4-4、 使用最少同動軸數進行抑制齒面扭轉 70
4-4-1. 變導程蝸桿砂輪配合工件轉角方法之隆齒修整範例 70
4-4-2. 變切向蝸桿砂輪配合工件轉角方法之隆齒修整範例 72
4-5、 加入變導程修砂方法修整複雜齒面 75
4-6、 本章小結 77
第五章 齒面偏置量控制與齒面接觸分析 78
5-1、 齒輪修整齒面的偏置誤差Bias-Error 78
5-2、 使用最小轉角法搜索齒輪對嚙合點與傳動誤差 82
5-3、 使用一維五元樹法搜索齒輪對咬合齒印 90
5-4、 齒輪對的接觸分析TCA範例 93
5-4-1. 徑向進給方法齒面接觸分析範例 93
5-4-2. Bias-Free無扭轉誤差齒面Twist negativeFree齒面接觸分析範例 95
5-4-3. Bias-in正扭轉誤差齒面Twist Plus齒面接觸分析範例 98
5-4-4. Bias-out正扭轉誤差齒面Twist negative齒面接觸分析範例 101
5-5、 本章小結 104
第六章 結論與未來展望 105
6-1、 結論 105
6-2、 未來展望 107
參考文獻 108

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