新式ZI型雙包絡蝸桿與螺旋齒輪組設計及接觸分析

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姓名

劉俊廷(Chun-Ting Liu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

新式ZI型雙包絡蝸桿與螺旋齒輪組設計及接觸分析
(Design and Tooth Contact Analysis of a Novel ZI-Type Double-Enveloping Worm and Helical Gear Set)

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摘要(中)

蝸桿蝸輪組為兩軸交錯之齒輪機構，依設計方法不同可分為圓柱型與雙包絡蝸桿蝸輪組，其中雙包絡蝸桿蝸輪組相較圓柱型蝸桿蝸輪組擁有高接觸率、傳動效率高以及承載能力大等優點。
本論文旨在分析新式ZI型雙包絡蝸桿與螺旋齒輪之特性，根據齒輪原理，採用齒條刀建立螺旋齒輪齒面數學模式，並以其齒形作為產形輪，推導與產形輪共軛之新式ZI型雙包絡蝸桿，再利用蝸桿與磨輪之相對運動關係得到磨輪齒形，同時配合B-spline函數擬合出磨輪之輪廓曲線。
接著透過產形輪與蝸桿齒面之關係，探討共軛齒輪組瞬時接觸線與接觸區域。為了將齒輪對之接觸型式改為點接觸，提出五種齒輪修整方法，對螺旋齒輪齒面分別進行齒形修整、導程隆齒修整、螺旋角修整，以及增加蝸桿之產形輪齒數，再將螺旋齒輪三種修整方式整合，進行齒面雙隆齒修整。後續利用拓樸誤差方式，分析螺旋齒輪齒面修整趨勢。最後，進行接觸軌跡、接觸齒印與傳動誤差等無負載齒面接觸分析，並探討在組裝誤差下對齒輪組的嚙合影響。

摘要(英)

The worm gear set is a gear mechanism with two crossed axes. It can be divided into cylindrical and double-enveloping worm gear sets according to different design methods. The double-enveloping worm drive has the advantage of higher contact ratio, higher transmission efficiency and larger load capacity than the cylindrical worm drive.
The purpose of this study is to analyze the characteristics of a novel ZI-type double-enveloping worm and helical gear set. According to the theory of gearing, the rack cutter is used to establish a mathematical model of the helical gear tooth surface, and its tooth shape is used as the media gear to derive a novel ZI-type double-enveloping worm that is conjugated with the media gear. Based on the relative motion relationship between the worm and the grinding wheel to obtain the grinding wheel profile, and the profile curve of the grinding wheel is fitted with the B-spline function.
Subsequently, through the relationship between the media gear and the worm tooth surface, the instantaneous contact line and contact area of the conjugate gear set were discussed. In order to change the tooth contact type from line contact to point contact, five methods were proposed on the gear tooth modified including tooth profile modification, lead crowning modification, helix angle modification, increasing the number of teeth of the media gear, and double crowning modification that integrates the three methods of the helical gear. Then, the topological error method was used to analyze the trend of the helical gear tooth surface modified. Finally, the contact paths, contact patterns and transmission errors were calculated by unloaded tooth contact analysis. The effects of assembly errors on the gear set were also investigated.

關鍵字(中)

★ ZI型雙包絡蝸桿
★ 螺旋齒輪齒面修整
★ 齒面接觸分析
★ 接觸軌跡
★ 接觸齒印
★ 組裝誤差
★ 傳動誤差

關鍵字(英)

★ ZI-Type Double-Enveloping Worm
★ Helical Gear Modification
★ Tooth Contact Analysis
★ Contact Path
★ Contact Pattern
★ Transmission Error

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VII
表目錄 XI
符號對照表 XII
第1章緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.2.1 螺旋齒輪 1
1.2.2 圓柱型蝸桿蝸輪組 2
1.2.3 雙包絡蝸桿蝸輪組 5
1.3 研究動機與目的 11
1.4 論文架構 12
第2章螺旋齒輪與ZI型雙包絡蝸桿之齒面數學模式 13
2.1 前言 13
2.2 雙貝茲曲線之假想齒條刀數學模式 13
2.2.1 貝茲曲線 13
2.2.2 雙貝茲曲線連接連續性 14
2.2.3 雙貝茲曲線直邊齒條刀法向剖面 15
2.3 螺旋齒輪齒面數學模式 16
2.4 ZI型雙包絡蝸桿齒面數學模式 21
2.5 數值範例 23
第3章 ZI型雙包絡蝸桿之磨輪輪廓設計 25
3.1 前言 25
3.2 ZI型雙包絡蝸桿磨輪數學模式 25
3.3 擬合與B-spline曲線方程式 29
第4章 ZI型雙包絡蝸桿與螺旋齒輪齒面瞬時接觸線及齒面修整 31
4.1 前言 31
4.2 ZI型雙包絡蝸桿與螺旋齒輪齒面之瞬時接觸線 31
4.3 螺旋齒輪齒面之拓樸點 32
4.4 齒輪修整方式 33
4.4.1 螺旋齒輪齒形之齒面修整 33
4.4.2 螺旋齒輪導程隆齒之齒面修整 34
4.4.3 螺旋齒輪螺旋角之齒面修整 37
4.4.4 蝸桿之產形輪齒數增加之齒面修整 38
4.4.5 綜合螺旋齒輪三種修整方式 40
4.5 小結 41
第5章齒面接觸分析 42
5.1 前言 42
5.2 齒面接觸分析方程式 42
5.3 組裝誤差分析 43
5.4 接觸齒印分析 47
5.5 齒面接觸分析結果 50
5.5.1 Case(0)無修整 51
5.5.2 Case(1)螺旋齒輪齒形修整 51
5.5.3 Case(2)螺旋齒輪齒形加導程隆齒修整 56
5.5.4 Case(3)螺旋齒輪齒形加螺旋角修整 61
5.5.5 Case(4)、Case(5)螺旋齒輪齒形修整加蝸桿之產形輪齒數增加 65
5.5.6 Case(6)螺旋齒輪齒形加導程隆齒修整加蝸桿之產形輪齒數增加 73
5.5.7 Case(7)、Case(8)綜合四種修整方式 77
5.6 討論 84
第6章結論與未來工作 85
6.1 結論 85
6.2 未來工作 86
參考文獻 87

參考文獻

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指導教授

陳怡呈(Yi-Cheng Chen)

審核日期

2023-11-29

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