ZK型雙包絡蝸桿蝸輪組接觸分析

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曹峻維(Chun-Wei Tsao) 查詢紙本館藏

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光機電工程研究所

論文名稱

ZK型雙包絡蝸桿蝸輪組接觸分析
(Tooth Contact Analysis of ZK-Type Double- Enveloping Worm Gear Set)

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摘要(中)

蝸桿蝸輪組為空間交錯軸傳動機構，相比於圓柱型蝸桿蝸輪組，雙包絡蝸桿蝸輪組具有較高接觸比、傳動效率高與負載能力大等特點。圓柱型蝸桿蝸輪組在工業中已經大量運用，且參數設計已有相關規範，但雙包絡蝸桿蝸輪組沒有明確的設計準則，導致設計參數取得困難、製造成本過高以及精度難以控制，使得無法量產普及，其優勢也無法得到有效的發揮。
本論文旨在分析ZK型雙包絡蝸桿蝸輪組，應用齒輪原理，根據刀具與工件齒輪交錯軸相對運動關係，建立此型蝸桿蝸輪組之齒面數學模式，並利用蝸桿型滾刀與蝸輪齒面之關係，探討共軛之齒輪組線接觸型式。此外，為了將齒輪組由線接觸型式改為點接觸型式，本文提出三種蝸輪齒面修整方式，將蝸輪齒面進行齒形修整、導程修整以及綜合前述兩者之修整方式，進行齒輪齒面修整。最後，進行無負載下齒面接觸分析，包含接觸軌跡、接觸齒印與傳動誤差等，並探討齒輪組各組裝誤差下對系統的影響。

摘要(英)

The worm gear set is a spatial crossed axis transmission mechanism, compared to the cylindrical worm drive, the double-enveloping worm drive has the characteristics of higher contact ratio, higher transmission efficiency and larger load capacity. Since cylindrical worm drive have been widely used in industry, and there are relevant specifications for standard parameter design, but the double-enveloping worm drive does not have a clear design standard. The difficulty design of the parameters, production costs stay at a relative high level, and difficult control of precision, contribute to mass production is popular, and its advantages cannot be effectively utilized.
The purpose of this study is to analyze ZK-Type double enveloping worm gear set. Firstly, the mathematical model of worm gear set was developed based on the theory of gearing. Based on the relationship between the ZK-Type worm-type hob cutter and the conjugate tooth surface of the worm gear, the line contact of the conjugate gear set were discussed. In addition, in order to change the worm gear set from line contact to point contact, three methods were proposed on the worm gear tooth surface modified including tooth profile modification, lead modification, and double crowning modification. Finally, the contact paths, contact patterns and transmission errors were calculated by unloaded tooth contact analysis. The effects of assembly errors on the contact paths and contact patterns were also investigated and discussed.

關鍵字(中)

★ ZK型雙包絡蝸桿蝸輪組
★ 蝸輪齒面修整
★ 齒面接觸分析
★ 接觸軌跡
★ 傳動誤差

關鍵字(英)

★ ZK-Type Double Enveloping Worm Gear Set
★ Worm Gear Modification
★ Tooth Contact Analysis
★ Contact Path
★ Transmission Error

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
表目錄 IX
符號對照表 X
第1章緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 圓柱型蝸桿蝸輪組 2
1.2.2 ZA型雙包絡蝸桿蝸輪組 3
1.2.3 ZN型雙包絡蝸桿蝸輪組 5
1.2.4 ZC型雙包絡蝸桿蝸輪組 6
1.2.5 TI型雙包絡蝸桿與漸開線螺旋齒輪組 8
1.2.6 TP型雙包絡蝸桿蝸輪組 9
1.3 研究目的 12
1.4 論文架構 13
第2章雙包絡蝸桿蝸輪組之齒面數學模式 14
2.1 前言 14
2.2 Double Bezier curve之磨輪軸向外形數學模式 14
2.2.1 Bezier curve 數學模式 14
2.2.2 Double Bezier curve連接連續性 16
2.2.3 數值範例－Double Bezier curve直邊磨輪軸向剖面 16
2.3 ZK型雙包絡蝸桿齒面數學模式 17
2.4 ZK型雙包絡蝸輪齒面數學模式 21
2.5 數值範例 24
第3章蝸輪齒面瞬時接觸線與齒面修整 27
3.1 前言 27
3.2 ZK型雙包絡蝸輪齒面之瞬時接觸線 27
3.3 ZK型雙包絡蝸輪齒面拓樸點 29
3.4 修整方式1-磨輪齒形之蝸輪齒面修整 30
3.5 修整方式2-增徑滾刀之蝸輪齒面修整 31
3.6 修整方式3-磨輪齒形加增徑滾刀之蝸輪齒面修整 34
第4章齒面接觸分析 36
4.1 前言 36
4.2 齒面接觸分析方程式 36
4.3 組裝誤差分析 37
4.4 接觸齒印分析 40
4.5 齒面接觸分析結果 43
4.5.1 齒面接觸分析結果－Case(I)磨輪齒形修整 44
4.5.2 齒面接觸分析結果－Case(II)增徑滾刀修整 48
4.5.3 齒面接觸分析結果－Case(III)磨輪齒形修整加增徑滾刀修整 50
第5章結論與未來展望 57
5.1 結論 57
5.2 未來展望 58
參考文獻 59

參考文獻

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指導教授

陳怡呈(Yi-Cheng Chen)

審核日期

2023-2-1

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