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博碩士論文 etd-0723101-203127 詳細資訊
Title page for etd-0723101-203127
論文名稱
Title
圓弧齒廓傘齒輪之研究
A Study on the Bevel Gear with Circular-Arc Tooth Profiles
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
70
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2001-06-29
繳交日期
Date of Submission
2001-07-23
關鍵字
Keywords
齒輪、傘齒輪、圓弧型
bevel gear, gear, circular-arc tooth profiles
統計
Statistics
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The thesis/dissertation has been browsed 5646 times, has been downloaded 3576 times.
中文摘要
在現今的工業界,傘齒輪在相交軸的傳遞系統中,可以說是受到相當廣泛的運用,但大都侷限在漸開線傘齒輪,對於具圓弧型之傘齒輪組之研究文獻卻是相當的少。本文依據共軛嚙合理論、座標轉移與嚙合拘束方程式,推導具共軛傳動特性之點接觸路徑。並結合球面圓弧曲線,與球面三角幾何之特性建構出具圓弧齒廓之傘齒輪組。
本文亦就所推導之圓弧齒廓傘齒輪組作干涉分析與探討。應用齒輪組球截面上之圓弧曲線運轉時相位差的觀念,判斷出是否有干涉情況發生。並提出預防干涉之理想條件。對於建構齒廓之齒廓圓錐角極大值的限制,亦做成圖表,以提供設計者參考使用。
最後本文亦將所建構之點接觸圓弧齒廓傘齒輪,以Pro/E 電腦軟體建構成3D 實體模型,並利用 Visual Nastran 電腦軟體作動態模擬,以驗證其可傳動性。相信本文對於圓弧齒廓傘齒輪之設計,提供了一可行的數學模式及設計方法,以作為進一步研究的基礎。

Abstract
Nowadays, the bevel gears are widely applied in the industry for the intersected-axial transmission system. But the applications of the bevel gears are mostly limited to the usage of involute bevel gears. In this thesis, the bevel gear with circular-arc tooth profiles is derived by using general theorem of conjugate surfaces, coordinate transformation, constrained meshing equation, and spherical trigonometry.
According to the bevel gears with circular-arc tooth profile derived above, the analyses and discussions of the interference are proposed. The interference situation is detected by applying the phase lead-lag concept while circular-arc curve is moving on the spherical cross-section. Furthermore, the ideal conditions to avoid occurrence of interference are proposed. Design charts for the maximum values of tooth profile angle are also constructed as a reference for designers.
The 3D solid models of the bevel gear with circular-arc tooth profiles are constructed by using the computer software (Pro/E). Finally, the transmission ability is verified through the computer animation using CAE software (Visual Nastran). It is believed that the mathematical models and design method developed in the thesis will provide a useful foundation for the further studies.

目次 Table of Contents
謝誌............................................I
摘要............................................I
Abstract.......................................II
目錄..........................................III
圖目錄..........................................V
表目錄........................................VII
符號說明.....................................VIII
第一章 緒論.....................................1
1-1研究背景及目的...............................1
1-2文獻回顧.....................................2
1-3論文組織與章節...............................3
第二章 圓弧齒廓之數學模式.......................4
2-1 球面圓弧齒廓...........................4
2-2 共軛嚙合理論之接觸路徑................12
2-2-1齒輪組之瞬間螺旋軸........................12
2-2-2齒廓曲面之參數式..........................14
2-2-3共軛齒形之拘束條件........................15
2-2-4齒輪組之點接觸路徑........................16
2-2-5共軛齒輪組之接觸路徑......................17
2-3 球面圓弧齒之幾何特性..................22
2-4 圓弧齒齒廓作動特性....................26
2-5 圓錐齒廓之建構........................28
第三章 圓弧齒廓干涉與特性之探討................31
3-1 圓弧齒廓之干涉探討....................32
3-1-1 球面上之齒廓.............................32
3-1-2 作動情形.................................34
3-1-3撰寫程式..................................37
3-2 相位差之特性..........................40
3-3 齒廓圓錐角之限制......................42
第四章 傘齒輪組之建構與探討....................47
4-1 建構一可變圓錐之正交軸傘齒輪組........49
4-1-1齒廓圓錐之齒面範圍........................50
4-1-2齒輪組之建構與組立........................54
4-1-3齒輪組點接觸之情形........................56
4-1-4干涉情況之探討............................58
4-2 建構一固定齒廓圓錐角之正交軸傘齒輪組..60
4-2-1轉速比 m = -0.8 傘齒輪組..................60
4-2-2轉速比 m = -0.5 齒輪組之建構..............62
4-3動態模擬....................................65
4-4快速成型加工................................67
第五章 結論與建議..............................68
參考文獻.......................................69


參考文獻 References
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11. C. B. Tsay, and Z. H. Fong, 1991, “Computer Simulation and Stress Analysis of Helical Gears with Pinion Circular Arc Teeth and Gear Involute Teeth,” Mechanism and Machine Theory, Vol.26, No.2, pp.145-154.
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