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研究生:王勝鋒
研究生(外文):Sheng-Feng Wang
論文名稱:錐形內齒輪對之接觸分析
論文名稱(外文):Tooth Contact Analysis of Internal conical Gear Pairs
指導教授:劉家彰劉家彰引用關係
指導教授(外文):Chia-Chang Liu
學位類別:碩士
校院名稱:清雲科技大學
系所名稱:機械工程研究所
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:2007
畢業學年度:95
語文別:中文
論文頁數:79
中文關鍵詞: 錐形內齒輪 齒輪嚙合原理 齒面接觸分析 接觸橢圓
外文關鍵詞:Conical Internal GearTheory of Gear MeshingTooth Contact AnalysisContact Ellipse.
相關次數:
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齒輪是機械傳動中不可或缺的重要元件,而設計、製造出低成本、低噪音、重量輕
及高效率的齒輪,一直是設計及製造人員追求的目標。內齒輪對(Internal Gear Pair)由於具有較高之減速比以及較小之空間需求,目前已廣泛地應用於平行軸減速機構之中,且由於內齒輪對其接觸齒面上之滑動速度小於等效之外齒輪對,因此一般來說具有較高之
傳動效率。此外,由於內齒輪具有內凹之齒廓形狀以及較大之基底齒寬,其強度要較等
效之外齒輪來得高。
本論文所探討之漸開線錐形內齒輪對是由刨齒創成之錐形內齒輪以及由滾齒創成之錐形小齒輪所共同組成。此一齒輪對除了具有一般內齒輪對之優點外,由於具有推拔(Taper)狀之齒厚,齒輪對可在不影響中心距之情形下,藉由調整嚙合齒輪的軸向位置以改變齒輪對在嚙合時之背隙(Backlash),使其背隙控制在一合理的範圍之內。
本文首先針對錐形內齒輪對進行齒面接觸分析,接下來進行錐形內齒輪對之接觸橢圓(Contact Ellipse)模擬,並探討不同之齒輪設計參數對於錐形內齒輪對接觸橢圓大小之
影響。此外,並發展建構三維的齒面網格自動分割程式,利用有限元素分析軟體ABAQUS進行錐形內齒輪對之有限元素 (Finite Element)應力與變形分析。接觸橢圓模擬以及有限
元素應力與變形分析之結果可相互印證。
The gear is one of the most important mechanical elements used in the machinery transmission system. It is the main target to design and manufacture gears with low cost,low noise, light weight and high efficiency. Internal gear pairs are widely used in reduction gear
systems for parallel axes gearing with high gear ratios and small space requirements.
Internal gears are generally more efficient since the sliding velocity along the mating tooth surfaces is lower than that of an equivalent external gear pair. Due to the concave nature of the internal tooth profile and the thicker tooth base, the tooth strength of an internal gear is higher than that of an equivalent external gear.
The conical internal gear pair investigated in this study is composed of a conical internal gear cut by shapers and a conical pinion cut by hobs. In addition to retain the advantages of
the conventional internal gear pair, the backlash of a conical internal gear pair can be easily controlled by axial adjustments without affecting its center distance owing to its tapered tooth
thickness.
In this study,tooth contact analysis of conical internal gear pair is proceeded firstly.Then contact ellipse simulation of the conical internal gear pair have been performed based on the concept of differential geometry. The effects of design parameters on the dimensions of contact ellipses were studied as well. Meanwhile, an automatic mesh-generation program was developed to discretize the three-dimensional tooth model for finite element analysis (FEA)
on the basis of the derived tooth geometry. Then, the general-purpose FEA software, ABAQUS, was applied to evaluate the formation of bearing contacts and stress distribution on the tooth surfaces. The results of the FEA and contact ellipse simulations can be verified mutually.
目錄

摘要 i
Abstract ii
謝誌 iv
目錄 v
圖目錄 vii
符號表 ix

第一章 緒論 1
1.1 前言 1
1.2 接觸分析 2
1.3 研究方向 3

第二章 基本理論 4
2.1 位置向量轉換 4
2.2 嚙合方程式 6
2.3 齒面方程式 8

第三章 錐形內齒輪對之齒面數學模式 10
3.1 錐形小齒輪之數學模式 14
3.2 錐形內齒輪之數學模式 17

第四章 錐形內齒輪對之齒面接觸分析 22
4.1 相切方程式 22
4.3 接觸橢圓模擬 28
4.4 範例 34
4.5 負載下之齒面接觸分析(Loaded Tooth Contact Analysis) 41

第五章 錐形內齒輪對之有限元素接觸應力分析 42
5.1 有限元素分析軟體ABAQUS 簡介 42
5.2 ABAQUS 接觸分析之演算規則 43
5.2.1 隱式(Implicit)與顯式(Explicit)分析之比較 46
5.2.2 隱式(Implicit)與顯式(Explicit)分析的選用 47
5.2.3 網格元素的介紹與選用 48
5.3 有限元素應力分析流程 50
5.3.1 幾何模形之建立 50
5.3.2 網格分割 54
5.3.3 材料性質 57
5.3.4 接觸面設定 57
5.3.5 邊界條件 58
5.4 結果討論 59
5.4.1 標準裝配 60
5.4.2 水平軸偏差 61
5.4.3 垂直軸偏差 63
第六章 結論 65
參考文獻 67
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