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Student Number 90323009
Author Szu-han Wu(吳思漢)
Author's Email Address s0323009@cc.ncu.edu.tw
Statistics This thesis had been viewed 1166 times. Download 927 times.
Department Mechanical Engineering
Year 2008
Semester 2
Degree Ph.D.
Type of Document Doctoral Dissertation
Language zh-TW.Big5 Chinese
Title Contact Strength of a Skew Conical Involute Gear Drive in Approximate Line Contact
Date of Defense 2009-07-10
Page Count 159
Keyword
  • approximate line contact
  • conical gear
  • edge contact
  • gear tooth surface failure
  • loaded tooth contact analysis
  • surface fatigue strength
  • Abstract Of all the different types of gears, conical gears as the special type of general spatial gearing makes them not only suitable for parallel axis transmission, but also for cases with intersecting or skew axes. However, one of the weak spots of conical gears is less surface durability in spatial applications due to point contact problems, although transmission accuracy is not correspondingly sensitive to assembly error. From the viewpoint of design, this study suggested two concepts to increase the surface durability of conical gears. Skew conical gear drives can be designed as gear pairs, with either “profile-shifted transmission”, or “approximate line contact”.
    The profile-shifted transmission can give us the possibility to adjust the contact position of a conical gear pair for better tooth contact bearing just only through changing certain gearing or assembly data. On the other hand, an approximate line contact drive has a contact ellipse with a large major-to-minor-axis ratio, which allows it to overcome the weakness of conical gear drives for application in power transmission. This gearing design approach is characterized by reduced edge contact sensitivity and increased surface durability.
    The edge contact sensitivity that can arise with this kind of gear drive due to assembly or manufacturing errors is evaluated by analyzing the value of the shift of the line of action caused by such errors. The surface durability is evaluated by calculating the Hertz stress. Some guidelines are developed based on the analysis of the influence of the gearing parameters on the edge contact sensitivity and the surface durability made possible using this design approach for conical gear drives in the approximate line contact.
    An efficient approach for loaded tooth contact analysis (LTCA) of conical gear drives is developed. Two new models are developed for the meshing and contact stress anslyses. This approach differs from conventional TCA methods in that the meshing analysis is based on the line of action characteristic of involute gearing. A numerical method is applied to calculate the contact stress. The non-Hertzian contact problem is solved giving due consideration to the influences of the tooth contact deformation and tooth bending deflection. The approach is not only suitable for application for cases of non-Hertzian contact, but also for practical cases, such as in gear drives with end-relief.
    A practical example is given to demonstrate the feasibility of the approximate line contact design. The LTCA results of the example are also compared with those of solved by the finite element method (FEM) to which they are in good consistence. Finally, a back-to-back testing equipment was developed for testing the surface fatigue strength of a skew conical gear drive. The objective of the tests was to determine the limited service life (number of load cycles) of the skew conical gear drive in approximate line contact for tooth pitting fatigue failure under several load levels. Three test gear pairs (S45C, hardening and tempering, but no case hardening) with different applied torques were tested: 200 Nm, 300 Nm, and 350 Nm. The results indicated that the surface durability of the approximate line contact design is indeed increased. Furthermore, the kinds of gear surface failures for the test were pitting, cold scuffing, and wear.
    Table of Content 摘要i
    Abstractiii
    誌謝v
    目錄vi
    圖目錄ix
    表目錄xv
    符號說明xvi
    第1章 緒論1
    1-1 研究背景1
    1-1-1 漸開線錐形齒輪之特性2
    1-1-2 漸開線錐形齒輪應用上之限制4
    1-2 文獻回顧4
    1-3 研究動機與目的6
    1-4 研究方法8
    1-5 論文架構10
    第2章 理論基礎12
    2-1 齒輪運動學12
    2-1-1 創成齒輪與刀具的相對速度螺旋12
    2-1-2 歪斜軸齒輪對的相對速度螺旋13
    2-2 漸開線錐形齒輪數學模式16
    2-2-1 標準齒形16
    2-2-2 具有齒端修整齒面20
    2-3 歪斜軸漸開線錐形齒輪對移位嚙合設計22
    2-3-1 橫向齒形角係數24
    2-3-2 組裝關係25
    2-3-3 運動學基本關係26
    2-3-4 無背隙嚙合關係28
    2-3-5 齒輪加工參數與工作參數關係29
    2-4 歪斜軸漸開線錐形齒輪對嚙合基本關係31
    2-4-1 作用線31
    2-4-2 漸開線錐形齒輪齒面的主曲率與主方向34
    2-4-3 Hertz 理論36
    2-4-4 傳動函數37
    第3章 近似線接觸之幾何設計40
    3-1 設計概念40
    3-1-1 基本構想40
    3-1-2 線接觸嚙合條件40
    3-2 齒端邊緣接觸分析42
    3-2-1 軸交角誤差之影響43
    3-2-2 偏位誤差之影響46
    3-2-3 加工誤差之影響47
    3-3 齒面承載能力分析50
    3-4 設計方法與準則52
    第4章 歪斜軸錐形齒輪對受負載接觸分析56
    4-1 嚙合模型56
    4-2 齒面接觸應力計算模型61
    4-2-1 非赫茲應力基本計算模型62
    4-2-2 多齒對嚙合計算模型66
    4-2-3 齒面接觸變形影響係數66
    4-2-4 輪齒懸臂梁撓曲影響係數68
    4-2-5 數值計算流程72
    4-3 有限元素模型75
    第5章 實例探討78
    5-1 近似線接觸與線接觸型態之歪斜軸錐形齒輪對78
    5-1-1 齒輪數據與容許誤差78
    5-1-2 近似線接觸型態受負載輪齒接觸分析81
    5-1-3 線接觸型態受負載輪齒接觸分析85
    5-1-4 相對速度分析91
    5-2 齒端修整對接觸應力的影響94
    第6章 齒面承載能力實驗驗證97
    6-1 齒面破壞的種類97
    6-1-1 點蝕100
    6-1-2 擦損或刮痕101
    6-2 實驗驗證設備設計102
    6-2-1 實驗設備工作原理與架構102
    6-2-2 實驗設備規格與設計重點104
    6-3 實驗基本條件108
    6-3-1 被測齒輪108
    6-3-2 潤滑條件109
    6-3-3 齒面強度試驗判定失效的標準110
    6-4 實驗內容規劃110
    6-4-1 負載規劃110
    6-4-2 實驗步驟111
    6-5 實驗結果與討論113
    6-5-1 齒面點蝕面積率114
    6-5-2 齒面破壞型態116
    第7章 結論與未來展望120
    7-1 結論120
    7-2 未來展望122
    參考文獻123
    附錄 被測齒輪檢驗報告132
    作者簡介134
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    Advisor
  • Shyi-Jeng Tsai(蔡錫錚)
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    Date of Submission 2009-07-29

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