| 摘要: | 由於漸開線齒輪具有加工簡單、中心距誤差敏感度低、傳動效率高等優點，因此廣泛應用於各種動力傳遞設備上。但是實際應用時，齒輪對在嚙合過程中會因嚙合剛性變動與齒頂邊緣接觸等問題，造成振動與噪音，甚至齒面破壞，因此一般會對齒輪進行齒形修整以改善嚙合過程的負載劇烈變動以及避免齒頂邊緣接觸現象。然而齒形修整相當於齒形誤差，因此必須對齒形修整前後所造成之應力變化進行研究，以瞭解齒輪對之齒形修整設計方式在實際應用上之結果本研究之目的為探討漸開線正齒輪對齒形修整方法常用之齒頂修整對齒面接觸應力之影響，研究方向包括無齒頂修整之齒輪對齒頂邊緣接觸發生時機與齒面接觸應力分布，以及不同齒頂修整方式對漸開線正齒輪對負載分配與齒面接觸應力分布的影響。論文首先以漸開線正齒輪對嚙合幾何關係式，探討無齒頂修整之漸開線正齒輪對在不同負載下之齒頂邊緣接觸發生時機。隨後應用剛性法與影響係數法分析無齒頂修整以及不同齒頂修整型式下齒輪對之靜態負載分配與齒面接觸應力分布。本研究探討之齒頂修整型式包括線性長、短齒頂修整，齒頂圓角，以及拋物線等。由負載分配分析結果可以發現線性齒頂修整與拋物線齒頂修整皆能有效改善漸開線正齒輪對的負載變動問題，而齒頂圓角或其他齒頂倒角方式修整則無法改善。根據齒面接觸應力分析結果，未修整齒對在理論接觸開始前與結束後一齒之齒頂邊緣與另一齒之齒根會產生非赫茲接觸應力，其應力值皆遠大於正常接觸狀況下之應力；發生最嚴重應力之嚙合位置則在接近理論接觸開始前以及理論接觸結束附近位置。此狀況在以拋物線以及線性長、短齒頂修整型式皆可有效避免。但具齒頂圓角之齒輪對在嚙合過程中仍會發生齒頂邊緣接觸現象。另外齒頂修整曲線若無平滑化，則會在修整起始位置產生應力集中現象。本研究結果顯示，論文中所建立之負載分配與齒面接觸應力計算模組具有相當之準確度，所需運算時間也較短，因此可有效運用在齒輪齒頂修整設計分析。關鍵字：齒頂邊緣接觸、齒頂修整、齒頂圓角、負載分配、齒面接觸應力Involute gears have advantages such as simple manufacturing process, low sensitivity due to the center distance deviation, and high transmission efficiency etc., so it is widely applied in various power transmission equipments. However, vibration, noise, and even tooth surface damage will occurr during the gear mesh because of variation of mesh stiffness and tooth tip corner contact. Therefore, profile modification on gear teeth is a commonly method to reduce the violent change of loading on teeth and to avoid tooth contact on tip corners beyond the normal line of action. But the profile modification is equivalent to a special kind of tooth profile deviation, it is necessary to analyze the loaded tooth contact stress of the gear pairs with or without profile modification to understand the influence of different profile modification design on the performace of gear drives in practical application.The aim of this study is to analyze the influence of tip relief, a common profile modification method for involute spur gear, on tooth contact stress. This study includes (a) identification of occurrence of tooth tip corner contact and analysis of contact stress distribution of the involute spur gear pair without profile modification, and (b) the influence of different tip relief types on load sharing and contact stress distribution of involute spur gear pairs. At first in the thesis, occurrence of tooth tip corner contact of involute spur gear pairs without profile modification under different loads is identified based on the geometric relation of gear mesh. Then static load sharing and tooth contact stress distribution of spur gear pairs without and with different tip relives are analyzed by using stiffness method and influence coefficient method respectively. The types of tip relief discussed in the study include linear long and short tip relief, tip rounding, parabolic tip relief, etc.The results of the load sharing analysis show that linear tip relief and parabolic tip relief can improve problem of the violent load change, but tip rounding or other tip chamfer types can not improve it.According to the results of the loaded tooth contact analysis, non-Hertzian contact of tooth pairs occurs at the positions before the theoretical contact begin and after the theoretical contact end of the tooth pair without tip relief. The values of the corresponding contact stress are much larger than the value of normal contact. The maximum contact stress occurs at the position nearby theoretical contact begin and end position. The type of non-Hertzian contact can be avoided effectively by using the linear tip relief and the parabolic tip relief, but tip corner contact of tooth pair with tip rounding still occurrs. In addition, stress concentration can be also found at starting position of the tip relief, if the tip relief curve is not smooth.The analysis results show that the calculation modules for load sharing and loaded tooth contact analysis developed in this study are reliable and time-saving for calculattion, so they can be used for tip relief design and analysis efiiciently.Keywords: Tooth Tip Corner Contact, Tip Relief, Tip rounding, Load Sharing, Tooth Contact Stress |
