| 摘要: | 曲線齒圓柱型齒輪 (Curvilinear Cylindrical Gears，以下簡稱為曲線齒輪)與正齒輪及螺旋齒輪相比，具有較高的彎曲強度與抗壓強度。其齒面有較佳之潤滑性，而且沒有螺旋齒輪的軸向推力問題，所以十分適用於高負載及精密的平行軸傳動。近年來雖有學者進行曲線齒輪之研究，但大多數的研究是針對直邊刀具所創成之曲線齒輪，其最大的問題在於當有軸向裝配誤差存在時，一般之曲線齒輪組將會有不連續的傳動誤差(Discontinuous Transmission Error)產生，或是造成高接觸應力的齒緣接觸(Edge Contact)現象。為了解決上述問題，本研究計畫將提出具齒形修整之曲線齒輪，使用具圓弧狀法向剖面之刀具，對所創成之曲線齒輪將造成齒形修整效果。當使用此新型曲線齒輪在曲線齒輪對之傳動時，會產生連續性拋物線形的傳動誤差(Parabolic-Shaped Transmission Error)，且接觸點將落於齒面中央區域，即使在齒輪組存在軸向裝配誤差之下，也不會產生齒緣接觸或是不連續的運動落差，可大幅提升齒輪組之壽命並降低振動與噪音，此為本研究之最大貢獻之處。本專題研究計畫為二年期之研究計畫，在第一年(98 年8 月至99 年7 月)研究中，首先將依據目前執行中國科會計畫所推導的具齒形修整之曲線小齒輪的齒面幾何數學模式，搭配由直邊公飛刀所創成之曲線大齒輪，組成一修整型曲線齒輪對。經由座標轉換後，建立包含組裝誤差的修整型曲線齒輪對在實際嚙合時之數學模式，然後撰寫齒面接觸分析(Tooth Contact Analysis)電腦程式，探討修整型曲線齒輪對在不同的裝配狀況與設計參數下的傳動誤差及接觸率(Contact Ratio)。此外，也將利用最佳化數值方法求得滿足特定傳動誤差之齒輪設計參數。然後，本研究將使用齒面接觸外形法 (Surface Topology Method)來預測接觸齒印，探討在不同的設計參數下的接觸齒印大小與位置。最後，將使用交通大學機械系的CNC 滾齒機，配合訂製刀具與所設計的夾治具，實際切製所提出之修整型曲線齒輪對；同時也將借用工研院之齒面量測儀量測所切製齒形之精度，並與理論齒面數學模式比較。在第二年(99 年8 月至100 年7 月)研究中，由於修整型曲線齒輪對為點接觸，將繼續深入探討此修整型曲線齒輪對之接觸橢圓(Contact Ellipse)及接觸應力。首先依據微分幾何與曲率分析的觀念，分別推導出大小兩齒輪的齒面主軸曲率與主軸方向 (Principal Directions and Principal Curvatures)數學方程式。撰寫電腦程式，由接觸點座標計算在輕負載下之齒面接觸橢圓大小及方向。然後利用赫茲接觸應力(Hertzian Contact Stress)公式推導兩接觸齒面之接觸應力。此外，由齒面數學模式，發展三維齒面之網格分割軟體，並建立接觸齒面的有限元素模型(Finite Element Model)，使用有限元素分析(Finite Element Analysis)軟體模擬齒輪對之齒面接觸應力及齒根應力。此外，本研究計畫亦將借用交通大學機械系所有之萬用齒輪嚙合測試機，將實際切製之修整型曲線齒輪對進行單齒腹測試與嚙合齒印實驗測試，並分別與模擬分析之傳動誤差與接觸橢圓進行比對。 ; Compared with spur gears and helical gears, curvilinear cylindrical gears have better bending strength and contact strength. The tooth profiles of curvilinear gears are advantageous for retaining lubrication oil, and unlike helical gears, curvilinear gears do not exert axial thrust load. Therefore curvilinear gears are very suitable for precise parallel-axes transmission with high loading. Although there are a few research about this type of gears, most of these research focused on curvilinear gears generated by straight-edged cutters. When there are axial misalignments, conventional curvilinear gear sets will have problems such as discontinuous transmission errors or edge contact with extremely high contact stress. To solve the above mentioned problems, this research project proposes a new type of curvilinear gears with tooth modifications which are generated by tools with circular-arc normal sections. When utilizing this new type of curvilinear gears, it will introduce inherent continuous parabolic-shaped kinematic errors and localized bearing contact in the middle of gear tooth. Consequently, neither edge contact nor discontinuous transmission errors will occur even under axial misalignments. The service lives of the curvilinear gear sets will increase, and the vibrations and noises will be reduced. These are the main contributions of this proposed research. This research project is a two-year project. In the first year (2009/08-2010/07), based on the mathematical model of modified curvilinear pinion developed in the current NSC research project, along with a conventional curvilinear gear, the mathematical model of the modified curvilinear gear pair considering real assembly errors will be developed after applying appropriate coordinate transformation. Tooth contact analysis computer programs then can be developed to investigate the transmission errors and contact ratios of the proposed modified curvilinear gear pair under various assembly misalignments. Optimization technique then can be applied to determine the suitable gear design parameters subject to specific transmission errors. Besides, this study will study the contact patterns using surface topology method. The locations and dimensions of contact patterns under various design parameters will be calculated. Finally, we will design and order gear cutters and fixtures, and use the CNC hobbing machine of National Chiao Tung University to manufacture the proposed modified curvilinear gear pair. Moreover, the tooth profiles can be inspected by using the gear profile measurement machine at Industrial Technology Research Institute, and the measured data can be compared with the theoretical mathematical models. In the second year (2010/08-2011/07), the contact ellipses and contact stress will be explored since the proposed modified curvilinear gear pair exhibits point contact. Based on differential geometry and curvature analysis, the principal directions and curvatures of the pinion and gear will be derived respectively in terms of those of the generating tool surfaces. Developing curvature analysis computer programs will enable us to calculate the dimensions and directions of the contact ellipses at the contact point when the gear pair is under a light load. Then, the contact stress can be determined according to Hertzian contact stress formula. Furthermore, a mesh generation program for three-dimensional gear tooth surfaces will be developed on the basis of the mathematical models developed in the current research project. Finite element analysis will then be performed to simulate the contact stresses and bending stresses of the contacting gear teeth. Furthermore, experiments of single flank test and contact patterns will be performed by using the universal gear meshing tester at National Chiao Tung University with the as manufactured modified curvilinear gear pair. The measured transmission errors and contact patterns can be compared with the simulation results obtained previously in this research. ; 研究期間 9808 ~ 9907 |
