| 摘要: | 擺線行星齒輪機構為擺線行星齒輪與漸開線行星齒輪的組成，一般業者多以商品名稱RV機構稱之。由於擺線齒輪齒形為短齒高，因此可達成少齒差的關係。此關係使擺線行星齒輪機構具有高減速比以及多接觸齒對等特性，而且相較於漸開線齒輪可以承受更高的負載、吸收更大的衝擊，而具有功率密度極高的特性。而另一方面，擺線行星齒輪的多接觸齒對特性亦可達成低背隙，進而使整體機構滿足高傳動精度的要求。以上特性使此擺線行星齒輪機構廣泛應用在重負載、高衝擊或需要高傳動精度的場合，如自動化機械、土木機械、風機偏航變槳系統等。但擺線行星齒輪機構的功率分流及多齒對嚙合的特性，使得三根曲軸、兩擺線盤的扭矩分配以及各接觸齒對之負載分配在分析上相當困難。另一方面，擺線行星齒輪機構中的擺線齒盤在運轉時為以偏心方式運動，而且軸承剛性亦不可忽略，因此與靜態條件相比，在動態負載關係上將額外受離心力、慣性力以及軸承剛性的影響，所以扭力分配及各齒對的負載分配在動態下之分析為必要的研究課題。
本論文之目的為應用電腦輔助分析軟體Adams建立一動態負載分析模型。在研究中首先利用有限元素分析結果調整接觸齒對之嚙合剛性，再以經過調整之剛性參數，分析準靜態狀況下的各齒對負載，所得結果與已有的受載齒面接觸分析數值模擬結果極為相近，顯見此方法具有極佳的可信度。因此在本研究中則以此方式建立分析模型，並將軸承設定為彈性體。負載分析案例則包括銷輪輸出及托架輸出等兩組不同應用場合之減速機，而此兩案例亦因應用場合不同，具有不同的齒廓修形設計。本研究所使用的分析條件包括準靜態，以及多組不同轉速的定速與具有加減速等動態條件，用以釐清動態條件對負載分配的影響；並同時將軸承設定為彈性體。而本研究中的分析項目包括無誤差與具擺線盤偏心誤差下的傳動誤差，擺線齒輪、漸開線齒輪接觸齒對之負載分配，擺線齒盤支撐軸承負載變化，曲軸扭力分配，以及兩擺線齒盤扭力分配等。
由分析結果顯示，不同的擺線齒廓修整參數會對傳動誤差及擺線盤各齒對的負載分配變化趨勢造成影響；同時軸承的非線性剛性亦會導致兩擺線齒盤及三曲軸扭力分配不均的現象，其中曲軸的負載變化的振幅值為理論值的13%，擺線齒盤則為1%。而轉速大小亦會明顯影響擺線盤齒對之分配負載大小及趨勢，當轉速提高後將使齒對接觸提早結束，且最大負載也隨之增加；例如在輸出轉速為30rpm的條件下，負載最大值可達到靜態條件的1.5倍。
透過分析結果顯示本研究所提出之電腦輔助分析方法，可以有效分析擺線行星齒輪機構中負載變化受軸承剛性對以及轉速等動態影響。
關鍵字：擺線行星齒輪減速機、動態負載分析、多齒對接觸、Adams
;The cycloid planetary gear drives, so-called RV-drives in the industries, consist of a cycloid planetary gear stage and an involute planetary gear stage. Due to the short tooth depth of cycloid profile, a small tooth number difference can be achieved for application with a high reduction ratio and multiple tooth pairs in contact. With these features the cycloid planetary gear drives can have higher durability, higher shock absorbability and higher power density than the conventional involute planetary gear drives. On the other hand, the multiple contact tooth pairs can also provide lower backlashes, which make precision transmission possible. Because of the above features the cycloid planetary gear drives are widely applied in the conditions with heavy load, shock or high precision, for example, automatic machinery, civil machinery, as well as yaw and pitch system of wind turbines. However, the analysis of the split torques among the crankshafts and the two cycloid disks as well as the shared loads among the contact tooth pairs becomes difficult, because of multiple tooth pairs in contact and power split. On the other hand, the cycloid disks move eccentrically and the bearing stiffness can not be ignored. The dynamic loading conditions are influenced additionally by centrifugal and inertia effect and the bearing stiffness with comparison of static analysis. The power distribution and the load sharing of tooth pairs in cycloid planetary gear drives are the essential research topics.
The purpose of this thesis is to establish a dynamic analysis model by using software Adams for load analysis of the cycloid planetary gear drives. In the study the meshing stiffness of the contact tooth pairs is at first determined by using FEM. The analysis result of load sharing of contact tooth pairs with the obtained stiffness parameters has a good agreement with a loaded tooth contact analysis (LTCA) approach. This method is obviously reliable. The analysis model is therefore established with aid of this approach, and the bearing stiffness is considered in the model. The study cases in the thesis for dynamic load analysis include two different reducers, each having the pin-wheel or the carrier as the output component. The tooth modification of the two cases are different due to different application conditions. The boundary conditions for dynamic load analysis include quasi-static, various constant speeds, and variable speed conditions. The analysis items in the thesis are the transmission error with/without eccentric error of cycloid disks, shared loads in cycloid and involute tooth pairs, variation of bearing loads for supporting the cycloid disks, and the distribution of the torques to the crankshafts and cycloid disks.
The results show that different kinds of tooth modification cause different variations in tooth contact force. The nonlinear bearing stiffness will cause also unevenly shared torques between crankshafts and cycloid disks. The variation of the unevenly shared torques among the three crankshafts is about 13%, and 1% between the two cycloid disks. The dynamic conditions affect also the tooth contact forces, not only in the trend and but also the maximum value of the shared forces. As the speed increases, the end of tooth contact occurs earlier, and the maximum value of the shared loads also increase, for example, the maximum value in the condition of the output speed 30 rpm is 1.5 times as much as that in the quasi-static condition.
The analysis results show that the computer-aided analysis approach proposed in this study can effectively analyze the varaition of dynamic loads in the cycloidal planetary gear deives due to the bearing stiffness and the rotational speed.
Keywords：Cycloid planetary gear drives, Dynamic load analysis, Multiple tooth contact, Adams |
