| 摘要: | 行星齒輪傳動具有功率重量比高、傳動比大以及傳動平穩效率高等優點，故被廣泛應用於車輛、船舶機械、產業機械與風力發電機等機械傳動系統上，但在實際運用上，卻會受到加工或組裝誤差等因素之影響，無法使行星齒輪間負載均勻分配，意味著行星齒輪機構無法因行星齒輪數目增加而能提供更大的扭力傳動。為了解決負載不均問題，一般常使用均載設，使齒輪構件浮動或利用撓性方法給予齒輪自由度，以達成行星齒輪間的負荷可以平均分佈。 本研究探討以行星齒輪浮動為均載機構之行星齒輪傳動在具加工與組裝等製造誤差下之靜態負載分析。論文首先以行星齒輪系嚙合幾何關係探討製造誤差對於齒隙之影響，並以影響係數法建立行星齒輪系之多齒輪對嚙合之靜態負載數值分析模式，透過此一方法可得到行星齒輪間負載分配與接觸齒面負載分佈。再進一步分析行星齒輪浮動下之靜態負載，分析模式以多齒輪對嚙合負載數值分析模型為基礎，配合行星齒輪系作用力平衡與齒對嚙合關係之齒間間隙之條件，以求解各行星齒輪浮動位置參數、齒輪齒面應力分佈以及每一對嚙合齒對分配負載。 為了驗證行星齒輪浮動靜態分析模式之可行性與可信度，本論文使用有限元素方法分析不同行星齒輪加工與組裝誤差情況下，分別比較行星齒輪固定與浮動齒輪的負載分配與齒面應力分佈，並得到相近結果。更進一步討論不同行星齒輪個數、不同行星齒輪彈性銷剛性以及不同輸入扭力下，行星齒輪浮動對於負載之影響。 根據各種誤差與設計參數對於行星齒輪負載分配影響分析顯示，在不同行星齒輪個數(3~6個)且齒輪不浮動下，齒輪切向銷孔誤差、齒厚誤差與徑向銷孔誤差皆會影響行星齒輪負載分配造成齒輪負載不均情形，其中以切向銷孔誤差影響最大，齒厚誤差影響次之，徑向銷孔誤差影響甚微。而在行星齒輪浮動時，可使行星齒輪負載分配均勻。比較兩種行星齒輪彈性銷剛性，其分析結果顯示當行星齒輪彈性銷剛性越小，行星齒輪負載分配越均勻。比較三種不同輸入扭力，當輸入扭力增加行星齒輪負載分配較為均勻。 Planetary gear drives have the advantages of high power-weight ratio, large gear ratio, as well as smooth transmission with high efficiency. They are often widely applied in mechanical power transmission system, such as vehicles, ship machinery, production machinery, and wind turbines. However, in the practice, the load sharing among the planets will be not even due to the presentence of manufacturing and assembling errors. It means the planetary gear set can’t provide power transmission with a larger torque even by increasing the number of planetary gears. In order to solve the problem, many load balancing mechanisms are applied to meet the requirement of even load sharing by using flexible elements or floating gears to have more degrees of freedom. One of the well-known methods for the planetary gear drives is the design with flexible pins, i.e. the planet gears are flexibly supported. The aim of this study is to analyze the static load sharing and load distribution in planetary gear sets with a floating planet gear in the presentence of manufacturing and assembly errors. The geometrical relation between the manufacturing errors and the gaps of the engaged teeth among the gears of the planetary gear drives is at first analyzed. Based the influence coefficient method, a numerical method of loaded tooth contact analysis for planetary gear sets in the case of multiple gear-pairs and multiple tooth-pairs is also developed to analyze the load sharing among the planet gears and the load distribution on the engaged tooth flanks., The loading in the planetary gear sets with flexible supported planet gears is further analyzed by using the developed LTCA method and the conditions of load equilibrium of the planets and the relation of the tooth gaps due to the position change of the planets. The unknowns can be thus solved, including the balanced positions of the planets, the contact stresses distribution on the flanks and also the load sharing among the planet gears. In order to verify the feasibility of this theory, the analyzed results for the planetary gear sets with manufacturing and assembly errors are also compared with the finite element method under consideration of the planetary gear sets with rigidly or flexibly supported planets. Both the calculated results are in good agreement. The influences of the number of the planets, the stiffness of the planet supporting, and the transmitted torque on the load sharing are also discussed. The analysis of the load sharing in planetary gear set under consideration of the influences of various types of errors and design parameters shows that with different planet number the tangential pinhole position error, tooth thickness error and the radial pinhole position error all can influence the load sharing of planet gears. Which the pinhole position error is the critical influence tolerance, the tooth thickness error is the second and the radial pinhole position error has little effect. In case of floating planet gears design, the even load sharing among planets can be achieved. In the comparison of design parameters, the smaller planet flex-pin stiffness the more even load sharing and increased input torque can reduce the uneven load sharing. |
