具太陽齒輪浮動之行星齒輪機構負載分析 ; Analysis of Load Sharing in Planetary Gear Sets with a Floating Sun Gear

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题名:	具太陽齒輪浮動之行星齒輪機構負載分析;Analysis of Load Sharing in Planetary Gear Sets with a Floating Sun Gear
作者:	黃冠霖;Guan-lin Huang
贡献者:	機械工程研究所
关键词:	物件導向程式;太陽齒輪浮動;負載分配;行星齒輪機構;object-oriented programming;floating sun gear;load sharing;planetary gear transmission
日期:	2010-12-08
上传时间:	2011-06-04 15:01:04 (UTC+8)
出版者:	國立中央大學
摘要:	行星齒輪傳動機構藉由多個行星齒輪分別承受分配負載方式，得以提高傳動功率。然而由於加工、組裝誤差與機構構件等變形因素，造成每個行星齒輪會承受大小不同的負載，因此對於多個行星齒輪的輪系皆會有均載設計，其中又以太陽齒輪浮動設計最為常見。目前對於行星齒輪機構負載分配的理論研究，多以簡化的齒輪數學模型分析為主，本論文之研究目的即在建立一套以漸開線齒輪幾何為基礎的行星齒輪系負載分析模式，以探討具太陽齒輪浮動之行星齒輪機構在組裝與加工誤差下，行星齒輪的可組裝性、太陽齒輪中心可動範圍以及行星齒輪間的負載分配等問題。在研究中首先利用二維漸開線齒輪幾何，建立行星齒輪系嚙合關係，在考慮各種設計參數與誤差下，透過行星齒輪組裝流程探討行星齒輪系的可組裝性，並以「單一齒輪兩齒對接觸」與「兩齒輪單齒對接觸」兩種不同的浮動太陽齒輪拘束形式，探討太陽齒輪中心可動範圍。接著分別利用解析法與數值方法解探討行星齒輪機構負載分配情形。同時本研究亦針對於太陽齒輪固定狀況下，以各齒輪對接觸齒數變化造成嚙合剛性的改變來解釋行星齒輪系在不同嚙合位置的負載分配會出現跳動的情形。本研究同時以物件化程式輔助分析，以提高計算速度。浮動太陽齒輪中心可動範圍的分析結果顯示，太陽齒輪在三至五個行星齒輪之輪系的中心可動範圍邊界呈現近似多邊形，其邊界數目為行星齒輪個數兩倍，而且太陽齒輪在可動範圍邊界上受拘束形式，以兩齒輪單一齒對拘束為主。此外在不同齒厚配合公差下的可動範圍會隨著齒輪對背隙增加而等比例放大。由對三個行星輪之行星齒輪系所進行可組裝性分析，發現在分別具有齒厚誤差、徑向銷孔誤差與切向銷孔誤差時，行星齒輪系可組裝之最大容忍誤差值與各種配合齒厚公差的背隙值會呈線性正比關係。根據各種誤差與設計參數對於行星齒輪分配負載的影響分析結果顯示，切向銷孔誤差對於行星齒輪負載分配影響為最大，其次是齒厚誤差，而徑向銷孔誤差影響甚微。此外當行星托架上某一銷孔存在切向位置誤差，若在該位置上裝設特定齒厚誤差的行星齒輪，則能夠補償切向銷孔誤差對於負載分配的影響。而增加輸入扭矩，也能改善負載分配不均的情形。在使用太陽齒輪浮動設計後，三個行星輪之輪系的負載分配能達到均載，在四、五個行星輪之設計雖也可改善負載不均，但無法達成均載。 Planetary gear sets can achieve higher power density levels, because of multiple parallel power paths by each planet branches. However, load sharing among planets are usually even, due to the manufacturing errors, assembly errors and deformation of parts in planetary gear sets. Therefore, load balancing mechanisms are widely used in multi-planet system. The most common load balancing mechanism is floating sun gear design. In the recent studies, simplified mathematical models are often used for analysis of load sharing in planetary gear system. The goal of the thesis is to establish an approach based on the involute gear geometry for analysis of load sharing among the planet gears, possibilities for assembly, and movable area of the sun gear. Mesh relation for the planetary gear set is at first derived based on two-dimension involute gear geometry. The possibility to assembly of the planetary gear train under consideration of various design parameters and errors is determined according to the assembly process. The movement of the sun gear is restricted by planets in two different types, i.e. restriction by single planet with double contact tooth pairs, and restriction by double planets with single contact gear tooth pair. In order to find out the movable area of the sun gear center, maximum movable distance of the sun gear in any direction will be obtained according to both the restriction types.. The shared loading among the planets in the planetary gear train is analyzed in the study by using an analytical approach as well as a numerical method. A jumping behavior of the load sharingin the planetary gear set with a fixed sun gear is also explained in the thesis based on the change of the meshing stiffness of the contact gear tooth pair due to the change of the number of the contact tooth pair. The study also introduced object-oriented programming for anakysis to enhance the calculation efficiency. The analysis result for the movable area of the floating sun gear center in the planetary gear train with 3 to 5 planets showed that the boundary of the movable area is a polygon and the number of the borders is twice the number of the planets. Double planets with single contact tooth pair is the most likely restriction type of the floating sun gear. Furthermore, the movable area of the floating sun gear is proportional to the backlash corresponding to the tooth thickness tolerance. Acoording to the the analysis result of the assembly condition of the planetary gear set with three planets under consideration of tooth thickness errors, radial pinhole position errors and tangential pinhole position errors, the maximum tolerable error value for assembility is linearly proportional to the backlash. The analysis of the load sharing in the planetary gear set under consideration of the influences of various types of errors and design parameters shows that the tangential pinhole position error is the critical influence tolerance. Second is the tooth thickness error. The radial pinhole position error has little effect on the load sharing behavior. In addition, the uneven load sharing due to a tangential pinhole position error can be compensated with installation of a planet gear on the pinhole position with specific tooth thickness. Furthermore, increased input torque is also ablbe to reduce the uneven load sharing. In case of floating sun design, the even load sharing among planets can be achieved for the planetary gear train with three planets. Similary the load sharing in the gear trains with four or five planets can be also improved, but uneven.
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