考慮軸承剛性影響下具兩齒差之擺線行星齒輪機構之受載齒面接觸分析;Loaded Tooth Contact Analysis of Cycloid Planetary Gear Drives With Tooth Number Difference of Two Considering Bearing Stiffness

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Title:	考慮軸承剛性影響下具兩齒差之擺線行星齒輪機構之受載齒面接觸分析;Loaded Tooth Contact Analysis of Cycloid Planetary Gear Drives With Tooth Number Difference of Two Considering Bearing Stiffness
Authors:	張甯喬;Chang, Ling-Chiao
Contributors:	機械工程學系
Keywords:	兩齒差擺線行星齒廓;瞬心法;接觸率;軸承撓性;受載齒面接觸分析模型;影響係數法;負載分配;接觸應力;Cycloid planetary gear drives with tooth number difference of two;Intantaneous center method;Contact ratio;Bearing stiffness;Loaded tooth contact analysis;Influence coefficient method;Load sharing;Contact stress
Date:	2018-01-24
Issue Date:	2018-04-13 11:29:43 (UTC+8)
Publisher:	國立中央大學
Abstract:	由於單齒差擺線行星齒輪機構的嚙合齒對與曲軸軸承負載過大，且因為在齒廓修形時，使齒對受載接觸率下降，而無法有效提高承載能力，因此本論文提出以兩齒差的概念來達成降低擺線行星齒輪機構齒對接觸負載之要求。兩齒差擺線齒廓係由兩個單齒差齒廓交錯一角度而形成非連續齒廓，因此兩齒差擺線齒輪機構之分析模型可由單齒差擺線齒輪的理論模型擴展而得。所以在本論文中以已發展之單齒差擺線齒輪齒廓、嚙合關係以及受載齒面接觸分析模型為基礎，整合奇、偶數齒對之幾何關係，發展出針對具兩齒差齒廓之擺線齒輪嚙合分析模型與受載齒面接觸分析模型，其中受載齒面接觸分析模型係以影響係數法為基礎，並納入曲軸軸承有、無撓性之兩種受載條件。本研究首先探討銷半徑以及偏心量等兩個設計參數對於齒廓特性、接觸率以及齒面接觸負載、應力之影響。並以此影響分析結果，挑選適當的設計參數，做為後續兩種負載分析之依據：(1)探討曲軸軸承為撓性對齒對受載狀況的影響，(2) 探討單、雙齒差擺線齒輪機構在受載狀況下之差異。設計參數影響分析研究結果顯示，較小的針銷半徑或較大的偏心量，會增加齒對接觸率，以及降低最大負載分配值。而較大偏心量可降低最大接觸應力值，但銷徑減小卻使得最大接觸應力值略為上升。由曲軸承撓性影響分析結果顯示，軸承撓性造成擺線盤增加三個自由度的位移量，使得嚙合齒對提前接觸，且在接觸開始後之齒對分配到更大的負載；此狀況影響程度大於軸承為剛性狀況下。另一方面，在軸承考慮為剛性狀況下，負載分配變化曲線會產生週期性鋸齒狀跳動的現象，而在軸承具有撓性情況下，週期性鋸齒狀跳動仍存在，但因奇偶數齒對交換，使得週期減半。在接觸應力分佈結果中，支撐軸承為撓性情況下，受到齒對提前接觸原因，使得較大接觸應力在嚙合過程中多發生於前半部，但後半部的接觸應力值小於軸承為剛性情況。由單、兩齒差擺線齒輪機構之受力分析結果比較，可以見到兩齒差擺線齒輪機構最大負載分配值相對於單齒差可以減少約35%，並且各齒對具有均勻負載分配。而兩齒差齒廓接觸應力值可以降低至單齒差狀況下之25%。但是在兩齒差之狀況，在接觸結束時齒頂處仍有負載存在。因此受到齒頂邊緣效應的影響，使得兩齒差之接觸應力在齒頂處會有突升之集中應力產生。另一方面兩齒差齒廓之曲軸支撐徑向力雖可以小於單齒差齒廓狀況約50%，但徑向力仍遠小於軸承圓周力，使得曲軸上軸承徑向力僅較單齒差齒廓狀況下降低約5%。由本論文結果顯示，透過使用兩齒差齒廓可以有效提高接觸率，降低最大負載分配以及最大接觸應力，同時使負載分配狀況更均勻分佈。然而卻不能有效降低曲軸上軸承負載。 ;Because the loads acting on the contact tooth pairs and the cranks of the cycloid planetary gear drives with tooth number difference (abbr. TND) of one are very large, and the contact ratio is reduced with flank modification, the load capicity cannot be enhanced effectively. Therefore the design concept by using TND of two is proposed in the study to give a possibility to improve the loaded contact characteristics. The cycloid disk with TND of two can be regarded as combination of two sam base cycloid profile rotated against each other with an pitch angle. Therefore the analysis model of the cycloid planetary gear reducers with TND of two can be expaned from the model with TND of one. With reguarding odd and even numbered tooth pairs, the gear meshing analysis and the loaded tooth contact analysis (LTCA) model of the cycloid profile with TND of two can be established based on the developed mathematic model and the related analysis models of the cycloid profile with TND of one. The LTCA approach in the study is based on the influence coefficient method with consideration of bearing stiffness. In this parper, the influences of the design parameters, i.e., the pin raidus and the eccentricity, on the loaded contact characterisitcs, such as the flank profile, the contact ratio, the shared loads and the contact stresses. Based on the analysis results, appropriate design parameters are determined for the following analysis: (1) the effect of the bearing stiffness of the loaded tooth contact characteristics, and (2) comparative analysis with the conventional drives with TND of one on the loaded contact charateristics. The results from the influence analysis of parameters show that the cycloid drive with TND of two having smaller pins and a larger eccentricity owns a larger contact ratio and reduced shared loads. The eccentricity affects the variation of the load sharing stronger than the pin radius, not only because of the tooth profile, but also because of the transmission angle. A larger eccentricity can lower the shared load and the contact stress, but smaller pins reduce shared load and increase larger contact stress sightly. The influence of the bearing stiffness, as the results show, causes the contact of the tooth pairs occuring earlier than the condtion without considering the bearing stiffness, because of additional displacements with three degrees of freedom. The maximum load sharing is enlarged because the displacement is closer to the front part of tooth pair due to the transmission angle. Moreover, the variation of the shared load on flank with considersing bearing stiffness performs in cyclic jumping type, but the period duration is reduced as a half due to the change of odd and even numbered tooth pair change. Even so the condition of bearing stiffness is not impact on the bearing load. The comparative analysis results with TND of one show that the maximum sharing load in the case of TND of two can be reduced 35% relative to TND of one, and is distributed more soomthly. On the other hand, the maximum contact stress for TND of two can be enlarged 25% with respect to TND of one. But the contact stress for TND of two still remains at the end of contact, and the contact stress concentration occurs due to the edge effect of the tip corner. Furthmore, the radial bearing load in the case of TND of two can reduce 50% relative to the case of TND of one. But the lowered radial force is still much smaller than the circumferential force. The radial bearing force reduce just 5% relative to TND of one. From the analysis results of this paper, the cycliod planetary gear drives with TND of two can effectively increase the contact ratio and reduce the maximum load sharing and the maximum contact stress. However, it can not efficiently reduce the bearing load on the crankshaft.
Appears in Collections:	[Graduate Institute of Mechanical Engineering] Electronic Thesis & Dissertation

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