| 摘要: | 行星齒輪機構因具功率分流設計，與一般平行軸齒輪對比較，具有較高功率體積密度、輸出輸入軸同軸心與設計緊實等優點，因此廣泛運用於各種傳動中。但實際運轉中，行星齒輪組一方面會因受到加工、組裝誤差與嚙合剛性影響，造成行星齒輪間負載分配不均與嚙合過程負載、應力變化跳動；另一方面，因受組件變形影響，如托架、行星銷軸與太陽齒輪扭轉等變形，皆會造成嚙合齒面負載分佈不均。一般而言，在工業應用上會以齒面修整方式，以改善前述問題，進而提升齒輪機構承載能力與傳動效能。但修整後之齒面在受載下的接觸結果卻必須要能事先預估，始得以掌握齒面修整特性。因此本論文之研究目標即為提出一可分析行星齒輪組之受載齒面接觸分析模型(LTCA)，以模擬、並分析在齒面修整、組件變形、以及存在各種誤差等真實狀況下之嚙合齒面接觸狀況。
在本論文中先以行星齒輪組齒面修整模式：太陽齒輪採螺旋角修整，行星齒輪採齒線隆起修整以及齒形修整形式，建立成形磨加工之三維齒面方程式。為求得行星齒輪組之接觸狀況，本研究並根據齒輪組特性，納入修整齒面與誤差，建立齒面接觸分析模型(TCA)，計算嚙合齒面接觸點參數，以及分析在齒面修整與各種誤差下之傳動誤差、背隙以及齒間間隙變化。納入所發展的分析模型的誤差包括行星齒輪齒厚誤差，行星銷孔位置偏差，托架、太陽齒輪、行星齒輪之偏心以及行星齒輪銷軸偏斜等誤差。
行星齒輪組受載齒面接觸分析模型(LTCA)係以影響係數法為基礎建立而得，可用以分析各種齒面受載下接觸特性。此LTCA分析模型納入組件變形之影響，包括輪齒齒面接觸、彎曲、剪力變形，托架與行星銷軸變形，太陽齒輪軸扭轉變形等。模型亦納入由齒面接觸分析模型(TCA)計算之接觸齒面幾何關係，可模擬各種赫茲、非赫茲接觸狀態，以及分析各項組件之加工、組裝誤差對受載接觸之影響。
為了驗證理論模型之可靠度，本研究以有限元素分析軟體計算所探討之行星齒輪組機構之受載下齒面應力與行星齒輪間負載分配，並與分析模型比較。結果顯示兩者應力變化趨勢相近且最大值差距少於10%，負載分配差距少於1%，證明理論分析模型具有相當的可信度。
本論文並以一實際之行星齒輪組為分析案例。首先以發展之TCA模型分析在有、無誤差以及齒面修整下，行星齒輪組之傳動誤差、背隙變化。再以LTCA模型分析在組件變形以不同誤差影響下，行星齒輪組嚙合過程之應力、負載與受載傳動誤差之變化，以及齒面上接觸斑大小與應力分佈情況。論文中亦包括模擬因變形造成之齒頂邊緣接觸以及因行星銷軸偏斜誤差所造成齒端邊緣接觸等之非赫茲接觸應力狀況，以及在具太陽齒輪浮動設計下，誤差對行星齒輪間負載分配與太陽齒輪中心軌跡。
分析結果顯示環齒輪與行星齒輪嚙合齒對因托架剛性影響，齒面負載分佈不均程度較大。行星齒輪組齒面經雙隆起修整後各嚙合齒對之齒面應力分佈可呈現左右對稱且最大應力落於齒面寬中間，嚙合過程應力與負載皆連續變化。在考慮相同誤差量影響下，托架偏心對行星齒輪負載分配與受載傳動誤差影響最大。
本論文所提出之行星齒輪組分析模型，可提供設計者有效分析嚙合過程齒面受載情況以及行星齒輪組齒面修整參數設計之依據，並可評估行星齒輪組之組件加工、組裝精度對傳動誤差與背隙之影響範圍，以及對行星齒輪間負載分配與受載傳動誤差之影響。
;Compared with the parallel axis gear drive, the planetary gear drive, as a power-split mechanism, has the advantages of high power density, coaxial input and output shaft, as well as compact design. Therefore, it is widely applied in various transmissions. But in actual operation, the time-variant mesh stiffness as well as manufacturing and assembly errors will cause the uneven load sharing among multiple planet gears and the jump in variation of contact stress and shared load of contact tooth pairs of the planetary gear set. On the other hand, the deformation of the components in the planetary gear set will also result in uneven load distribution on the tooth flanks. The effective solution in the practice is to apply flank modification to enhance the load capacity and also to improve transmission performance. But the loaded contact characteristics of the drive have to be simulated in advance, so as to proceed suitable flank modification. The goal of the dissertation is thus to propose a loaded tooth contact analysis model for planetary gear drives, so as to simulate and analyze the contact characteristics of the engaged teeth under the real condition.
The equations of the three-dimensional modified flanks, manufactured by profile grinding, are at first derived in the dissertation. Considering the flank modification and the errors, a tooth contact analysis model (TCA) is developed for calculating the variables of the contact points. The transmission errors, the backlashes and the clearances in the planetary gear sets can be analyzed accordingly. The errors, involved in the TCA model, include the tooth thickness error of the planets, the position errors of the pin-hole, the eccentric errors of the carrier, the sun gear and the planet gears, as well as the angular misalignments of the planet pin.
The proposed loaded tooth contact analysis (LTCA) model for planetary gear sets, is based on the influence coefficient method, and involves the influences of the deformation of the teeth, the carrier, the sun gear and the planet pins. The topological conditions of the contact teeth calculated by the TCA model are also involved in the analysis, so as to simulate the Hertzian and Non-Hertzian tooth contact and to analyze the influences of the various manufacturing/assembly errors on the loaded tooth contact.
In order to verify the reliability of the proposed LTCA model, the analyzed results are compared with the finite element method (FEM). The results include the contact stress on the tooth flank along the face-width and the load sharing among each planet gear with the non-floating and floating sun gear. The comparative results show the same trend of contact stress and the difference with less than 10%. This indicates the model is in a good agreement with FEM.
A planetary gear set used in the practice is analyzed by the proposed TCA and LTCA model. The variation of the transmission errors and the backlashes of the planetary gear set is analyzed by applying the developed TCA approach, considering various cases with and without flank modification and errors. The variation of shared loads, contact stress and loaded transmission errors stress during gear meshing, as well as the contact pattern and stress distribution on each engaged tooth flank are analyzed by using the LTCA model. The non-Hertzian contact stresses of tip corner edge contact due to deformation and the face-end edge contact due to misalignment of the planet pin are also simulated. The influence of the errors on the load sharing among planets and the trajectory of the floating sun gear are also analyzed in the dissertation.
The analysis results show that tip corner contact occurs more likely in the planet-annulus gear pairs than sun-planet gear pairs. The contact stress on the flanks of planet-annulus gear pairs distributes more uneven due to the stiffness of the carrier. The stress distributions of the engaged tooth pairs are even and symmetric after flank modification. On the other hand, the eccentric error of the carrier has a larger influence on the load sharing among planet gear and loaded transmission errors.
The proposed LTCA model for planetary gear sets in the dissertation can simulate effectively and efficiently contact characteristics of engaged teeth with or without loading during gear meshing. The results can provide good evidence for designing flank modification of a planetary gear set. It can serve as the model for evaluating the influence of the manufacturing/assembly accuracy on loaded or unloaded transmission errors, backlash, as well as load sharing among planet gears. |
