| 摘要: | 高接觸率正齒輪對由於不會產生軸向力，且因高接觸率減緩因齒對交換對嚙合剛性變動的影響，因此常應用在高負載或高轉速的場合。然而在設計高接觸率齒輪對時，也必須考慮相關問題。首先在多齒對接觸下，各齒對負載分配會影響到嚙合時變剛性。此特性在高速運轉下，會影響傳動噪音和振動。此外，輪齒、軸和軸承的變形也會影響齒輪對的齒面接觸特性與嚙合剛性。
由於傳統齒輪動態分析多以系統角度分析傳動之動態特性，而無法探討嚙合齒面在受動態負載下的接觸特性。因此本論文以電腦輔助分析軟體MSC.Marc與MSC.Adams對高接觸率正齒輪對進行協同分析，以瞭解齒輪對在動態負載下齒面接觸各種特性。齒輪對之主動軸採懸臂支撐，從動軸則為簡單支撐方式。分析條件則包括有、無修整齒面以及有、無軸平行度誤差。
在分析建模方面，齒輪部分使用MSC.Marc建立5個齒對進行動態受載齒面接觸分析。主動齒輪在不同齒面寬使用多個rbe2元素進行運動控制，並在此設為協同模擬連接點，以分析傳動軸在高速轉動下對齒輪對的影響。從動齒輪內孔以圓柱剛體貼合，圓柱中心設定連接點。從動齒輪的運動設為由該點帶動，且扭力作用於此。傳動軸則使用MSC.Adams進行動態模擬。軸段設為FE Part，並將連接點設於齒輪部連接點相同座標處。最後使用MSC.CoSim結合MSC.Adams和MSC.Marc進行協同模擬。
考慮分析時間，初始條件採啟動時有瞬間速度變化，以透過暫態分析來瞭解電腦輔助協同模擬之效能。從CoSim協同模擬結果發現Marc可以正常分析，但Adams在分析上仍有問題尚未克服如CoSim僅能擇一傳輸Adams計算得到的速度或作用力資料到Marc。另一方面為了使計算更精確，Adams的分析步階數採用Marc的倍數。但在Marc的步階間隔中，Adams會以上一步接收的剛性值沿著剛度曲線的切線方向獨自計算並將計算結果呈現出來。此設定導致Adams計算結果與真實狀況有所差異。
在各項分析結果皆在起始產生極大振盪，之後隨時間而慢慢平緩。而在無修整齒輪對分析結果中，接觸斑會因軸剛性關係集中於靠近軸承側。在無修整齒輪對具有軸歪斜誤差時，皆在換齒時發生齒頂接觸而導致接觸應力產生極大突跳。而接觸斑形狀會受到軸誤差與軸變形方向影響。在方向同側時，接觸斑會更集中於靠近軸承側；方向相反時，軸變形會與軸誤差相互抵消，反而產生近似正常線接觸型式。而軸傾斜誤差影響相對小，接觸斑未因誤差而出現明顯變化。而修整齒輪對的分析結果顯示，嚙合作用力之振盪值相對小；而接觸斑在嚙合過程中一直保持在齒面中心處。同時軸誤差對於修整齒輪對的影響甚小。
;High-contact ratio spur gear pair are often used in high-load or high-speed applications, due to the absence of axial forces and the reduction in the impact of mesh stiffness resulting from the exchange of gear pairs. Nevertheless, additional considerations must be taken into account when designing spur gear pairs for high contact ratio applications. Firstly, in the case of multi-tooth contact, the load distribution among the tooth pairs will affect the time-variant mesh stiffness. This characteristic can influence transmission noise and vibration at high speeds. Furthermore, the deformation of the gears, shafts, and bearings will also impact the tooth contact characteristics and mesh stiffness of the gear pairs.
The conventional dynamic analysis of gears is based on a systems perspective, which makes it impossible to investigate the contact characteristics of the engaged tooth surface under dynamic loading. Therefore, the objective of this study is to employ computer-aided analysis software, MSC.Marc and MSC.Adams, to conduct a co-simulation of high contact ratio spur gear pairs. This approach is intended to enable an understanding of dynamically loaded tooth contact characteristics of gear pairs. The driving shaft of the gear pair is modeled as cantilever support, while the driven shaft as simple support. The high-contact-ratio gear pairs are analyzed according to the conditions with or without flank modification and shaft misalignment.
In terms of modeling for analysis, five pairs of teeth of the gear were modeled using MSC.Marc for dynamically loaded tooth contact analysis. The motion control of the driving gear is done using several rbe2 elements at different tooth widths, where they are set up as the connection points for co-simulation in order to analyze the influence of the shaft on the gear pairs at high speeds. The inner bore of the driven gear is fitted with a cylindrical rigid body and the centre of the cylinder is set as the connection point. The motion of the driven gear is set to be driven from this point and the torque is applied there. The shafts are dynamically simulated using MSC. Adams. The shaft sections are set up as FE Parts and the connection points are set to the same coordinates as the connection points of the gear sections. Finally, the co-simulation is carried out by using MSC.CoSim in combination with MSC.Adams and MSC.Marc.
Considering the analysis time, the initial condition is a transient velocity change at the time of startup, in order to understand the effect of computer-aided co-simulation through the transient analysis. From the results of the CoSim simulation, it is found that Marc can be analyzed normally, but there are still some problems in the analysis of Adams that have not been overcome, e.g., CoSim can only select and transmit either the velocity or the force data calculated by Adams to Marc; on the other hand, in order to make the calculations more accurate, the number of steps of the analysis of Adams adopts a multiple of that of Marc. However, in the step intervals of Marc, the stiffness value received in the previous step is calculated and presented by Adams independently along the tangential direction of the stiffness curve. This setting causes the Adams calculations to differ from the real situation.
In all analyses, the results begin with a high amplitude, which slowly decrease with time. In the results of the analyses of non-modified gear pairs, the contact patterns are concentrated near the side of the bearing, due to the stiffness of the shaft. In the case of non-modified gear pairs with shaft skew errors, contact on the top of the tooth during the exchange of tooth pairs, results a significant increase in contact stresses. The direction of shaft misalignment and shaft deformation exert a significant influence on the contact pattern. When the direction is identical, the contact pattern will be more concentrated close to of the bearing; conversely, when the direction is opposite, the shaft deformation and shaft error will compensate for each other, resulting in a contact pattern that is analogous to the typical line contact pattern. The impact of shaft inclination error is relatively minor, with no notable alteration in the contact pattern resulting from the error. The results of the analysis of the modified gear pairs demonstrate that the vibration value of the mesh force is relatively minimal, and that the contact pattern remains center on the tooth flank throughout the mesh process. Conversely, the impact of shaft misalignment on the modified gear pair is found to be insignificant. |
