| 摘要: | 大型旋轉軸承，一般直徑大於1米，且在內環或外環之一側結合齒輪使用，用於驅動工作設備，如土木工程設備之轉塔，軍事武器之砲塔或是大型旋轉驅動設備。為能節省空間，大型旋轉軸承通常為單獨配置，而且須能承受各個方向極高負載，因此常見以交叉滾柱軸承與四點接觸滾珠軸承等二種軸承型式設計。由於在應用上轉速相對較慢，多在10rpm以下，因此軸承承載能力以準靜態條件計算。而軸承滾子之受載情況又屬於靜不定問題，在受到間隙影響下，增加的五個變形位移使得負載分析更加困難。
本論文之研究目的為建立交叉滾柱軸承與四點接觸滾珠軸承等二種大型旋轉軸承之設計與負載分析方法。此方法可用以分析軸承在具有間隙情況下，承受不同工作負載時，全體滾子負載分配以及各滾子與滾道接觸特性，並比較具不同修形方式之交叉滾柱軸承與四點接觸滾珠軸承在相同負載條件下的受載特性。
在論文中將先使用影響係數法建立滾道與滾子之接觸分析模型。滾道與滾子之接觸剛性圖亦可以藉此求得。再以剛性圖建立完整軸承分析模型，並計算出滾子負載分佈與軸承位移。當軸承存在間隙時，將以軸承受載下轉動環之最終位置做為變數，進行迭代收斂計算。首先，根據求解轉動環位置猜值，求解各滾子與滾道干涉量，再從剛性圖求出各滾子的負載，並以軸承受載轉動環之負載平衡狀態為收斂條件，進行迭代收斂，最終求得轉動環位置以及各滾子負載分佈與對應之接觸應力。
在本研究則以實際案例，分別對交叉滾柱與四點接觸二種型式之大型旋轉軸承在習用軸承間隙下進行負載分析。其中交叉滾柱軸承之滾柱輪廓則探討不同修形設計；四點接觸滾珠軸承之接觸角與滾道輪廓圓弧半徑則根據負載條件決定。
負載分配分析結果顯示，當二種軸承僅受軸向負載時，間隙對滾子負載分佈影響不大；當軸承僅受徑向負載時，間隙增大會使滾子接觸對個數減少；當軸承僅受傾覆力矩時，間隙增大亦會使滾子接觸對個數減少。而滾子接觸個數減少會導致軸承剛性下降，以及承受負載加大。當軸承受綜合負載時，軸承間隙影響亦相同。
二種軸承之間的比較結果顯示，交叉滾柱軸承之軸承剛性都大於四點接觸滾珠軸承。而交叉滾柱軸承之滾子修形雖然可以改善應力分佈，但同時也會降低軸承剛性。
而分析結果也顯示隨著間隙增大，外環的傾覆角度也會隨之增大。此狀況會對交叉滾柱軸承之滾柱接觸應力產生影響。從滾子修形比較分析可知，外環傾覆會導致滾柱應力偏向一側。其中對數修整可避免應力集中；無修整會在邊緣產生應力集中效應；大圓修整則因修整量過大，在應力大小和分佈上表現皆不好，需要再調整參數。另一方面，外環傾覆會導致四點接觸滾珠軸承中滾珠之接觸角產生變化。隨著間隙增大，接觸角度變動差值最後大更可以接近10度。
從分析結果可知，本論文提出之分析方法可以有效且快速分析交叉滾柱和四點接觸滾珠等兩性種旋轉軸承，在有間隙情況下軸承整體滾子的負載分佈情形以及各接觸對之接觸應力分佈情況。
關鍵字：大型旋轉軸承，交叉滾柱軸承，四點接觸滾珠軸承，接觸負載分析，影響係數法，剛性圖法，軸承間隙，滾子輪廓修整，接觸角，軸承剛性，滾子負載分佈，滾子接觸應力與接觸斑。
;Large-scale slewing bearings, typically with a diameter greater than 1 meter, and commonly combined with gears on the side of either the inner or outer ring, are used to drive rotary working equipment, e.g., turrets for civil engineering equipment of military weapons. In order to optimize the utilization of space, these bearings are often typically configured as a single unit and must demonstrate the capacity to withstand extremely high loads in all directions. It is therefore common to distinguish between cross roller bearings and four-point contact ball bearings as the two main types of bearing design. In applications where the rotational speeds are relatively slow, typically below 10 rpm, the load capacity of these slewing bearings is calculated under quasi-static conditions. The loading of the bearing rollers poses a statically indeterminate problem. Because of the influences of the clearance, the additional five deformation displacements make the load analysis more difficult.
This paper aims to establish design and load analysis method for the mentioned two types of large-scale slewing bearings, namely cross-roller bearing and four-point contact ball bearing. This method can be used to analyze the load distribution of all the rollers (or balls) and the contact characteristics of each roller (ball) with the inner and outer raceway when the bearings are subjected to different working loads with clearances. It is also used to compare the loading characteristics of crossed roller bearings with different roller profile modifications, as well as four-point contact ball bearings under the same loading conditions.
In this paper, the influence coefficient method will be used to establish a contact analysis model of the raceways and the rollers. The contact stiffness maps of the raceway and the rollers can also be obtained by this method. The stiffness map is then used to establish a complete analysis model of the bearing and to analyze the load distribution and bearing displacement. When there is clearance in the bearing, the convergence calculation is performed iteratively using the final position of the rotating ring under the load of the bearing as a variable. First, the interference between each roller (ball) and the raceway is solved based on the guessed value of the position of the rotating ring, and then the load of each contact roller (ball) is determined from the stiffness map, and then the load equilibrium of the loaded rotating ring is used as a convergence condition for the iterative calculation, so that the position of the rotating ring as well as the distribution of the load on each roller and the corresponding contact stress are finally determined.
In this study, two types of large slewing bearings, namely crossed roller bearing and four point contact ball bearing, are analyzed under the usual bearing clearances with a practical example. The roller profiles of the crossed roller bearings are studied in different profile modification, while the contact angle and the curvature radius of the raceway profile of the four point contact ball bearings are determined according to the loading conditions.
The results of the load distribution analysis demonstrate that when both types of bearings are subjected to axial loading only, the clearance has a negligible influence on the roller load distribution. Conversely, when the bearings are subjected to radial loading or tilting moments only, an increase in the clearance results in a reduction in the number of pairs of roller contacts. A reduction in the number of roller contacts results also in a corresponding decrease in bearing stiffness and an increase in the acting load on the rollers (balls). The same effect of bearing clearance can be also found when the outer ring is subjected to combined loading.
The results of the comparison between the two types of slewing bearings demonstrate that the bearing stiffness of crossed roller bearings is superior to that of four-point contact ball bearings. The roller profile of crossed roller bearings enhances the stress distribution, yet concurrently reduces the bearing stiffness.
Furthermore, the analysis indicates that as the clearance increases, the tilting angle of the outer ring also increases. This condition has an impact on the roller contact stresses in crossed roller bearings. A comparative analysis of various roller profiles reveals that the tilting of the outer ring results in unequal distribution of roller stresses. The application of logarithmic profile can effectively reduce stress concentration. Conversely, the standard profile will cause stress concentration at the edges. However, the implementation of large circular end relief is not optimal, as it tends to be overly expansive, leading to suboptimal stress size and distribution. Consequently, an adjustment of the parameters is needed. On the other hand, the tilting of the outer ring results in alterations to the contact angle of the balls in four-point contact ball bearings. With an increase in clearance, the maximum difference in contact angle change can reach approximately 10 degrees.
The results demonstrate that the analysis method proposed in this paper can be effectively and efficiently employed to analyze the load distribution of the rollers (balls) in the bearing as a whole and the contact stress distribution of the contact pairs for both types of rotary bearings, such as crossed rollers and four-point contact ball bearings, in the context of clearance.
Keywords: Larger-scaled slewing bearing, Cross-roller bearings, Four-point contact ball bearings, Contact load analysis, Influence coefficient method, Stiffness map method, Bearing clearance, Roller profile modification, Contact angle, Bearing stiffness, Roller load distribution, Roller contact stress and contact pattern. |
