| 摘要: | 交叉滾子軸承的應用非常廣泛，適用於高精度及高負載之傳動上，然而因交叉滾子軸承之滾子交叉排列，在不同負載的交互作用下滾子的負載分配會較為複雜。因此本論文的研究目的即在建立交叉滾子軸承分析模型，分析軸承中各滾子之分配負載與接觸應力。在論文中先以等剛性接觸假設，利用軸承外環與滾子之位移關係求解軸承在承受綜合負載下各滾子之負載分配。而為求得滾子受載後之接觸應力分布，利用交叉滾子軸承在空間中的幾何特性，以影響係數法建立受載接觸分析模型，並以等剛性接觸方法作為預判接觸滾子，以加速計算流程。此模型除可得到各滾子負載分配，並可得到不同滾子修整輪廓與不同負載下滾子與滾道間的接觸應力分布。
在本論文中以大尺寸之旋轉齒輪軸承以及小尺寸之一般交叉滾子軸承等兩種案例進行分析，以了解軸承滾子受載下的接觸特性。分析中則考慮無修整、大圓、對數修整等三種修整輪廓，以及滾子接觸長度，滾子直徑誤差，滾子分布位置誤差對各滾子負載分配與接觸應力所造成的影響。
負載分配分析結果顯示，交叉滾子軸承因為相鄰滾子軸線交錯配置，在外環承受軸向負載時，僅相同軸線方向之滾子承受負載；承受正x方向之徑向負載時，由第二、三象限內所有滾子承受大小不等之負載；承受傾覆力矩時，力矩轉軸每側區域內所有相同軸線方向之滾子承受大小不等之負載。而無承受負載之滾子則因軸承外環位移而與滾道產生間隙，因此在綜合負載下，相同軸線之滾子有各自的負載分配曲線，其中某一軸線方向之滾子在部分區域內可能不受負載。
應力分布分析結果顯示，無修整滾子的接觸邊緣會出現應力集中的情形，而在大圓及對數修整的輪廓下，滾子應力集中的情形可以得到改善，使得應力在接觸面上分布的更加平均。而在接觸長度與迴轉半徑比值較大時，接觸長度對負載之影響較為顯著，其中又以受到傾覆力矩時影響較為顯著。滾子直徑誤差對於滾子負載分配整體趨勢大致相同，但因滾子直徑的不同而有不規則跳動。滾子因不同厚薄保持器之配置而造成的位置誤差，則僅會造成整體負載分配曲線之移動。
本研究同時建立旋轉齒輪軸承之承載能力界限圖，透過軸向及徑向負載交互影響之關係曲線，可快速挑選符合安全係數要求之對應軸向與徑向負載。
由分析結果可知本論文發展之分析方法，能夠快速並且準確的分析在不同幾何外形下，交叉滾子軸承整體的負載分配趨勢以及各滾子與滾道間接觸應力之分布情況。
;Cross roller bearings are widely used in high-precision and high-load drives. However, due to the cross-arrangement of the rollers of bearings. The load distribution of rollers is complicated because of the interaction of different loads. Therefore, the purpose of this paper is to establish a cross roller bearing analysis model to analyze the distributed load and contact stress of each roller in the bearing. At first, use constant contact stiffness method to solve the load distribution of the bearings under the integrated load with the displacement relationship between the outer ring and the rollers. In order to obtain the contact stress distribution of loaded roller, the loaded contact analysis model is established by the influence coefficient method by using the geometric characteristics of the cross roller bearing, and the constant contact stiffness method is used for predicting contact roller in order to speed up the calculation process. In addition to the roller load distribution, the model can also obtain the contact stress distribution of different roller crowning profiles. And the contact stress distribution of rollers and raceways under different loads.
In this paper, two cases of large-sized slewing gear bearings and small-sized general cross roller bearings are analyzed. To understand the contact characteristics of bearing rollers under load. In the analysis, three crowning profiles such as non-crowning, circular, and logarithmic crowning are considered, as well as the effects of roller contact length, error of roller diameter, and error of roller position.
The result of load distribution analysis of each roller shows when the outer ring of cross roller bearings is subjected to the axial load, only the rollers in the same axial direction are subjected to the load due to the adjacent roller axes are staggered; when subjected to the radial load in the positive x direction, all the rollers between second and third quadrants are subjected to loads; when subjected to the overturning moment, all the rollers of the same axial direction in each side of the torque shaft are subjected to loads. Rollers that do not bear the load have gaps with the raceway due to the displacement of the outer ring. Therefore, under the integrated load, the rollers of the same axis have their respective load distribution curves, and the roller of one axial direction in a partial area may not be overloaded.
The result of stress distribution analysis shows that stress concentration occurs at the contact edge of the non-crowning roller, and under the circular and logarithmic crowning, the stress concentration of the roller can be improved, so that the stress is more evenly distributed on the contact surface. When the ratio of the contact length to the radius of bearing is large, the contact length has a significant influence on the load, and the influence is more significant when the overturning moment is applied. The error of roller diameter is roughly the same for the trend of roller load distribution, but there is irregular runout due to the difference in roller diameter. The error of roller position caused by different thickness holders only result in the load distribution curve to move.
This paper also establishes the limit diagram of the bearing capacity of the slewing gear bearing. Through the relationship between the axial and radial load, the corresponding axial and radial loads meeting the safety factor can be quickly selected.
From the analysis results, the analysis method developed in this paper can quickly and accurately analyze the load distribution trend of the cross roller bearing and the distribution of the contact stress between different geometric shapes of the rollers and the raceway. |
