四點接觸軸承負載分析;Load Analysis of Four Point Contact Ball Bearings

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Title:	四點接觸軸承負載分析;Load Analysis of Four Point Contact Ball Bearings
Authors:	連庭緯;Lien, Ting-Wei
Contributors:	機械工程學系
Keywords:	四點接觸軸承;旋轉齒輪軸承;接觸負載分析;軸承間隙;接觸角;加工誤差分析;Four-point contact bearing;Slewing bearing;contact load analysis;bearing clearance;contact angle;machining error analysis
Date:	2021-12-28
Issue Date:	2022-07-14 01:19:55 (UTC+8)
Publisher:	國立中央大學
Abstract:	四點接觸軸承之滾珠與內外環滾道面的接觸型式為點接觸，且同時會有兩交叉接觸對。在軸承受到外部負載時，會因滾珠接觸剛性為非線性以及具有間隙條件下，使得各個滾珠負載分析相對複雜。因此本論文之研究目的為提出一套四點接觸軸承設計與負載分析方法，分析軸承在有間隙情況下，承受不同負載時整體滾珠負載分配以及各滾珠與滾道接觸情形，藉以評估軸承強度是否滿足要求。在論文中先使用影響係數法建立無間隙下軸承的多接觸對受載分析模型，以分析滾珠負載分配以及接觸應力分佈。在分析模型中，為加快計算速度與提高精度，則以接觸剛性法先求出滾珠的負載，以預判接觸滾珠個數以及預估各接觸對之接觸斑面積，藉以規劃接觸網格。軸承存在間隙時，在外環固定、且滾珠受保持架約束而緊靠在外環滾道面之條件下，內環受載將產生位移並抵銷間隙後，各滾珠與滾道的接觸狀況，包含滾珠接觸角、接觸法線方向以及滾珠與滾道間的輪廓間隙等皆會改變。因此軸承具間隙分析則先透過對環體最終位移的猜值求出各接觸狀況，並在無間隙受載接觸分析模型基礎上進行迭代收斂，求得軸承負載最終平衡狀態，以及各滾珠負載分佈和接觸應力分佈。其中各滾珠接觸對之法線以及與內環間的法向干涉量則以空間幾何關係求得。論文以某款大型四點接觸旋轉軸承為案例進行分析。首先分析軸承在不同方向負載作用下滾珠負載分配情形，並探討軸承存在間隙時各滾珠負載分配和接觸應力分佈情況。接著分析軸承設計參數對於整體負載之影響，包括接觸角以及滾珠與滾道曲率半徑差。最後以模擬滾道在加工過程產生的偏擺誤差，探討其對軸承負載之影響。由負載分佈分析結果顯示，軸承內環承受軸向負載時，所有滾珠僅其中一個接觸對受載；承受正x方向之徑向負載時，第Ⅰ、Ⅳ象限內的滾珠隨位置不同而承受大小不等之負載，且各滾珠中的兩個接觸對承受相等之負載；承受傾覆力矩時，力矩轉軸兩側分別由相反之接觸對受載，且隨滾珠位置不同而承受大小不等之負載。而軸承間隙的增加會造成負載分佈更集中，且最大負載值也會提升。滾道加工過程造成的偏擺誤差則會使最大負載之滾珠位置發生改變。接觸應力分佈結果顯示，軸承在不同負載作用下各接觸對上的接觸應力斑均為橢圓形狀，且橢圓長軸在滾道輪廓切向方向上。而軸承間隙的增加則會造成最大接觸應力值提升，且實際接觸位置與理論接觸點之差距加大。另外，接觸角的改變對於軸承負載情形沒有固定的趨勢，在不同的綜合負載案例下會有不同的數值。另一方面，滾珠與滾道曲率越接近，接觸應力雖會下降，但接觸位置偏離理論接觸點狀況更明顯，因此必須進一步評估是否造成應力集中，影響結構體強度。從分析結果可知，針對四點接觸軸承在有間隙且多種設計參數下，本論文提出之分析方法可以有效且快速分析軸承整體滾珠的負載分佈情形以及各接觸對之接觸應力分佈情況。 ;The contact between the ball and the raceway surface of the inner or the outer ring of four-point slewing bearings is point contact. And there are two cross-contact pairs in each ball. When the bearing bears an external load, the load analysis of each ball load will be more complicated due to the nonlinearity of the ball contact stiffness and the presence of clearances. Therefore, the aim of this thesis is to propose a load analysis method for the four-point-contact slewing bearing with clearance, which is used to solve load distribution and the contact stress of each ball under different loads, so as to validate the required safety of the bearing. In this thesis, a loaded contact analysis model based on the influence coefficient method is at first established for the slewing bearing without clearance to analyze the load distribution and contact stress distribution of each ball. In order to speed up the calculation and to improve the accuracy, a constant stiffness method is used before conducting of the numerical contact analysis model. With using this method, the load of the balls can be determined, then the number of contact balls and the area of the contact spots of each contact pair can be also predicted, so as to obtain the suitable discretized contact mesh. In the case of bearings with clearances, the outer ring in the study is regarded as fixed and the balls are constrained by the ball cage and close to the outer ring raceway surface. When the inner ring is loaded, it will be displaced and the clearance is reduced. As a cosquence, the contact status of each ball and the raceway will be changed, including the contact angle of the ball, the contact normal, and the contour gaps between the ball and the raceway. Therefore, the loaded contact analysis of the bearing with clearance is based on the final contact conditions of the ring body. The corresponding final displacements are regarded initially as guessed values and solved iteratively by using convergence conditions of load equilibrium on the base of the loaded contact analysis model without clearance. The load distribution and contact stress distribution of each ball are obtained accordingly. In the proposed model, the normal line of each ball contact pair and the normal interference between the ball and the inner ring are calculated according to the spatial geometrical relation. A large sized four-point contact slewing bearing is analyzed as a study case in this thesis. Firstly, the load distribution and the contact stress of each ball under loads in different directions are analyzed, and the effects of clearances on the loaded contact characteristics are also explored. Next, the influence of bearing design parameters, such as the contact angle and the curvature radius of the ball and the raceway, on the load distribution is analyzed. Finally, waviness errors of the raceway generated during the machining process is also simulated. The effects of this manufacturing error on the load capacity of bearing is discussed. The result of load distribution analysis shows that all the balls are only loaded by one contact pair when the inner ring is loaded axially. When a radial load in the positive x direction is applied, the balls in the first and fourth quadrants are loaded with different values depending on their positions relative to the x-direction. In such case, each loaded ball has two contact pairs with equal loading values. When a tilting moment is applied, the balls on the two sides of the torque applying axis are loaded by opposite contact pairs. The increase in the bearing clearance causes the load distribution to be more concentrated in less numbers of balls and the maximum load to increase. In addition, the waviness error caused by the raceway manufacturing process lead to location change of the maximum contact load ball. The result of contact stress distribution shows that the contact pattern of each contact pair of the bearing under different loads are all elliptical, and the major axis of the ellipse is in the tangential direction of the raceway profile. The increase in the bearing clearance enlarge the maximum contact stress due to reduced number of loaded balls. The position between the actual contact point and the theoretical will also be shifted larger with increased clearance. In addition, there is no correlation between the contact angle and the maximum contact stress, it depends on the different combinations of loads. Furthermore, reduction in the difference of curvature radius between the ball and the raceway reduce also the maximum contact stress. However, the deviation of the contact position from the theoretical contact point will be also enlarged accordingly. Therefore, it is necessary to evaluate whether it causes stress concentration and affects the strength of the structure. From the analysis results of the research, it can be seen that the load analysis method proposed in this thesis can effectively and quickly analyze the load distribution and the contact stress distribution of each contact pair for the four-point contact bearing with clearance and in various design parameters.
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