| 摘要(英) |
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. |
| 參考文獻 |
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[2] Liu, R., Wang, H., Pang, B.T., Gao, X.H. & Zong, H.Y., “Load distribution calculation of a four-point-contact slewing bearing and its experimental verification,” Experimental Techniques, Vol. 42, pp. 243–252, 2018.
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[16] ISO 76 Rolling Bearing – Static Load Ratings, Third edition, 2006. |
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