Results and Discussion of Static Analysis of Hybrid Ceramic Angular Contact Ball Bearings1

The finite element results of the ceramic ball bearing converge with the mesh density. The contact area of u200bu200bthe ball bearing is small and long, so it is necessary to arrange a sufficiently dense mesh in the contact area to obtain a satisfactory solution. Figure 2 shows that when the axial load is 1KN, as the mesh length of the contact area decreases, that is, the mesh density increases, the contact load, contact area and contact stress gradually approach the theoretical values, showing good convergence. When the mesh length is 0.065mm, the FEA results have converged, and it is meaningless to continue to refine the mesh. At this time, 7 elements are divided in the direction of the short axis of the contact ellipse. Figure 2a shows that the contact load FEA results are close to the theoretical value when the mesh is coarser, which indicates that if only the internal force of the ball bearing is concerned, a coarser mesh is divided (for example, the mesh length of the contact area is equal to the short half of the contact ellipse). axis length) to obtain a satisfactory solution. As the mesh density increases, the number of elements involved in contact increases, the contact area approaches the theoretical value, and the stress solution becomes more accurate. In Fig. 3, the contact area is cut off by 1/4, the planes OXZ and OYZ are two sections, and OZ is the depth direction under the contact surface. The maximum Tresca stress is located below the contact surface, and the stress field pattern is narrow and flat. Since the shear stress is equal to half of the Tresca equivalent stress, the maximum shear stress is also located below the contact surface, which is in agreement with the theory. The finite element model test and verification document [8] simplified the ceramic ball bearing as the contact between the steel plate-ceramic ball-steel plate, and carried out the test to measure the approaching amount of the two steel plates in the loading direction, that is, the total approaching amount of the simplified bearing. In this paper, based on the contact test of the literature [8], the finite element model of the contact between the ceramic ball and the steel plate is established by the aforementioned modeling method that takes into account the efficiency and accuracy (Fig. 4), and the finite element analysis results are compared with the experimental data in the literature [8]. comparing. Figure 5 shows that the finite element analysis, Herz theory and the experimental results of the contact elastic approach of the ceramic ball and the steel plate are consistent, and the finite element and Herz theoretical results are in good agreement with the experimental results. When the load reaches 100N, the maximum Mises stress of the steel plate reaches 1783MPa, which exceeds the initial yield stress of 1612MPa given in the literature [8], that is, a small amount of plastic deformation occurs in the steel plate. Since the material nonlinearity is not considered in this paper, the load in Fig. 5 is not more than 100N. The effect of axial load on the hybrid ceramic ball bearing was analyzed with a grid density of 0.065mm with the shortest element length in the contact area, and the axial load from 0 to 3 KN. The results are shown in Figures 6 to 9. Figure 6 shows that the FEA value of the contact angle between the ceramic ball and the inner ring is in good agreement with the theoretical value, the contact angle increases with the increase of the axial load, and the contact angle has a nonlinear relationship with the axial load. Figure 7 shows that the FEA values u200bu200bof the bearing axial approach agree well with the theoretical values. As the axial load increases monotonically, the axial approach increases monotonically. Figure 8 shows that the contact load FEA value is in good agreement with the theoretical value. Figure 9 shows that with the monotonically increasing axial load, the maximum contact stress between the ball and the inner and outer rings increases monotonically. The FEA values u200bu200bof the maximum contact stress between the ball and the inner and outer rings are 2% and 1.5% larger than the theoretical values, respectively. Conclusion For the hybrid ceramic angular contact ball bearing that only bears the axial load: (1) The local finite element model of the ball bearing established in this paper and the reasonable local mesh refinement technology can effectively improve the calculation accuracy and efficiency of static analysis; Because the bearing contact area is small and long, and the stress changes greatly, at least 7 elements need to be divided in the short axis direction of the contact ellipse to obtain a solution with satisfactory accuracy; (2) Finite element analysis of contact angle, axial approach and contact load The results are in good agreement with the classical theoretical calculations. The FEA values u200bu200bof the maximum contact stress between the ball and the inner and outer rings are 2% and 1.5% larger than the theoretical values, respectively. References: [1] Harris, T A. Rolling bearing analysis[M]. New York: Wiley, 2006. [2] Liao, N T, Lin J F. 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