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

The finite element results of ceramic ball bearings follow the convergence of the mesh density. The contact area of u200bu200bthe ball bearing is small and narrow. This requires a dense enough mesh in the contact area to obtain a satisfactory solution. Figure 2 shows that when the axial load is 1KN, as the mesh length in the contact zone 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 result has converged, and it is meaningless to continue to refine the mesh. At this time, 7 elements are divided in the direction of the minor axis of the contact ellipse. Figure 2a shows that when the mesh is thicker, the FEA result of the contact load is already close to the theoretical value. Shaft length) to obtain a satisfactory solution. The mesh density increases, the number of contact elements increases, the contact area approaches the theoretical value, and the stress solution is more accurate. In Figure 3, the contact area is cut off by 1/4, the plane OXZ and OYZ are two cross-sections, and OZ is the depth direction under the contact surface. The maximum Tresca stress is below the contact surface, and the stress field pattern is narrow and long. Since the shear stress is equal to half of Tresca's equivalent stress, that is, the maximum shear stress is also located below the contact surface, which is consistent with the theory. The finite element model test verification document [8] simplified the ceramic ball bearing as the contact of steel plate-ceramic ball-steel plate, and conducted experiments to measure the approaching amount of the two steel plates in the loading direction, that is, simplifying the total approaching amount of the bearing. Based on the contact test in literature [8], this paper uses the aforementioned modeling method that takes into account both efficiency and accuracy to establish a finite element model of the contact between the ceramic ball and the steel plate (Figure 4), and compares the finite element analysis results with the experimental data in literature [8] comparing. Figure 5 shows that the finite element analysis, Herz theory and the experimental results of the contact elasticity 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 1783 MPa, which exceeds the initial yield stress of 1612 MPa given in the literature [8], that is, a small amount of plastic deformation of the steel plate occurs. Since material nonlinearity is not considered in this paper, the load in Figure 5 is not greater than 100N. The influence of the axial load on the hybrid ceramic ball bearing is analyzed with the mesh density of the shortest element length in the contact area of u200bu200b0.065mm and the axial load from 0 to 3 KN. The results are shown in Figure 6 to Figure 9. Figure 6 shows that the FEA value of the contact angle between the ceramic ball and the inner ring is consistent 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 value of the bearing axial approach is consistent with the theoretical value. As the axial load increases monotonously, the axial approach amount increases monotonously. Figure 8 shows that the FEA value of the contact load agrees with the theoretical value. Figure 9 shows that as the axial load increases monotonically, the maximum contact stress between the ball and the inner and outer rings increases monotonously. The FEA values u200bu200bof the maximum contact stress between the ball and the inner and outer rings are respectively 2% and 1.5% larger than the theoretical values. Conclusion For hybrid ceramic angular contact ball bearings that only bear 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 the 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 satisfactory solution; (2) Finite element analysis of contact angle, axial approach and contact load The result is consistent with the calculation result of classical theory. The FEA values u200bu200bof the maximum contact stress between the ball and the inner and outer rings are respectively 2% and 1.5% larger than the theoretical values.