3D Local Finite Element Model for Static Analysis of Hybrid Ceramic Angular Contact Ball Bearings
Under high-speed conditions (DN value greater than 1M), the performance of ceramic ball bearings is significantly better than that of steel bearings, because the density of ceramics is only 41% of that of steel, and the centrifugal force of ceramic balls is 41% of that of steel balls. Due to the differences in the properties of ceramic and steel materials, the classical analytical theory  is not applicable to ceramic ball bearings. To predict the fatigue life of ceramic ball bearings under complex working conditions (such as considering friction, centrifugal force, and thermal effects), it is necessary to know the stress field under the surface of the bearing contact area. The contact load, contact angle and friction of the ring are equivalently loaded in the finite element model of the static analysis of the ceramic ball bearing, which needs to be based on the accurate static analysis of the ceramic ball bearing under a simple load. The main goal of this paper is to establish a three-dimensional finite element model of the FAG hybrid ceramic angular contact ball bearing that takes into account accuracy and computational efficiency, and lay the foundation for the subsequent finite element analysis of hybrid ceramic ball bearings that introduce friction, heat, and centrifugal effects. The effect of axial load on the contact load, contact stress, contact angle and axial elastic approach of the hybrid ceramic angular contact ball bearing is analyzed by this model, and the FEA results are compared with the theoretical results. Three-dimensional local finite element model: 1.1 Model simplification and assumptions For the convenience of comparison with Harris theory , taking the hybrid ceramic angular contact ball bearing 7218B/HQ1 as an example, the simplifications and assumptions are as follows: (1) The rolling bearing has small plastic deformation, The material is assumed to be linear elastic. (2) Geometric features such as chamfers and fillets that have little effect on static contact analysis are not considered. (3) Considering only the axial load, the load on each ball is equal, so a local bearing model including one ball can be used for analysis. (4) In the static analysis, the cage has little effect, so the cage is ignored. (5) In the static analysis, the friction force has little effect on the results, and the friction is not considered. The bearing geometry is shown in Table 1, and the partial bearing model is shown in Figure 1. 1.2 Material performance parameters The material of the bearing ball is silicon nitride, and the material of the inner and outer rings is bearing steel GCr15. The performance parameters of the two materials are listed in Table 2. Contact Definition In the ABAQUS surface-surface-surface contact definition, the main surface is generally selected as a surface with greater stiffness or a relatively sparse mesh. Therefore, the surface-surface contact pair is established with the spherical surface with high rigidity as the main surface and the raceway surfaces of the inner and outer rings as the slave surface. Analysis steps, boundary conditions and loads In order to facilitate the application of loads and boundary conditions, the inner cylindrical surface of the inner ring is defined as a rigid surface, and a reference point is specified for the rigid surface, and the load and boundary conditions are applied to the reference point. The load applied to the reference point and boundary conditions will be equivalent to the rigid surface corresponding to this reference point. In the analysis of static contact problems, the initial contact state has not been established, which may cause uncertain rigid body displacement, resulting in the analysis not converging. There are three commonly used methods to eliminate uncertain rigid body displacement: (1) give a certain initial interference to the contact part to establish contact constraints at the beginning of the analysis; (2) add appropriate grounding spring constraints to the parts that may have rigid body displacement, The spring stiffness is relatively small, so that the rigid body displacement is eliminated without affecting the analysis results; (3) Temporary displacement boundary conditions are applied to components that may have rigid body displacements, and then the temporary boundary conditions are removed after establishing stable contact constraints. This paper comprehensively adopts methods (1) and (3), which are divided into two analysis steps: the first step, the general implicit static analysis step. During assembly, the ball and the inner and outer rings have an interference of 0.005mm respectively; the axial displacement boundary condition is applied to the inner cylindrical rigid surface of the inner ring; the three displacement degrees of freedom of the local nodes of the ball and the bottom surface nodes of the outer ring are restricted; Symmetry constraints are imposed on the section of ; the second step is the general implicit static analysis step. Cancel the displacement boundary condition of the inner ring; cancel the degree of freedom constraint of the local nodes on the sphere; apply an axial concentrated force to the reference point of the rigid surface of the inner ring of the inner ring. Element selection and meshing include contact problems, so the three-dimensional hexahedral 8-node non-coordinated element C3D8I is used for the contact part (Cell) to obtain better stress solutions and avoid the hourglass problem. The remaining part adopts the three-dimensional hexahedral 8-node reduced-integration element C3D8R with enhanced hourglass control. The mesh is refined locally in the contact area, and the result is shown in Figure 1.