This invention relates to the fields of
computational mechanics and computer-aided
engineering, specifically a
mathematical model capable of predicting the forming shape of spherical bearings. The model takes the blank's geometric dimensions, mold parameters, and material
elastic modulus as input. Based on the precise geometric relationships of the compression process, it establishes a
system of equations, deriving the core relationship between the compression amount and the theoretical
mean diameter, and solving for the theoretical shape without considering springback. By introducing the theory of compression-bending springback, it establishes springback geometric constraints and expressions for reverse stress. Based on the static
equilibrium conditions under
pure bending, it derives the explicit relationship between the
radius after springback and the
radius before springback, elastically correcting the theoretical shape to obtain a predicted shape closer to the actual forming result. The model's output can be compared and verified with finite element simulations and actual experimental data, exhibiting high prediction accuracy in the stable deformation stage with large compression amounts. This invention provides effective guidance for process
parameter design and optimization, reducing the number of experiments and development cycles.