A Hybrid Finite Element–Deep Learning Framework for Bearing Structure Optimization

Abstract

The groove curvature coefficient plays a critical role in determining the thermo-mechanical performance of angular-contact ball bearings. However, its optimization remains challenging due to strong nonlinear coupling among stress, stiffness, heat generation, and fatigue capacity. To address this issue, this study proposes a hybrid optimization framework integrating a corrected two-dimensional axisymmetric finite element method (2D-AxFEM) model, a deep learning surrogate model, and a genetic algorithm. Firstly, an efficient 2D-AxFEM model calibrated by a bearing dynamic model is developed to accurately predict key performance metrics, including contact stress, stiffness, heat generation, and dynamic load rating, with significantly reduced computational cost compared to the conventional 3D FEM model. Based on the generated data, a multi-layer perceptron deep learning surrogate model is trained to establish a fast nonlinear mapping between groove curvature coefficients and performance indicators. The model achieves high accuracy, with R2 values of 0.9745, 0.9414, and 0.9756 at three different rotational speeds, as well as significantly improved computational efficiency. Building upon this, single- and multi-constraint optimization problems are solved using a genetic algorithm. The results reveal clear trade-offs among stiffness, heat generation, and load capacity. Under stiffness constraints, optimal solutions consistently converge to the constraint boundary, indicating its dominant role in thermal optimization. Under multiple constraints, the framework effectively identifies feasible design regions, enabling reduced heat generation while maintaining acceptable stress and load capacity. Overall, the proposed framework enables efficient exploration of multi-physics design spaces and provides a scalable solution for high-speed bearing optimization.