Physics-informed neural network for solving the coupled Reynolds–energy equations with viscosity–temperature effects in hydrodynamic journal bearings

This study presents an efficient solution framework for energy–Reynolds-coupled equations in hydrodynamic journal bearings (HJBs) incorporating the viscosity–temperature effect through a physics-informed neural network (PINN). The proposed framework is termed Reynolds-and-energy-coupled physics-informed neural network, abbreviated as RAE-PINN. Leveraging the unsupervised learning capabilities of PINN, an adaptive sampling strategy is introduced to optimize the spatial distribution of computational points. Additionally, a hard-constraint method is employed to ensure the physical consistency of boundary conditions and cavitation regions. To further enhance the generalization capability of RAE-PINN, a transfer learning strategy is implemented, enabling adaptation to variations in bearing structural parameters (such as aspect ratio, eccentricity, and radial clearance) and operating conditions (e.g., rotational speed). The results demonstrate that RAE-PINN achieves high accuracy in predicting oil film pressure and temperature distributions, closely aligning with high-fidelity finite element method (FEM) simulations. Furthermore, RAE-PINN achieves a computational speedup of over 300 times, reducing the solution time for a single bearing case from several minutes to less than one second, thereby significantly enhancing computational efficiency. Compared to traditional numerical methods, RAE-PINN not only preserves computational accuracy but also substantially reduces computational costs, providing an efficient, stable, and scalable numerical solution framework for intelligent modeling, optimized design, and real-time analysis of rotating machinery bearing systems.