Physics-enhanced neural operator for predicting hydrodynamic lubrication in slipper pairs

Abstract

The transient dynamics of the micrometer-scale slipper-pair oil film in axial piston pumps are governed by multi-factor coupling effects, rendering traditional numerical methods inadequate for real-time simulation and rapid design optimization. This paper proposes a physics-enhanced neural operator (PENO) to predict transient lubrication characteristics. PENO combines a motion module that predicts the film thickness at three feature points with a hard-constrained Fourier neural operator for pressure reconstruction. The pressure field is decomposed into a logarithmic, boundary-compatible background field and a masked residual field that analytically enforces the radial Dirichlet pressure boundary conditions. Reynolds-equation residuals and force/moment equilibrium residuals are incorporated into the loss function to improve physical consistency. Evaluations across various operating conditions show that PENO can accurately predict the lubrication characteristics of the slipper-pair oil film. Across the evaluated operating conditions, the full-cycle relative L2 errors of the predicted pressure fields range in order of magnitude from 10−4 to 10−2, while the full-cycle oil-film thickness root mean square errors (RMSEs) range from 10−3 to 10−1 μm. The prediction results meet the physical consistency requirements, with the largest full-cycle RMSEs for the axial supporting force and supporting moments being 7.4 N and 3.8 × 10−3 N m, respectively. Compared to traditional numerical methods, PENO reduces the average full-cycle prediction time from 3.32 × 103 to 6.96 × 10−2 s, representing a speedup of 4.76 × 104. When the mesh size increases from 31 × 121 to 98 × 382, the inference time remains at 7.64 × 10−1 s, indicating favorable inference-time scaling over the tested mesh resolutions.