Semi-Analytical Modelling of Oil Friction Torque for Oil-immersed Motors Based on Flow Regime and Rotor Surface Topography

The inherent thermal management and lubrication advantages of oil‑immersed permanent magnet synchronous motors (OPMSM) are compromised by considerable oil friction torque (OFT) at high speeds. This paper proposes a semi‑analytical model for calculating OFT, incorporating the effects of Taylor‑Couette flow (TCF) regimes and surface topography. First, typical surface topography features of the rotor and stator are investigated. An equivalent roughness height method introducing kurtosis is proposed, which significantly reduces the error between experiments and equivalent values. Second, the mapping relationship between motor parameters and TCF system parameters is established, and the influence of flow regime transitions under different driving strengths on OFT is introduced, yielding refined and accurate mathematical expressions for OFT under four flow regimes. Third, the effect of rotor surface topography is incorporated into computational fluid dynamics (CFD) modelling of the TCF inside the gap, clarifying the effects of flow regimes and surface topography on flow field characteristics and response parameters. Coefficients of the power‑law relationship for OFT are determined based on CFD results. Finally, a test platform is built to validate the proposed model experimentally, and comparisons with existing analytical methods demonstrate its effectiveness.