Investigation and revision of the viscous torque formula based on inertial effects and nonlinear dissipative effects

The hydro-viscous drive clutch, a speed-regulating device utilizing oil film shear to transmit torque, exhibits discrepancies between traditional viscous torque models and experimental results due to the neglect of radial flow and rotational inertial effects. This study revises the conventional torque model based on Couette flow by re-deriving it from the Navier–Stokes equations in cylindrical coordinates, accounting for the coupled effects of radial and rotational flows. Through a detailed analysis of the convective acceleration and viscous diffusion terms, a novel viscous torque model is proposed, comprising three components: the viscous shear term (representing pure shear), the nonlinear term (capturing radial inertial effects), and the dissipation term (reflecting angular-flow coupling). Computational fluid dynamics simulations with mesh independence verification validate the model. Results show that within typical operating ranges—flow rate (Q = 0–30 l/min), oil film thickness (h = 0.1–0.5 mm), and angular velocity difference (Δω = 10–100 rad/s)—the revised model improves torque prediction accuracy by up to 28% compared to traditional formulations. Pressure contours and velocity streamline analyses reveal shear stress distributions dominated by inertial effects, highlighting the role of radial momentum transport in rotational energy dissipation. This work establishes a refined theoretical framework for accurate torque estimation and efficiency optimization in hydro-viscous drive systems operating under high-speed, variable-flow conditions.