Investigation and revision of the viscous torque formula for a non-parallel friction pair with a wedge-shaped oil film

A hydro-viscous drive clutch transmits torque through viscous shear in the oil film between friction elements. Axisymmetric conical deformation produces a radially varying clearance and limits the accuracy of conventional parallel-disk models. An axisymmetric non-parallel friction-pair model with linearly varying film thickness was derived from the Navier–Stokes equations in cylindrical coordinates. The revised torque expression incorporates the coupling between radial flow and circumferential motion into the local shear formulation and torque integration. Computational fluid dynamics (CFD) simulations were conducted using single-factor, pairwise-factor, and four-factor three-level L27 designs. Across the four single-factor cases, the revised-model mean errors ranged from 1.44% to 5.57%, compared with 14.83% to 18.10% for the conventional model evaluated at the intermediate film thickness. For the three pairwise cases, the corresponding ranges were 1.32%–5.75% and 14.27%–17.95%, respectively. Analysis of variance of the L27 results showed that angular velocity difference and inclination angle contributed 44.09% and 30.22% of the CFD-torque variation, respectively, whereas flow rate contributed 66.46% of the revised-model error variation. The 27-case mean and maximum errors were 5.474% and 14.282%, respectively. The revised model improves torque prediction for smooth, axisymmetrically coned, continuous liquid films, while high-flow rate conditions remain a limitation.