Viscoelastic friction reduction in the infinite length journal bearing

Viscoelastic fluids in shear produce normal stresses. In rotating devices, these normal stresses produce a non-zero pressure field that would not exist in the same flow conditions with purely viscous fluids. This additional elastic pressure field has been used to increase the load carrying capacity and decrease the coefficient of friction in thrust bearings, and that same analysis can be extended to journal bearings. Here, the Cauchy momentum equations in polar coordinates are solved in the thin film limit using a perturbation expansion in the Deborah number (De) for both velocity and pressure. Viscoelasticity is included through an upper convected Maxwell model with a solvent viscosity (upper convected Jeffreys model). When De = 0, the model resembles the Reynolds equation (a restatement of conservation of mass and momentum for a purely viscous fluid) for an infinite length journal bearing. The De = 0 results match the predictions of the Reynolds equation over all eccentricity ratios, validating the model. As the De increases, the elastic contributions to the pressure and velocity fields increase the load carrying capacity and decrease the coefficient of friction compared to the results with the purely viscous fluid in the same flow conditions. This suggests that viscoelasticity is beneficial in journal bearing applications and provides designers another mechanism for decreasing friction in lubricated journal bearings.