An extended Reynold equation applicable to high reduced Reynolds number operation of journal bearings

• The development of a new extended Reynolds equation for finite length bearings.
• Inclusion of temporal and convective inertia in addition to turbulence in the formulation.
• Identification of primary and secondary temporal inertia terms.
• Study of the new temporal inertia terms on the lubricant added mass characteristics of bearings.
• Focus on the high Reynolds number effects on a wide range of bearings operations.

The introduction of this paper serves as a review of previous studies on extending the Reynolds equation. This paper develops an extended Reynolds equation and includes turbulence and inertia effects. Use of low viscosity lubricants and/or high rotational speed applications yield high Reynolds and high reduced Reynolds numbers. Our approach fully realizes the convective inertia effects on the static and dynamic properties of journal bearings as nonlinear with reduced Reynolds number. Two types of temporal inertia terms are identified for the first time: primary and secondary, in both laminar and turbulent regimes. The contribution of the secondary inertia effects can be up to 30% of the lubricant added mass coefficients. Lubricant added mass coefficients are potentially comparable to journal mass.