Numerical Calculation of Fluid Film Force on Journal Bearings Based on a Biconjugate Gradient-Stabilized Algorithm

Abstract

The aim of this work is to present a technical numerical method to improve the efficiency of solving the Reynolds equation for hydrodynamic bearings. Hydrodynamic bearings are largely employed in the shafting of high-speed rotating machinery to provide adequate support. The distribution of hydrodynamic pressure inside the bearing can be obtained by solving the Reynolds equation. Improving the efficiency of solving the Reynolds equation plays an essential role in the design and analysis of journal bearings. A numerical model has been developed to support the analysis and future design of hydrodynamic bearings. The primary objective of the model is to improve the efficiency of solving the Reynold equation during the steady-state and dynamic analysis. The developed method effectively combines the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm with the Reynolds boundary conditions, resulting in an effective methodology to characterize the pressure distribution within the lubricant for hydrodynamic bearings. A c++ program was implemented, and the difference between the BI-CGSTAB method and the successive over relaxation (SOR) method was evaluated against accuracy, convergence, and computational consumption. The Bi-CGSTAB algorithm has shown promising application in steady-state and dynamic analyses of hydrodynamic bearings. Validation of the results has been made with reference and analytical solutions.