Performance of Multibody Mechanical Systems With Lubricated Joints: Finite Length Corrections for the Conventional Infinite Length-Joint Model

Abstract This research introduces a new analytical framework for modeling finite-length lubricated journal bearings in multibody systems, striking a balance between the simplicity of traditional infinite-length models and the precision of detailed finite-length solutions. Although infinite-length approximations are computationally and implementationally efficient, they ignore axial leakage and 3D pressure effects, leading to inaccuracies in real-world scenarios. On the other hand, existing exact finite-length models provide high accuracy but are mathematically complex, apply domain transformations and implementation inefficient, and hindering widespread use. The proposed method employs a separation of variables approach to the Reynolds equation, deriving closed-form expressions for hydrodynamic pressure and forces that incorporate side leakage while remaining implementing efficient for system-level simulations. Implemented within a dynamic multibody framework using an augmented Lagrangian formulation, the model allows physical lubricated bearings to replace idealized revolute joints. Validation against numerical benchmarks confirms the accuracy of the analytical solutions. Case studies - including a loaded journal-bearing system and a high-speed crank-slider mechanism—demonstrate the model's ability to capture finite-length effects, such as elevated eccentricity ratios and dynamic force overshoots caused by axial leakage, without sacrificing simplicity. The findings underscore the substantial influence of finite-length corrections on dynamic behavior, including journal orbit stability, force distribution, and torque variations. This study provides a scientifically rigorous yet practical approach for integrating realistic lubrication effects into multibody dynamics, enhancing simulation accuracy for engineering systems with lubricated clearance joints.