Rotor System Modeling with 8 Degrees of Freedom using a Lumped-Mass Approach: Application to Hydrodynamic Journal Bearing
摘要
Machinery equipment in industry is commonly represented as rotor systems supported by hydrodynamic journal bearings. Dynamic analysis of such systems is essential to ensure operational stability and to prevent excessive vibrations that may lead to failure. However, experimental investigations are limited due to the high complexity and precision required in journal bearing manufacturing. Although finite element methods (FEM) are widely used in rotor dynamics, they are computationally intensive, particularly for nonlinear or speed-dependent bearing characteristics, making them less suitable for rapid parameter studies or iterative design processes.
PurposeThis study aims to develop a computationally efficient numerical model of a rotor–bearing system using a lumped-parameter approach with eight degrees of freedom (8-DOF), and to evaluate its capability in predicting the dynamic behavior of rotors supported by hydrodynamic journal bearings.
MethodsAn 8-DOF lumped-parameter rotor model is formulated to capture lateral and angular motions at both disk and bearing locations. The equations of motion are derived using Lagrange’s method. Shaft stiffness is obtained from beam strain energy formulations, while gyroscopic effects, unbalanced mass forces, and bearing forces are modeled as external loads. Speed-dependent stiffness and damping coefficients are introduced using hydrodynamic journal bearing theory. Model validation is performed by comparing the first natural frequencies for different disk positions with reference results. Time-domain responses, bearing orbits, spectrograms, and spectral maps are generated to analyze system behavior.
ResultsThe proposed model accurately predicts the first natural frequencies for disk positions up to a 20% offset from the shaft center, with deviations increasing beyond this range due to lumped-mass assumptions. In the journal bearing case study, the model effectively captures rotor dynamic behavior during both startup and steady-state conditions. The simulated responses show good agreement with theoretical predictions and reference results, including resonance crossing and stable bearing orbit characteristics.
ConclusionsThe developed 8-DOF lumped-parameter rotor model provides an efficient and reliable framework for analyzing rotor systems supported by hydrodynamic journal bearings. It offers a practical alternative to FEM for preliminary design, parametric studies, and dynamic analysis while maintaining acceptable accuracy within defined validity limits.