Numerical Vibration Analysis and Nonlinear Stability Prediction of Hydrodynamic Journal Bearings: Short and Long Bearing Configurations

This study investigates a two-degree-of-freedom model of a rigid, symmetrical, and balanced rotor supported by two identical journal bearings. Hydrodynamic fluid forces are described using half Sommerfeld solutions combined with both short and long bearing approximations. Accurate prediction of stability boundaries and nonlinear behaviors near these limits, such as stable and unstable limit cycles, hysteresis, and jump phenomena, is essential for reliable rotor-bearing system design and operation. To achieve this, a continuation approach based on a predictor–corrector methodology is employed to trace equilibrium paths and bifurcation points. The results show that for short bearings (aspect ratio D/L < 0.5), a bearing parameter of 0.8 produces subcritical bifurcation at rotational speeds below the dimensionless threshold of 2.64. In contrast, for long bearings (D/L > 1), a parameter of 0.42 leads to supercritical bifurcation for speeds exceeding 1.67. These findings highlight the significant influence of bearing parameters and rotor dynamics on system stability and nonlinear response. Finally, numerical integration of the journal center motion validates the accuracy and robustness of the continuation-based predictions.

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