Dynamic Stability Analysis of Grooved Rubber Hydrodynamic Journal Bearings Considering Elastic Deformation of the Liner

This study investigates the influence of liner elastic deformation on the static performance and dynamic stability of grooved rubber journal bearings (GRJBs) using the finite element method (FEM) in conjunction with a Winkler elastic foundation model. The formulation is validated through comparison with the limiting case of a plain circular bearing. Increasing the effective liner stiffness (k^) reduces liner compliance and consequently shifts the overall system response toward that of a rigid bearing. For configurations with 6, 9, and 12 grooves, raising the effective liner stiffness from 0.4 to 4 GPa/mm increases the maximum hydrodynamic pressure by approximately 8–15% and enhances the load-carrying capacity by about 5–8%. The variation in key performance indicators becomes progressively less sensitive beyond an approximate threshold, entering a low-sensitivity region near 1.5 GPa/mm. Dynamic stability is assessed through linear perturbation of the journal center about its static equilibrium position. The stiffness and damping matrices are derived from the perturbed lubricant-film pressure response, capturing both restoring forces and squeeze-film effects. The results indicate that increasing effective liner stiffness generally strengthens the direct stiffness and damping behavior and raises the dimensionless critical mass, suggesting an improved stability margin under the investigated conditions. The influence of groove number on dynamic response is also significant. Fewer grooves tend to promote a more favorable balance between restoring and damping actions, whereas higher groove counts can reduce the stability margin despite improvements in lubricant supply characteristics. Among the studied cases, the 6-groove bearing yields the highest predicted critical mass and linear stability margin, while the 9-groove configuration provides the highest vertical direct stiffness coefficient. Overall, the findings emphasize that the groove number and effective liner stiffness should be optimized jointly, as static performance improvements do not necessarily translate into proportional gains in dynamic stability.