Planar dynamic modeling of a rotor-bearing-housing system with polyurethane support layer

This study examines a planar dynamic model of a rotor-bearing-housing system incorporating a polyurethane support insert. The formulation takes into account the inertial, stiffness, and damping properties of the shaft, raceways, rolling elements, and cage, while the polyurethane layer is treated as an additional elastic–dissipative element. The equations of motion are derived using the Lagrangian formalism, based on kinetic, potential, and dissipation energies. Within the article, a frequency response analysis for different coating thicknesses is carried out, showing that the polyurethane insert reduces resonance frequencies by approximately 50-64 % while increasing vibration amplitudes by 67-146 %. A 2 mm layer provides a compromise between stiffness and damping, whereas thicker coatings (3-4 mm) enhance high-frequency vibration isolation but lead to higher sensitivity to low-frequency excitations. The novelty of this study lies in the introduction of a polyurethane elastic-dissipative layer into the planar dynamic model of the rotor-bearing-housing system. This approach enables an analytical representation of the polymer’s stiffness and damping effects and establishes a direct relationship between the polyurethane thickness and the system’s resonance behavior a topic not explicitly treated in previous works.