This study focuses on a rigid rotor supported by radial journal bearings. Initially, models for the unsteady oil film force in bearing lubrication and the dynamics of the bearing-rotor system are established. Subsequently, the Reynolds equation for dynamic lubricating oil films is discretely solved using the meshless barycentric rational interpolation collocation method. By combining this with the equation of motion for the axis orbit, the oil film pressure distribution, the dynamic response of the rotor, and the axis orbit are calculated. Furthermore, the study investigates the dynamic response of the rotor at different rotational speeds, both with and without considering unbalanced loads. Finally, the influence of step load on the stability of rotor motion is analyzed, revealing that applying an appropriate step load to the rotor can effectively mitigate the lubricating oil films oscillation conditions. The findings of this study hold significant reference value and practical utility for engineering applications.