To achieve a compact design, reduced noise, and extended operational lifespan of the air conditioner indoor unit, a novel motor rotor system was implemented. This system utilizes three engineering plastic bearings, encased in high-elasticity rubber bushings and lubricated with grease. Yet, the absence of a simulation model that accurately represents the structural and material properties of this bearing-rotor assembly hampers the precise evaluation of how design parameters influence system performance. As such, in the present study, an innovative tribo-dynamics model was established using a coupling approach that integrates dynamics and tribology. This model encompasses a 4-degree-of-freedom rotor dynamics framework and a grease elastohydrodynamic model, which accounts for the deformation of both rubber bushings and plastic bearings. Utilizing this tribo-dynamics model, the effects of the elastic modulus of the bushing on the tribological properties of the system were explored. The results show that a small elastic modulus of the bushing effectively reduced the local high contact pressure between the journal and the bearing during startup. However, the elastic modulus cannot be excessively low, as it would adversely affect the range of journal motion and the film thickness under rated operating conditions.