A novel dynamic model of the sliding bearing-rotor system was established with unbalance- misalignment-rubbing coupling faults under the influence of the nonlinear oil film force. In the model, the nonlinear oil film force was fully considered, based on which the dynamic model with the coupling faults was established. Finite element analysis was utilized to obtain the vibration response. Meanwhile, coupling faults experiment was carried out on the rotor test device, and the measured signals were acquired and compared with the simulation response of the model. Considering the frequency aliasing of the vibration response, Differential Coupling EMD (DCEMD) was proposed and used to decompose the response signals. Simulation and experiment results demonstrate the accuracy of the dynamic model and the effectiveness of the DCEMD.