Along with the rotating machinery advances toward high speeds, the significance of the excitation force of the seal fluid in the rotor system is growing, which can cause serious accidents. Most of the previous research on rotors in rotating machinery has predominantly focused on the effects of misalignment in couplings. In this article, a novel model is proposed, introducing an analytical approach that combines both internal friction in couplings and loosening support faults. Additionally, an analysis and discussion of the vibration characteristics of the rotating system under the influence of internal friction are presented. This method allows for a more comprehensive assessment of the performance of rotors in engineering applications. Assuming that the left support of the rotor is loose, this model focused on how various factors such as rotor speeds, eccentricity, seal disc mass, and left-end support mass affect the labyrinth seal rotor system's dynamic characteristics. Based on the findings, The emergence of internal friction forces advances the chaos of the rotor. It seems that as the rotating speed increases, there will be a small frequency range, resulting in fluid oscillation, and the system stability will be reduced at this time. The improvement in the seal disc's quality has minimal impact on the stability of the left journal, but it will reduce the stability of the seal disc. The increase in the mass of the left end support will increase the stability of the movement at the left journal and reduce the stability of the movement at the seal disc.