<p>Static parallel misalignment (SPM) between eccentric rotors is a common installation error in dual-rotor systems. The clearance between rotors is reduced and further leading to rotor-rotor rubbing faults. However, the influence of the SPM phase difference, which determines the spatial offset and potential multi-point contact between rotors, has rarely been studied in the context of nonlinear vibration and fault initiation. In this paper, a novel investigation into the effects of SPM phase difference on rubbing-induced vibration characteristics is presented in a gear-coupled dual-rotor system. A new dynamic model is developed using finite element method, incorporating the geometric effects of SPM by Timoshenko beam and lumped-mass elements. In addition, a nonlinear rotor-rotor rubbing model is proposed based on the penalty stiffness method and Coulomb friction, explicitly capturing SPM-induced clearance asymmetry and time-varying contact conditions. The influence of varying SPM phase differences on both the rubbing rotating speed threshold and the rubbing unbalance threshold is systematically examined, which are critical indicators of fault susceptibility. The results reveal that increasing the phase difference significantly lowers these thresholds, making the system more prone to rubbing even under mild unbalance or low-speed conditions. Moreover, the rubbing response displays strong nonlinear behavior characterized by multi-frequency and combination-frequency components, especially under conditions of multi-position contact induced by large SPM phase differences. These findings provide the first comprehensive numerical evidence linking SPM phase variation to dynamic fault mechanisms in coupled rotor systems. The study can offer new theoretical insights and practical guidance for improving rotor alignment strategies to mitigate rubbing risks in high-speed rotating machinery.</p>