•A dynamic model of gear-bearing system with multi-mesh state and deterministic-random excitation is established.•The coupling effect of gear pair meshing vibration and gear bearing radial vibration is discussed.•The disengaging proportion of a gear-bearing system is calculated and analyzed based on the multi-mesh-state model.•Intrinsic mechanism between disengaging proportion and multi-mesh state is revealed.•Effects of dynamics type and its topology on the disengaging proportion are clearly acquired. Backlash induces gear-teeth separation or back-side tooth mesh (BTM), resulting in gear disengagement (GD), which heavily aggravates the dynamic performance and transmission quality of gear drivetrains. This study focuses on the disengaging proportion (DP) characteristics of a gear- bearing systems based on a multi-meshing-state (MMS) model. A new nonlinear dynamic model of gear-bearing system with MMS and deterministic-random external excitation is established considering the synergistic effect of backlash and non-integer contact ratio. A modified time-varying mesh stiffness with temperature stiffness is included in the model. Afterwards, the effect of the gear pair meshing vibration on bearing radial vibration is studied. The bifurcation and evolution of the MMS behavior are investigated changing the system parameters. An algorithm of DP is proposed in the time domain based on the established MMS model. The characteristics of DP are systematically discussed with the effects of dynamic response type, phase trajectory topology, bifurcation and chaos, and correlation between parameters. The results demonstrate that grazing bifurcation reduces the number of GD and chaos is prone to BTM. The disengaging proportion is highly dependent on the phase trajectory topology and generally increases from period-1 to quasi-periodic and then to chaotic responses. Bifurcation changes the variation trend of DP, thus there is a peak near period-doubling bifurcation and a trough near grazing bifurcation. The chaotic response leads to a jump in DP. The correlation between parameters considerably dominates the DP. This study provides a reference for revealing the mechanism of gear system disengagement and improving the dynamic performance.