Time-varying mesh stiffness is a significant excitation source within gear systems. Split gear (or laminated gear, phase gear) is an interesting design using equally phased gear-slices, which can remarkably reduce the mesh stiffness fluctuation like helical gears but completely avoid the axial force. This work examines a split gear pair to address the suppression of the mesh stiffness fluctuation and rotational vibration thereof, especially the relationship between the key design parameters including the number of slice, contact ratio, and damping, and the parametric vibration. For these aims, this work develops a purely rotational model, based on which the multi-scale method is employed to determine stability boundaries. The results imply that the unstable zones are related to the mesh phase determined by the number of slices and contact ratio, and these zones can be diminished by the damping. The analytical predictions are numerically verified by Floquet theory.