A lumped mass gear-rattling model with backlash is established by considering the time varying mesh stiffness, composite transmission error and the torque fluctuation. Based on the principle that no separation will occur if the response amplitude is not larger than the static response,the threshold is obtained by theoretical derivation. The validity of the theoretical derivation is verified by the numerical method. The results show that the time-varying mesh stiffness has little effect on the threshold. When the exciting frequency is less than the system natural frequency, the theoretical agrees well with the numerical one. The higher the exciting frequency or the smaller the average input torque is, the easier the separation will occur. When the exciting frequency is larger than the natural frequency by a certain value, the theoretical threshold does not agree with the numerical results. The numerical results show that the motion state will change from the meshing state to the separating state directly. The phenomenon that the gear pair sometimes separates and sometimes meshes occurs only when the exciting frequency is smaller.