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In a series of resent articles, study on vibration of spur gear transmission system involved surface friction is rare.In practice, the value and direction of the surface friction vary periodically all over the meshing process, which produces a kind of internal excitation making great effect to the dynamic behaviours of gear transmission system along with time varying stiffness and static transmission error.Vaishya and Singh[1:2] developed a single-degree-of-freedom (SDOF) dynamic model with periodic tooth stiffness and sliding friction based on the assumption that load is equally shared among the teeth in contact and simplified approach of rectangular shaped variation in mesh stiffness.Song He and his coworkers[3] presented a new linear model which including realistic time-varying tooth stiffness and the sliding friction.But in their study the influence of the static transmission error and its differentiation components are neglected during the numerically integration.