Parameter excited oscillations induced by the varying tooth mesh stiffnesses of the gear pairs cause severe vibration in gear systems. The oscillations become more complex and serious in multi-mesh gear system because more mesh stiffnesses variation occur, which are necessary to be investigated in deeply. To illustrate the complex oscillation phenomena, a 8 degrees of freedom (DOF) non-linear dynamic model of a multi-mesh gear system is developed to study the responses of the system with considering time-varying mesh stiffnesses. Interactions between the mesh stiffness variations at the two meshes are examined. Seven different mesh phases are defined according to the alternating engagement of single and double gear teeth. The effects of different phases of the mesh stiffnesses between the two meshes on the typical multi-mesh gear system are identified by using numerical simulation. The results show that the oscillations of the multi-mesh gear system could be reduced by changing the phase of the mesh stiffnesses.

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