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In this study, the nonlinear vibration of a meshing gear pair with the teeth elasticity is investigated. The elastic elements between the teeth and the body of each gear wheel are introduced to partially incorporate the teeth elasticity in the model. This model was originally considered by the second author as a rigid-elastic modeling approach of meshing gear wheels, which is well-suited for multibody systems. The contact analysis of the meshing teeth is performed using the Kelvin-Voigt method. By deriving the equations of motion for the mentioned model, the results of the numerical solution are presented. The method of multiple scales is utilized here for the first time to analytically analyze the nonlinear vibration of a gear system in which the teeth elasticity is partially incorporated by considering identical elastic elements between the teeth and the gear body. In this study, the effect of system parameters on the frequency response including the primary, sub-harmonic, and super-harmonic resonances is investigated. The results of the analytical solution show that the effect of external excitation amplitude and intensity on the system response amplitude is the same in the primary and sub-harmonic resonances. The results obtained numerically and analytically for the model have an acceptable agreement.

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