Dynamic analysis of a spur gear by the dynamic stiffness method

This study treats a spur gear tooth as a variable cross-section Timoshenko beam to construct a dynamic model, being able to obtain transient response for spur gears of involute profiles. The dynamic responses of a single tooth and a gear pair are investigated. Firstly, polynomials are used to represent the gear blank and the tooth profile. The dynamic stiffness matrix and natural frequencies of the gear are in turn calculated. The forced response of a tooth subject to a shaft-driven transmission torque is calculated by performing modal analysis. This study takes into account time-varying stiffness and mass matrices and the gear meshing forces at moving meshing points. The forced response at arbitrary points in a gear tooth can be obtained. Calculation results of fillet stresses and strains are compared with those in the literature to verify the proposed method.

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