Nonlinear dynamic analysis of spur gear system based on fractional-order calculus

Abstract

In this paper, nonlinear dynamic model of spur gear pairs with fractional-order damping under the condition of time-varying stiffness, backlash and static transmission error is established. The general formula of fractional-order damping term is derived by using the incremental harmonic balance method (IHBM), and the approximate analytical solution of the system is obtained by use of the iterative formula. The correctness of the results is verified by comparing with the numerical solutions in the existing literature. The effects of mesh stiffness, internal excitation amplitude and fractional order on the dynamic behavior of the system are analyzed. The results show that changing the fractional order can effectively control the resonance position and amplitude in the meshing process. Both the mesh stiffness and internal excitation can control the collision state and the stability.