# Research on vibration characteristics of reducer speed integrated gear based on harmonic balance method

According to the meshing principle and gear dynamics theory, the multi parameter variable vibration model of the new type of orthogonal shaft reducer variable speed integrated gear is established. Based on the harmonic balance method, the vibration characteristics of the gear are studied in depth

(1) Geometric model and internal excitation of reducer variable speed integrated gear

According to the meshing principle of reducer variable speed integrated gear, the pitch curve and tooth profile model are established, and the mathematical description of time-varying instantaneous center, stiffness, damping and gear tooth error is given.

(2) Multi parameter variable vibration characteristics of reducer variable speed integrated gear

Considering the factors of time-varying instantaneous center, stiffness, damping and error, the dynamic model of reducer variable speed integrated gear is established. The periodic steady-state solution of the system is obtained by harmonic balance method, and the influence of system parameters on vibration under multi frequency parametric excitation is analyzed.

(3) Nonlinear vibration characteristics of reducer variable speed integrated gear with backlash

Furthermore, considering the clearance of gear teeth, the nonlinear dynamic model of gear clearance is established. The function relationship between nonlinear restoring force and displacement is dealt with by discrete Fourier transform. The nonlinear algebraic equation of the system is constructed by harmonic balance method. Finally, the steady-state response of the system is solved by quasi Newton method, and the nonlinear dynamic characteristics are analyzed.

(4) Dynamic characteristic test of reducer variable speed integrated gear

The vibration test platform is set up to test the vibration acceleration signal of the gear system under different working conditions of speed change and load change. The original measured data are preprocessed by noise reduction method, and then the vibration characteristics of the gear system with input speed and load change are analyzed, and the results of theoretical analysis are verified. 