Vibratory Power Flow in the Gear System with Backlash Nonlinearity and Time Varying Stiffness

摘要

The work aims at utilizing vibratory power flow as a synthesized criterion for the evaluation and control of nonlinear vibration of gear systems.Based on its dynamic model and movement equation,the source power of a meshing gear pair with time-varying mesh stiffness and backlash nonlinearity is deduced,and the time-averaged power flowing into the receiver is proposed as a generalization of classical power flow.By analytic method,the property of time-averaged power in periodic and non-periodic motions is studied,and the relationship between time-averaged power and vibratory power flow is discussed.Then by regarding the time-averaged power as the third state space variable besides displacement and velocity,a time-domain simulation arithmetic is derived.Furthermore,via time-domain simulation of the system with Runge-Kutta-Felhberg method and Poincare mapping method,factors essentially deciding the system power flow level are revealed,and characteristic of power flow and bifurcation of the system are compared and analyzed with different mesh parameters changing continuously.The theoretical analysis and simulation results prove the validity and rationality of the method of power flow analysis in the nonlinear gear dynamics.The important influence of some parameters' alteration on power flow is summarized,to provide some reference for the vibration and noise control of gear transmission systems.