| Gear transmission system is considered as a driving machine of a high efficiency,high stability,compact structure and high safety.It is widely used in aerospace equipment,high-speed railway,military equipment,precision machine tools and other equipment in mechanical industry.The more complex structure of the gear system,the more obvious vibration and greater noise the system will have.This paper makes common multi-stage gear system as an object to research and analysis,based on nonlinear vibration analysis theory,by considering time-varied meshing stiffness,combined transmission error with tooth friction and other factors,dynamic models of straight tooth cylindrical gear systems are established from simple to complex and by means of numerical calculation method obtained the maximum amplitude response diagrams,bifurcation diagrams,maximum Lyapnov index diagrams,safe basin evolution diagrams,cell mapping diagrams and displacement-time diagrams and analyzes the global nonlinear dynamics properties of gear system which can provide a theoretical basis for design and optimization of gear transmission system security.The main research contents of this paper are as follows:Based on the lumped-mass method,a single degree of freedom gear transmission system dynamics model is established,with variable step size 4-5-order Runge-Kutta method,simulating the non-dimensional equations of the system.Maximum amplitude diagrams of the system were analyzed and select out reasonable torque and error which meet gear system security requirements.Then through the analysis of systems' bifurcation diagrams,phase diagrams,sectional diagrams and safe basins erosion diagrams,the influence of meshing frequency of gear system dynamics on characteristics and safety are obtained.A single degree of freedom gear transmission system dynamics model which contains friction was established,then through numerical simulation,bifurcation diagrams,phase diagrams and displacement-time diagrams of the system were obtained.When frequency changes,the effects of boundary crises,saddle-node bifurcation,cycle bifurcation and Hopf bifurcation on system dynamic characteristics and safety features are obtained.To make the system fit for the actual condition properly,this paper establishes single degree of freedom gear transmission system dynamics model which contains wearing.According to the multi-initial bifurcation diagram of the system,analyzing multiple attractors coexist phenomenon and many bifurcation forms and coexistence form of the system with the variation of meshing frequency.With the evolution diagrams of attraction domain,analyzing the local and global nonlinear dynamics and the impact of mesh frequency on gear transmission system global stability and then security is further comprehended.Lastly,the dynamic model of multi-degree of freedoms gear transmission system with multi-clearance is established and the reasonable supporting clearance and the supporting stiffness are selected by the analysis of the displacement-time diagrams.Through bifurcation diagrams,Poincare diagrams and phase diagrams,the effects of various bifurcation forms on the safety performance of multi-degree of freedoms gear system are analyzed. |
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