| Among all mechanical equipment,gear transmission system has been adopted most frequently as transmission device.Its reliability and dynamic characteristics play an important role in entire operation of machine.Gear transmission system is composed of gears,transmission shaft and support bearing,which forms an elastic mechanical system.In the process of its transmission,the tooth of gear,shaft and bearings will have elastic deformation,causing the system to couple torsional vibration and transverse vibration together.Additionally,the gear system has become a strongly nonlinear system because of the effection of time-varying meshing stiffness,gear back lash and etc,which are regarded as nonlinear factors.Consequently,it is essential to employ nonlinear theory to analyze the dynamic characteristics of gear transmission system.However,due to the randomness of gear transmission system’s coefficients,the former methods of reliability evaluation are hard to apply in strongly nonlinear system.Therefore,it has great significance to research and develop a Reliability Evaluation Algorithm adopted suitably in strongly nonlinear system.Firstly,the methods of material mechanics and AN SYS finite element simulation are adopted to obtain gear’s time-varying meshing stiffness as the stiffness excitation of gear transmission system.Then,a three degrees of freedom nonlinear coupling vibration analytical model under consideration of time-varying meshing stiffness,gear error,meshing damping,gear back lash,the stiffness and damping of support bearing is built.Runge-Kutta numerical integration is used to gain the numerical value of vibration differential equations from gear transmission system,then the dynamic response of the system is obtained.Time process graph,displacement-speed phase plane,Poincare cross section diagram,power spectrum chart,bifurcation diagrams and Lyaounov index diagram is used to analyze the dynamic characteristics of gear transmission system.Also,this paper discusses the effections of the randomness of related coefficients to the stability of gear transmission system.Finally,a reliability analysis method is put forward,which is suitable for implicit and strongly nonlinear function,and the method is based on Kriging model and Monte-Carlo active learning algorithm,then this paper analyzed the reliability of systems in various condition and the sensitivity of its reliability.The reliability of vibration of gear transmission system can be calculated accurately and more efficiently by our research.The effections of each related coefficients to the reliability of vibration of the gear transmission can be gained,which provides a theory to reliability design and optimization of gear transmission system. |
