Research On Dynamic Characteristics And Tooth Profile Design Of Swing Teeth Transmission

The swing teeth transmission with two teeth differential has the advantages of large range of transmission ratio,big load-carrying capacity,high power density and steady transmission,which highly meets the requirements of mechanical and electrical equipments in many fields such as metallurgy,mining,ships,vehicles and so on.In this paper,the meshing stiffness of the meshing pairs,the equivalent contact stiffness between the main components and the family of swing-tooth system,dynamic modeling of the system,dynamic response and dynamical tooth profile designing of the two teeth differential swing teeth transmission are systematically studied.In this paper,based on the tooth profile design of swing teeth transmission system which sets the motion law of swing rod,the concept of elastic rotation angle was proposed.And the deformation compatibility equation of meshing components was deduced.The meshing stiffness and time-varying characteristics of meshing pairs are solved and analyzed by combining the torque balance equation and the Palmgren empirical formula of roller bearing.The instantaneous meshing stiffness and its time-varying characteristics of the meshing pairs are analysed.On these basis,the equivalent contact stiffness were analysed.A simplified dynamic model of the transmission system was established through the lumped-parameter method,and the kinetic energy,potential energy and Rayleigh dissipation function of each part of the system are derived based on the equivalent contact stiffness among components.The non-linear dynamic differential equations of the swing teeth transmission system are derived on the basis of Lagrange dynamic equation.The natural frequencies and vibration modes of the system,along with the transient and steady-state responses of the subsystems in the time domain of displacement,velocity and acceleration at rated operating conditions were solved through Duhamel integral.Parametric impact analysis of the dynamic response of each subsystem was analyzed with the influence of kinematics design variables of the mechanism.The stability and dynamic load determination coefficients of each subsystem were defined and calculated.On these basis,the concept and method of active dynamic design of swing teeth transmission system are put forward.The evaluation function and objective function were set up,and the influence of each single design variable on the dynamic behaviour of the whole machine was compared.Based on the linear weighting method,the complex multi-objective optimization problem was simplified to a single-objective optimization problem.And a set of optimal design parameters of the prototype with the best dynamic characteristics of the whole machine was selected from a set of designing parameters.Simplified virtual prototype model of swing teeth transmission system was obtained by importing parametric model through the interface between Solidworks and Ansys Workbench.Static strength analysis and modal analysis were carried out and compared with the results of theoretical analysis.The research results in this paper provide a theoretical reference for meshing stiffness analysis,dynamic characteristics and optimization of kinematics design parameters of swing teeth transmission system.And layed a foundation for improving the dynamic characteristics of the transmission system.