Load Sharing Analysis Of Double Power Input Split-torque Transmission System With Face Gears And Cylindrical Gears

This paper conducts research on the load sharing analysis of double input twice split-torque transmission system with face gears and cylindrical gears.The main research contents include analysis of static load-sharing characteristics,natural frequency and natural mode of the system and analysis of dynamic load-sharing characteristics.Firstly,statics model of the system is established,and static equilibrium equations are deduced and solved.Thus,load-sharing coefficients of each branch are obtained.Influences of torsional stiffness,supporting stiffness and installation errors on static load-sharing characteristic are analyzed.Results show that torsional stiffness of spilt-torque shafts and support stiffness of input shaft have a great influence on load sharing performance of input stage,that torsional stiffness of double gear shafts and installation errors have significant influence on load sharing of the system.Secondly,considering time-varying meshing stiffness,torsional stiffness,supporting stiffness and backlash,bending-torsional coupled dynamic model of the system is developed based on theory of lumped parameter method.With characteristic of closed loop structure,rigid body displacements of the dynamic equations are eliminated,and non-dimensional equations are obtained.Thirdly,mass matrix and stiffness matrix of the system are obtained by solving the dynamic equations,then,get the natural frequency.Influences of torsional stiffness,supporting stiffness and meshing stiffness on natural frequency are analyzed.Results show that in addition to the torsional stiffness of the input shaft and the output shaft,all other stiffness has little effect on the first natural frequency,that except the supporting stiffness of the output shaft,the second natural frequency increases as the supporting stiffness increases,and that apart from the torsional and supporting stiffness the third natural frequency increases with the increase of other stiffness.Finally,through solving the dynamic equations using Runge-Kutta method,dynamic load-sharing coefficients are acquired.Influence of backlash,torsional stiffness and supporting stiffness on dynamic load-sharing characteristics are analyzed.Results show that radial fluctuation of input shaft can effectively improve dynamic load sharing performance of input stage,that increasing backlash or rationally configuring the torsional stiffness of transmission shafts can improve dynamic load sharing performance of system.