Research On The Design And Dynamic Characteristics Of The Planetary Gear Train With Non-equivalent Modulus And Pressure Angle

An investigation on the design and dynamic characteristics of the planetary gear train system with non-equivalent modulus and pressure angle is conducted in this paper. The geometric calculation and optimization design of planetary gear train system with non-equivalent modulus and pressure angle, the calculation and analysis of the strength of gear, the analysis of the load sharing performance for planetary gear train system, and the experimental verification for the system are included in the investigation. The nonlinear dynamic model is established and also the nonlinear dynamic behaviors are analyzed. The main content is as follows:(1)The non-clearance meshing equation for the gear pair with non-equivalent modulus and pressure angle is deduced, and the calculate methods of the geometric parameters of gear pair such as the operating center distance, the gear addendum coefficient of variation and the contact ratio are put forward. The above methods are applied to the parameter calculation of the planetary gear train system. The calculation equation of the gear pair with non-equivalent modulus and pressure angle of contact stress is proposed, and with the variety modulus ratio of internal and external gear meshing pair, the trends of the safety factor of gear pair contact strength, bending strength and bonding strength are analyzed. With the smallest volume and the optimal number of planetary gear being taken as the objective functions, the optimization design model for planetary gear train system is built. After solving the model, the ideal optimization design model is obtained. It exerted the advantage of meshing performance for the gear pair with non-equivalent modulus and pressure angle.(2)In consideration of the eccentric error and tooth frequency error of parts, average mesh stiffness of gear pair, the static model and dynamic model for the planetary gear train system with non-equivalent modulus and pressure angle are developed. The mechanical equilibrium method and Fourier series method are used to do the numerical simulation of the mechanical equations respectively, and the static response and the dynamic response of system are obtained. The load sharing characteristics are compared under the situations where the modulus and pressure angle of gear system are equivalent or not and the influence laws of the main parameters on the load sharing characteristics are obtained. An analyze software of the load sharing for the planetary gear train system is developed.The load sharing performance is tested, and the correctness of the above calculation methods is verified.(3)With the gear backlashes, time-varying mesh stiffness and comprehensive error of gear pair, the lumped mass method is used to established the nonlinear dynamic model of bending-torsion coupled vibration for the planetary gear train system with non-equivalent modulus and pressure angle. The nonlinear dimensionless differential equations for the planetary gear train system with non-equivalent modulus and pressure angle are deduced, which have multi-degree-of-freedom with the action of multi-clearances and varying parameters.(4)The harmonic balance method is used to carry out the numerical simulation of the dynamic differential equations, and the nonlinear dynamic frequency response of system is obtained, and the typical nonlinear characteristics of the system which appears the phenomenon of amplitude jump with the existence of the gear pair clearance is analyzed. For the nonlinear systems and linear systems, as well as the system with non-equivalent modulus and pressure angle and the system with equivalent modulus and pressure angle, the comparative analysis of dynamic responses are made. The influence of the damping coefficient, the mesh stiffness coefficient of variation and the magnitude of the error on the dynamic behaviors of system are researched, the regular pattern of variation for the nonlinear system that is inconsistent with the response of the linear system is obtained.(5)The Runge-kutta method is used to carry out the numerical simulation of the dynamic differential equations for the planetary gear train system with non-equivalent modulus and pressure angle, and the feature of the nonlinear dynamic behaviors of system is obtained under the different excitation frequencies. The dynamics bifurcation characteristics of the system are researched, and the bifurcation rules of system changing with the excitation frequency under the different damping coefficient and system changing with the backlash under the different excitation frequency are obtained.The load sharing characteristic of power split for planetary gear train system under the nonlinear model is researched, and the influence law of the gear pair modulus and clearance on the load sharing performance is obtained.