Study On Dynamic Characteristics And Dynamic Load Sharing Of A Herringbone Planetary Gear With Manufacturing Errors

The planetary gear train(PGT) has advantages such as compactness, large transmission ratio, high load capacity, etc. Planetary gear trains usually use either spur, helical or herringbone gears as teeth forms. Compared with spur and helical planetary gear train, the herringbone planetary gear train(HPGT) has significant advantages of larger contact ratio, lower axial force and higher power density. Hence, HPGT has been used in the field of heavy load transmission such as nuclear power, wind power, lifting machine, etc., and it also has a good application prospect in the field of underground mining, excavation equipment and aerospace. However, since HPGT has more complex structure form, and the dynamic model of HPGT is difficult to establish and slove, at present investigation of HPGT dynamic characteristics is quite sparse. In the thesis, based on research task of the national 973 program and other subject undertaken by the research group, in order to realize high capacity and low vibration of HPGT, dynamic characteristics and dynamic load sharing performance of HPGT are studied more deeply, especially the effects of manufacturing errors on the above characteris are analysed in-depth, it has great significance for the theoretical study and engineering application. The main research work is summarized as follows:(1)Based on the structure characteristics of herringbone gears, a generalized bending-torsional-axial coupling lumped-parameter dynamic model of HPGT is presented, and the motion differential equation and its matrix form of HPGT is derived. Tooth profile errors of each gear, manufacturing eccentric errors of each component, time-varying mesh stiffness, bearing supporting stiffness, mesh phase relationship as well as gyroscopic effect of each component are considered in the HPGT dynamic model. Meanwhile, lateral and torsional vibration of each system component as well as axial vibration caused by manufacturing errors are included in the proposed model. The computational formulas of the HPGT main excitations such as each component manufacturing error, time-varying mesh stiffness, planet mesh phase, etc. are analysed and derived. These studies lay the foundation for the study of dynamics and load sharing characteristics of HPGT.(2)The undamped free vibration equation used in the analysis of natural characteristics can be obtained by the HPGT coupling dynamic model presented in chapter 2. By solving the corresponding eigenvalue problem, HPGT natural frequencies, modal shapes and modal characteristics are analysed, and the system vibration mode is summarized. In order to reveal HPGT natural properties more fully and accurately, the computational formulas of modal strain energy and modal kinetic energy of the system are analysed and derived by using the modal energy method, the distribution rules of the modal strain energy and kinetic energy of different vibration modals are studied. Finally, the effects of mesh stiffness and supporting stiffness on the HPGT natural frequencies are investigated.(3)The HPGT dynamic model can be obtained by the HPGT coupling dynamic model proposed in chapter 2. Based on the model, the dynamic responses of the herringbone planetary gear train under the running condition are respectively sloved and analysed by using the numerical integration approach, including the vibration displacement, vibration velocity, vibration acceleration of each system components in each DOF direction, dynamic mesh force and dynamic bearing force. The effect of time-varying mesh stiffness of the system on the system dynamic response is studied.(4)Based on the HPGT dynamic model considering manufacturing errors, the dynamic responses of the herringbone planetary gear train under the influence of different manufacturing errors including manufacturing eccentric error of each component, tooth profile error of each gear are respectively solved and analysed, and compared to the dynamic responses of each component of the system without manufacturing errors in chapter 4, from the time-domain and frequency-domain perspective, the effects of different manufacturing errors on the dynamic response characteristics of the herringbone planetary gear train are discussed.(5)Based on the dynamic mesh force of the herringbone planetary gear train obtained by the dynamic response analysis, the dynaimic load sharing coefficient of the transmission system is computed. The effect of each component error of the system on the dynamic load sharing characteristics is studied. The influences of working condition parameters(the input speed, the input torque), physics and geometrical parameters(supporting stiffness of the center part, the number of the planet gear) on the system load sharing performances are studied. The computational method of the floating amount of basic floating components of HPGT is proposed, the relationships between the floating amount of the component and manufacturing errors, physical parameters(supporting stiffness of the sun gear, the sun-gear mass) as well as geometrical parameters(the number of the planet gear) and influence rules are analysed. These studies lay the foundation for the floating and load sharing design of the herringbone planetary gear train under the influence of manufacturing errors.