| Comparing with the Low contact ratio(LCR) spur gear transmission, high contact ratio(HCR) spur gear transmission has more simultaneous meshing tooths which make it has lower tooth load and less meshing stiffness variety on each gear pair. As a result, HCR spur gear transmission has the benefits of higher and more stable power transmission. However, current design standard doesn’t cover the HCR spur gear transmission, and very less related literature about the strength and dynamics could be retrieved as well. This paper proposed the research on the area of design, strength and dynamics of the HCR planetary transmission system, and the relevant study results provide theoretical technic support for HCR spur gear transmission system.Planetary transmission system could be divided into external and internal meshing gears, and the design region, meshing stiffness and tooth load of HCR are investigated in this paper. The influence of the addendum coefficient, pressure angle, and modification coefficient are analyzed, and the design regions of the external and internal meshing HCR gears are determined accordingly. The stiffness of the external and internal gears considering gear wheel body deformation are computed by using material mechanics method, and the influence of the addendum coefficient, pressure angle, modification coefficient are taken into consideration. By the average stiffness of of the single tooth meshing, the fitting formula of the single tooth stiffness of the internal and external meshing for HCR and LCR gears are derived, and his formula is validated by using finite element method. Additionally, the load distribution ratio coefficient of the internal and external meshing HCR gears is calculated, and its influence caused by system parameters is analyzed as well. The results reveal that HCR gear can effectively reduce the gear load. Besides, the load distribution ratio of HCR planetary gear is verified by CL-100 gear testing machine.The calculation method of bending stress and contact stress for planetary gear’s internal and external meshing pair are proposed, and the calculation formulas of the tooth root bending stress and tooth form factor of internal and external meshing gears of HCR planetary transmission system are deduced as well, and the influences of bending stress and the position of the maximum load caused by the main factors, including addendum coefficient, pressure angle of the HCR and LCR planetary gear, are analyzed. The contact stress formulation for internal and external HCR meshing pair of planetary gear is derived, and the formulation is transformed into GB form by introducing curvature correction coefficient and node correction coefficient. The influence of main system parameters on the contact stress and maximum load position of HCR and LCR planetary gear is studied. The theoretical calculation formulation is validated by CL-100 gear test machine and could be satisfied for engineering requirement.The dynamical behavior of the external meshing HCR planetary transmission system is studied. The fitting formula of the time-varing meshing stiffness of external meshing HCR and LCR gears are calculated by using finite element method. By using lumped mass method, the dynamic model of external meshing HCR gear pair which including the gear backlashes, bearing clearance and time-varying meshing stiffness is established. The dynamic equations are non-dimensionlized and solved by 4th Runge-Kutta and the influence of HCR and LCR load sharing caused by bearing clearance, damp ratio, and gear backlash is analyzed as well as the differences of bifurcation and periodical motion.The dynamic behavior of the HCR planetary transmission system is studied. The fitting meshing stiffnesses of internal and external meshing HCR gears pair are calculated. The bending-torsional coupled dynamic model of the HCR planetary transmission system which considering the backlash and time-varying mesh stiffness and ring gear’s rotational coupling effect is established. The govern equation is derived by using the energy method, and the relative coordinates is introduced to avoid the rigid displacement. The dynamic responses of the HCR planetary transmission system with different parameters are studied, and the influence of the contact ratio and operation parameters on the dynamical response is analyzed. The main parameters about the contact ratio are analyzed and the influence of these parameters on the dynamical load sharing property of HCR and LCR planetary transmission system is discussed as well. The dynamic load sharing behavior of the HCR planetary transmission system is analyzed and verified by using the planetary gear transmission test-bed designed. The influence of speed, power, gear backlash, stiffness and damping on the bifurcation characteristics of the HCR planetary transmission system is studied and some references for the selection of operating parameters of HCR planetary transmission system are presented. |
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