| Firstly, the pure torsion-impact model of the compound planetary gear transmission system, the vibro-impact-torsion model of the spiral bevel gear transmission system and the vibro-impact-torsion model of the face gear transmission system with tooth surface friction are considered in the thesis. The 3D entity of the three gear transmission systems are established based on solidworks software, and the corresponding basic parameters of systems are obtained.Then, using the theory of Poincaré map, and the fourth order Runge-Kutta numerical integral method with variable step and by virtue of two-parameter plane of periodic motion,impact state-duty cycle of the mesh apart and the maximum dynamic load equipotential, as well as single bifurcation diagram, duty cycle of the mesh apart, phase diagram, Poincaré map,the maximum dynamic load diagram and impact state diagram in the time/frequency domain,the influence of changing control parameters to characteristics of periodic motion,meshing-impact state, degree of the mesh apart and tooth surface dynamic load characteristics of the gear systems, and the size corresponding control parameters domain, distribution rule,the optimal parameters interval and sensitive areas are analyzed under the function of meshing excitation frequency respectively and the system parameters: km, ka, ξ, b, em, T1, η.The results show: In low frequency range, compound planetary gear system exists continuous motion of 1~8T, and mainly exhibits 1T and 2T meshing motion. As the periodicity is greater than 8, the cycle number appears discontinuous phenomenon, and the border area of 1T and grey movement is the sensitive parameters area which frequently shows“Cataclysmic” phenomenon, “jump” bifurcation and Hopf bifurcation; in high frequency range, the compound planetary gear system displays basically 1T, 2T and 4T meshing motions.A similar dynamic characteristics are presented in the spiral bevel gear transmission system and the face gear transmission system. The boundary of 0/1T and 1/1T motion is constituted by “Grazing” bifurcation curve and “Jump” bifurcation curve. Under the periodic meshing motion, compared with the frequency of periodic meshing motion, the frequency of meshing-impact is the two times or same times as much. For parameter area of the no impact meshing motion 0/1T, duty cycle of the mesh apart is DC=0.0, and the range of the maximum dynamic load coefficient G?(1.0,2.0) is the optimal design parameters of the region, because of the stable of meshing motion, load ability, no impact phenomenon and low noise; In the case of 1/1T meshing motion area, as the maximum dynamic load coefficient belongs to G?[2.0,4.0], DC value is relatively small, the system exhibits less disengaging, a certain load ability, weaker impact characteristics and the maximum dynamic load of tooth surface shows smooth continuous change followed by the control parameters, as well as meshing movementshows good stability. Consequently, for G?[2.0,4.0], the corresponding control parameters region can choose as optional design parameters area; For G>4.0, the gradient of maximum dynamic load changes significantly and systems show the sub-harmonic motion, almost periodic or chaotic motion, and DC value is very large, and degree of the disengaging is very serious, as well as the system exhibits weaker load ability, which is a undesirable parameter area. By analyzing the dynamic characteristics of gear transmission system, and the relationship and matching rule of the system parameters, that can provide a theoretical guidance to design gear system with higher performance requirements. |
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