| Gear transmission systems are broadly adopted in the engineering field if aircraft and space, transportation, mechanical engineering and instruments as well. The gear transmission systems are elastic mechanical system included gear pair, shaft, bearing and box. The static and/or dynamics contact characteristic, transmission behaviors and dynamics transmission error are affected by gear mesh elastic deformation, tooth impact, backlash, manufacturing error, tooth modification and assembling error in the mesh process. Therefore, nonlinear dynamics analysis of gear transmission system with these nonlinear factors is an imperative request to improve performance of the mechanical system. From the perspectives of dynamic, it's an important research direction to systematically analyze the gear design, static analysis, dynamics analysis and experimental investigationFirstly, parametric equations of standard and modified spur gear are deduced based on gear mesh theory. The contact patterns of modified spur gears are studied with the effect of three kinds of assembling error based on TCA.A test rig for measuring the static and/or dynamics transmission error, vibration and noise is built based on Ni.Labview and LMS.test systems. With the help of high precision optical encoder, effects of gear misalignment on unloaded and lightly loaded dynamic transmission errors, which are relative to gear rattle, are investigated. The gear mesh misalignment is introduced by eccentric sleeve assembled on the output shaft. Effects of modification and misalignment on the dynamic transmission error, are studied at different load and driving velocity conditions.Based on nonlinear Hertz impact damping model, a new impact model of gear transmission system combining with time varying stiffness and friction is developed. The time varying stiffness and friction force functions are obtained at each contact point, which are functions of rotation angles of gear and pinion. The numerical program is constructed to analyze the transient impact dynamics behaviors with different load and friction conditions. The numerical results shown that,(1) the main parts of dynamics transmission error is impact frequency component, which is determined by initial impact velocity.(2) Fluctuation of load is less effect to the dynamics transmission error and output velocity with lower input velocity. But in higher input velocity condition, the fluctuation of load made the meshing frequency component of dynamics transmission error increasing rapidly. And the impact frequency change slightly. However,(3) when the fluctuation of load is formularized with shaft frequency, the system occurs loss contact motions moreover double side impact motion.(4) The friction force can reduce the loss contact impact motion at low input shaft condition. The low frequency vibrations are affected by friction obviously but it has less effect on the high frequency vibration. The main results gotten in this paper is appeared in previous research. The transient impact dynamics behavior analysis is essential step to disclose the gear rattling.Effects of impact damping on impact dynamic characteristics of crowned gear transmission system are investigated numerically. The results show that jump induced by backlash are not changed with parameter n, but the length of jump region changes obviously and the system vibration is aggravating at heavy load. Under lightly loaded condition, the jump deduced by backlash disappears with the effect of parameter n. The flank modification applied to gear pairs can vary the parameter n then the relation between modification and vibration behavior can be analyzed directly, which may be a new stratagem for dynamic characteristic design. Moreover, impact damping can suppress the amplitude of sub-harmonic component and slightly affect the main and second meshing frequency component. And the effect of coefficient of restitution, depended on initial impact velocity, should be involved into the analyses of gear impact when the system undergoes gear rattling or intermittent motion. And the process of collision process described by the constant coefficient of constitution method is inappropriate.The static transmission error (TE) can be combined with backlash parameter with comparative analysis of experimental dynamic transmission error directly. At low speed condition, the dynamic load is mainly connected with high frequency component of transmission error. The high frequency amplitude of transmission error can be suppressed with the increase of tooth surface accuracy, improvement of tooth profile error and roughness effectively. At high speed condition, the shaft frequency component of transmission error has a dominate influence on dynamic load, though the gear may be in the resonance area. Parameter n is decreasing and dynamic load coefficient is increasing especially in resonance area. When n is1.0, loss contact impact area exists in the system, and the amplitudes of shaft frequency component in dynamic transmission error are almost equal, which indicates that dynamic characteristics are little affected by load and parameter n when there is no loss contact impact condition. It proves that the nonlinear impact model is sufficient to study the rattling process of gear pairs. When n is1.5, loss contact impact do not exist in system, and the ratios of prior three harmonic components are approximate to the linear increase of load.The dynamics model considered in this paper are reduced to a new non-smooth dynamics model with varying domain. A multiple shooting method and Floquet theory are developed to get the stable periodic solution. The numerical strategy is performed to analyze the co-dimension one and co-dimension two bifurcations. And the effects of frequency parameter ω and backlash b0and fluctuation load f1on co-dimension two bifurcations are investigated.
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