| Planetary gears yield several advantages over conventional parallel shaft gear systems. They produce high speed reductions in compact spaces, greater load sharing, higher torque to weight ratio, and diminished bearing loads. They are used in automobiles, helicopters, aircrafts, and a variety of other applications. It is extremely meaningful for mechanical industry to study the dynamics of the planetary train, to analyze the vibration mechanism,to present the measures to improve performance, and to design planetary gear trains with super performance. This dissertation mainly explores the dynamics of the helical planetary gear trains. The research works are listed as followings: An elasto-dynamic model is established in the rotating Cartesian coordinates. Moment of momentum theorem about center of mass is used in the model so that gyroscopic effects, induced by carrier rotation, are modeled, in rotation equations as well as in translation equations. Each component has in general six rigid-body degree-of-freedom. Furthermore, many factors are taken into account, such as time varying stiffness, gear run-out errors, mass eccentricity, pinion-pin position errors, and gear profile errors, etc. The natural vibration characteristics of the system and their sensitivities to parameters are analyzed in details. It is revealed that vibration modes can be classified into three groups: the axial translation-torsion mode, the radial translation-rotation mode, and the planet mode. The characteristics of each mode are generalized, and the sensitivities of natural frequencies to the stiffness and mass are obtained. A closed-form numerical algorithm for the periodic dynamic response of the asymmetry system is developed based on complex modal analysis. Besides the excellences of the traditional closed-form algorithm, it can also solve the equations that cannot be decoupled by real modes when exist non-classical damping matrix or gyroscopic matrix in them. Some measures of vibration reduction and load distribution balancing are conducted, such as floating of components and planet run-out error phasing. The effect of the planet run-out error to the system dynamic behavior is both demonstrated by theoretical analysis and simulation results. It is proved that two different aims, vibration absorption and improving of transmitting accuracy can be achieved by selecting proper parameters following the principles presented in this paper. A sensitivity analytical method for steady state response based on the Fourier method is developed. This method has higher computational efficiency than the difference method and differential method. Because the sensitivity of response in frequency domain can be worked out directly, this algorithm is applicable to condition monitoring and fault diagnosis.
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