Research On Dynamic Characteristics Of Closed-form Planetary Gear Train

Planetary gears were extensively used in a variety of industrial field including aerospace, marine and automobiles, etc. The popularity mainly comes from their substantial advantages such as excellent bearing capacity, compactness and large gear ratios. In some cases, vibration and noise were still the key factors to system reliability, and durability. Because the planetary gears often endure both the external and internal excitation, its dynamics behavior is very complex. In addition, the noise created by the vibration has seriously worsened machine’s operating environment and the use of comfort. Therefore, in order to enhance the product security and market competitiveness, it is necessary to conduct dynamic design method researches about the dynamics modeling of the mechanical system, the dynamic response solutions, the parameter stability analysis and the vibration noise reduction etc.Compared with the non-closed-form planetary gear system, the torque transmitted by closed-form planet transmission system could be transmitted from several ways to the next stage, What’s more, the closed-form planetary gear transmission system has advantages of larger torque, more compact structure, higher transmission ration, etc. In other words, it has great property in torque-up and wider range of transmission ratio. As one from of planetary gears, the closed-form planetary gear system is widely used due to its unique features. The research on its dynamic method has great practical significance in providing reference and guidance for the optimization design.In this dissertation, researches on the non-linear dynamics of two-level closed-form planetary gear system of power split (confluence) has been conducted. The main work includes:the establishment of planetary gear mathematical model, the natural characteristic analysis, the frequency response characteristics analysis, the impact of system parameters on the dynamic response, vibration suppression and the related experiments. The outline of the paper was as follows:The application background of closed-form planetary gear system and advantages were outlined compared with the ordinary planet transmission. Then the formerly related research was summarized. In this dissertation, the present research situations about the intrinsic property, dynamic characteristic, vibration suppression as well as the experimental study were emphatically elaborated, which makes a good guidance to the research in that paper.A dynamic model was established to analyze the intrinsic property of the system. According to the kinematics relationship, the displacement of system components has been inferred in detail. Without consideration of non-linear factors such as time-varying mesh stiffness, gear backlash as well as system damping, purely rotational model and translational-rotational coupled model, were established based on the second kind Lagrange equation separately. The models can be described for the lumped mass model of two-stage closed-form planetary gear system. According to the dynamics models, the intrinsic property has been analyzed. Finally, the two-stage rotational-translational coupled dynamic equation has been promoted to a N-stage planet transmission system with similar structure.The non-linear frequency response characteristic of the above system has been analyzed based on the harmonic balance method. Non-linear factors such as time-varying mesh stiffness, gear backlash and the meshing error have been mathematically described. Moreover, based on the linear and un-damped purely rotational dynamics model, the non-linear parameters have been introduced to revise the model. The equations to describe the purely rotational dynamics model of non-linear of dissipative system were derived and nondimensionalized. By using the harmonic balance method, the differential equations were transformed to non-linear algebra equation set and can be solved by Newton iteration method (BFS rank2). Considering actual synthesis factors of project requirements, parameter influence as well as computation cost, the dissertation only studied the fundamental frequency steady-state response. The influence of several key parameters such as meshing stiffness, gear backlash, exterior excitation on the non-linearity dynamic characteristic of the system was quantified. The typical non-linear characteristics of the frequency response characteristic curve, such as the amplitude jumping, multiple solutions, and unstable solution branch were also analyzed.The vibration suppression based on mesh phasing relation has been studied At first, the relative mesh phasing of the system was analyzed. And then, the analytic expressions of main resonance amplitude of the system were derived using the multi-scale method. In different relative mesh phasing conditions, the vibration differs dramatically. The vibration suppression based on planet phasing was analyzed emphatically. The vibration response amplitude of different mesh phasing was compared frankly. Finally, the impact of key parameters on the vibration response amplitude was investigated.The experiment platform of planetary gear transmission system was established, which could detect the rotation speed, torque and power of the planetary gearbox. The experiment platform could be used to control speed and apply load. Moreover, the frequency response function was tested to obtain the natural frequency. Through the comparison of experimental and theoretical research results, the mathematical model for the transmission system was verified to be reasonable.The main research work and the important conclusions, as well as the issues to be further studied were summarized. In this dissertation, the non-linear dynamic characteristics of closed-form planetary gear system have been studied, the influence of some parameters on the system dynamic characteristics has been discovered. The conclusions provide theoretical foundation for realizing dynamic design of the closed-form planetary gear system.The author gratefully acknowledges the support of the Chinese National Science Foundation (No.51175299) and Shandong Provincial Natural Science Foundation, China (No.ZR2010EM012).