Research On Nonlinear Dynamic Characteristics Of Compound Planetary Gear Transmission System With Manufacturing Errors

Compound planetary gear transmission system,taking the advantages of compacting structure,strong load capacity and multiple power flow,is widely used in wind power generation,military defense,aerospace,heavy machinery and energy exploration.With higher performance requirements of designing and manufacturing of the high speed and heavy load,efficient and reliable,intelligent precision gear transmission system,dynamic design and optimization design have become a development trend to improve the dynamic performance of the transmission system design.The knowledge of the dynamics characteristics of the system is the foundation of dynamic and optimization design.However,there are many dynamic excitations that affect its dynamic characteristics because of its complex structures,which directly affect the vibration and noise,load distribution and service life of the system.Therefore,theoretical modeling,numerical analysis and experimental verification are utilized to study the nonlinear dynamic characteristics of the compound planetary gear transmission system with manufacturing errors in this paper.The main contents and results are listed as follows:1.The translational and torsional nonlinear dynamic model is established by lumped mass method,and the corresponding nonlinear differential equations of motion are derived of the compound planetary gear transmission system.The dynamic model,involving the translational and torsional vibration of all the gear components,including the effect of random load,bearing supporting stiffness,time-varying mesh stiffness,mesh damping,and manufacturing errors,has been established.The dynamic model and analysis are applied for the dynamic excitations.The derived differential equations of motion is applicable to different number of planetary gear set and different power flow,which laid the foundation for dynamic characteristics study.2.The dynamic response characteristics of the compound planetary gear transmission system with manufacturing errors are investigated,which provides a theoretical basis for improving the response characteristics of the system.Firstly,the response and the response spectrum of the system under dynamic excitations are solved.Meanwhile,the vibration regulation of the components and the influences of the random load and the time-varying mesh stiffness on the dynamic response characteristics are revealed.Secondly,the effects of the mesh frequency on the bifurcation and chaos characteristics are analyzed to find out the intervals that easily cause the chaotic motion,combined with the global bifurcation diagrams,time history curve,phase trajectories and Poincare section.The results show that,in order to work in the stable periodic motion for the system,the input speed should be avoided from some range that easily causes the chaotic motion from the point of restraining the vibration.Lastly,the influences of the manufacturing errors on the frequency response characteristics are analyzed based on the harmonic balance method,which provide the theoretical basis of improving the response characteristics of the system.3.The influences of the manufacturing errors on the load sharing characteristics are analyzed by calculating the load sharing coefficient of system under the circular runout error,the installation error of the center gear,the position error of the planetary gears and the phase angle of the error.The results show that:the different manufacturing errors have different effects on the load sharing performance of the system.The circular runout and installation errors of center gears affect each meshing pair periodically.However,the circular runout and installation error of planet gears can lead to the planet gear with persistent partial load.The phase angle of the position error of the planetary gears has great effect on the load sharing coefficient of the system but others don't.It has the least effects on the the load sharing coefficient of the system when the phase angle of the short planet is 40° and the phase angle of the long planet is 175°.The influence of the random load on the load sharing characteristics is also analyzed.The random load has a great impact on the load sharing performance,and the impact becomes stronger with the random part of the random load increasing,wihle the load sharing coefficient becomes smaller with the constant part of the random load increasing.The errors will have interaction effects and the errors of the big sun gear and the ring gear influence the load sharing performance most when the system has all the errors.The load sharing performance will improve with the improvement of the machining precision level of the system.The contact loss and impact phenomenon exist in the system with the machining precision level six and below under the combination of all the errors.However,it can improve the load sharing performance obviously by improving the machining precision and using the load balancing mechanism with flexible support of the error component.4.The compound planetary gear transmission system dynamic characteristics simulation system has the advantages of simple code,fast calculation,powerful functions,and quick analysis,which was developed by the C#design language.It is easy to be used for the engineering technicians with its good interactivity and usability.The simulation system has the functions of the solving and analysis for the dynamic characteristics like the natural frequency,the modal shape,dynamic characteristics and the load sharing characteristics of the simple and compound planetary gear transmission system with the intelligent detection algorithm.The simulation system is convenient to be applied widely in the engineering application,which can simplify the process of the modeling and the analysis,and increase the efficiency of the dynamic design and optimization design.5.The experimental platform with electric power closed structure and multiple functions of the compound planetary gear transmission system is designed and built,which has the advantages of simple operation,versatility,energy-efficient.The experimental platform can meets the various demands of the testing like the natural frequency,dynamic response characteristics and the load sharing characteristics.The data acquisition module implements the technique of convenient stress acquisition based on the wireless communication and the storage online,which solved the problem of hard to the wiring arrangement of the load sharing test for the rotating gear pair.The partial natural frequencies and the meshing frequency are achieved by natural frequency and dynamic response test.Meanwhile,the load sharing coefficient of the system and the strain of the meshing gear tooth under stress are achieved by load sharing performance test.The results show that,the test results are similar to the results in the theoretical analysis.The rationality of the method and conclusions made by the theoretical study in the dissertation is proved by physical test,and the rationality of the experimental study is also proved by theoretical study.