| In recent years,the double helical planetary gear drive is highly applied in aviation power transmission system and vehicle(especially heavy vehicle)reducer,which has the characteristics of high speed and strong load capacity.However,the vibration and noise problems are the main reasons of affecting the equipment in the gear train.In the existing gear research,backlash is regarded as a strong nonlinear factor,which is an important cause of nonlinear vibration of gear system.However,there are multi backlash in planetary gear transmission system,so the nonlinear vibration of the system is more complex.In this paper,based on the double helical planetary gear transmission system under the condition of multi backlash,a series of research work related to gear nonlinear dynamics is carried out,focusing on the nonlinear frequency response characteristics of the system.The main contents are as follows(1)The equivalent model of the double helical gear is determined,and the middle non tooth segment of the double helical gear is regarded as the middle transmission shaft with elastic deformation,which is connected with the left and right helical teeth of the double helical gear through the coupling relationship.According to the internal and external meshing relationship of planetary gear train,the nonlinear dynamic models and equations of double helical gear external meshing pair and double helical gear internal meshing pair are established respectively.The mathematical models and calculation methods of four excitation forms including backlash are analyzed,and the solving process of incremental harmonic balance method is deduced.(2)Taking the single side helical planetary gear system as the research object,considering the backlash in the system,establishing the nonlinear vibration model and equation of helical planetary gear train.Then,obtaining the time displacement diagram and displacement velocity diagram of the system by the incremental harmonic balance method,and studying the nonlinear vibration response of the system.Finally,the frequency response curve of the system is analyzed by changing the internal and external excitation parameters,and the results are verified by Runge-Kutta.(3)Based on the equivalent model of double helical gear,the double helical planetary gear train is analyzed.Considering the nonlinear factors such as backlash and support clearance and establishing the system model and equations when the system model was established.The system model was settled by numerical method,and the vibration responses of the internal and external meshing pairs and the supporting direction of each wheel were analyzed by time displacement diagram,displacement velocity diagram and frequency spectrum diagram.Finally,the influence of excitation factors and support on the nonlinear frequency response of the system is studied.(4)The vibration test of single stage planetary gear system is carried out by means of test.The vibration signals of gearbox at different speeds are measured by the test platform.The vibration displacement spectrum of different motor speeds is obtained by signal processing and analysis.Finally,it is compared with the numerical simulation results.Through the above research,the nonlinear frequency response characteristics of herringbone gear planetary system are revealed.The nonlinear jump phenomenon and multi value solution appear in the frequency response curve of the system under the action of the backlash and other factors.At the same time,when the backlash is 0 or the meshing stiffness harmonic coefficient is 0 or the meshing resistance ratio is 0.1,the nonlinear phenomenon of the frequency response curve disappears,the nonlinear vibration of the system is obviously suppressed.Finally,the general law of suppressing the nonlinear vibration of the system is obtained through the analysis,which provides a theoretical reference for the vibration and noise reduction of herringbone gear planetary system. |
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