| The double-helical planetary gear trains is widely used in high-speed and heavy-load applications such as jet propulsion systems,rotorcraft transmissions,and vehicle automatic transmission due to its advantages of higher power-density,reduced size,and smooth transmission.However,there are still many technical difficulties in the design,manufacturing and application due to its complicity.To develop quiet and reliable double-helical planetary gear trains,researches on static contact analysis and dynamic response prediction were carried out in the dissertation.A three-dimensional helical gear finite element model is established directly from node to element based on the tooth profile equations obtained by the generating method.Through reasonable planning and the hierarchical division of the hexahedral grid in the contact area,a well-refined three-dimensional finite element model of the gear is established.All nodes generated by interpolation on the tooth surface are moved to the theoretical position to ensure the accuracy of the model.The combination of tooth contact analysis and the refined finite element model is applied to explore high-precision tooth contact analysis such as time-variable mesh stiffness calculation and profile modification optimization.Taking the minimum transmission error as the optimization objective,the tooth profiles modification optimization is carried out and the modification parameter interval is obtained.The influence of tooth surface modification on the results of gear contact analysis is analyzed,and the transmission error and time-varying meshing stiffness of the modified gear are obtained,which is the excitation parameters for dynamic analysis.A nonlinear time-varying three-dimensional discrete dynamic model of a double-helical planetary gear trains is proposed,including all gear mesh,bearing and support structure compliances,as well as all six degrees of freedom for each gear and the carrier.Gyroscopic effects,time varying mesh stiffness and gear mesh excitations will all be incorporated in the model.The effect of floating sun and planet gear and stagger angle are included.Then,the natrual properties of double-helical planetary gear trains are studied.Four types vibation strucutre modes are observed in the double-helical planetart gear trains,called torsional vibration modes,oscillating vibration modes,axial vibration modes and ring gear vibration modes.The planet vibration modes accounts for the majority in all the modes.In high-order vibration modes,the ring vibration and the planet oscillating vibration modes are dominant.As the bearing stiffness and meshing stiffness increase,the natural frequency of the system increases.The modal transition points exhibit clustering,which can be divided into three groups: high,medium,and low frequency groups.The sensitive positions of the middle and high order natural frequencies to the stiffness are relatively concentrated,while the sensitive positions of the low order natural frequencies to the stiffness are distributed throughout the change process.The gyro effect reduces the natural frequency of each order of the system is observed.As the manufacturing error increases,the imbalance of the system load gradually increases,and the mesh forces increase dramatically.A parametric study was carried out to investigate the influence of different design parameters and variations such as right-to left stagger angle,support stiffnesses and planet mesh phasing conditions on the dynamic behavior of the system.The installation form of full floating of the sun gear and axial floating of the planet gear is helpful to compensate the unbalanced load caused by system errors.Finally,a test bench for the double-helical planetary gear trains was built to verify the theoretical calculation results.Multi-level slip rings are applied to prevent wire entanglement and real-time data acquisition.Multi-channel data synchronous acquisition system was developed.The experimental results agree well with the theoretical analysis.This paper combines gear contact analysis with the refined finite element model to study the time-varying mesh stiffness calculation and optimization of tooth surface modification.A non-linear time-varing dynamic model is established to study the dynamic properties of the double-helical planetary gear trains and verification experiment was carried out.This study improves the dynamic theory of double-helical planetary gear trains,and embodies important theoretical significance and engineering practical value. |
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