Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification...Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.展开更多
The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In conside...The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In consideration of the parts manufacturing errors, assembly errors, bearing stiffness and float, the power splitting rate of each star gear and the system were calculated by using the theory of equivalent mesh error. The effects of the errors, float and the bearing stiffness on power splitting were studied. The study provides a useful theoretical guideline for the design of star gearing.展开更多
The tooth surface friction stiffness and friction torque coefficient equations of cylindrical gear are derived.On the basis of factors such as time varying friction coefficient and mesh stiffness,support stiffness,tor...The tooth surface friction stiffness and friction torque coefficient equations of cylindrical gear are derived.On the basis of factors such as time varying friction coefficient and mesh stiffness,support stiffness,torsional stiffness and comprehensive error,the dynamic equations of the gear trains with bending torsional coupling are established.Using the Fourier series method,the total response of the system is obtained,and the influence of friction on it is analyzed.The results show that when the spur gear enters the meshing,the frictional amplitude of the tooth surface is larger than that of the gear when it is withdrawn from engagement,and the meshing force fluctuates greatly.The frictional force and dynamic meshing force of the herringbone gear tooth surface are relatively stable,and the fluctuation amplitude is much smaller than that of the spur gear.The amplitude of the bearing vibration is not affected by the friction,but the friction has a certain influence on the bearing force of the output shaft.The first order natural frequency of the split stage and the power confluence stage has a large influence on the vibration of the bearing force.In general,the natural frequency of the power confluence stage has a large proportion of influence.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.2009AA04Z404)
文摘Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.
基金supported by the Natural Science Foundation of China (51175423)
文摘The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In consideration of the parts manufacturing errors, assembly errors, bearing stiffness and float, the power splitting rate of each star gear and the system were calculated by using the theory of equivalent mesh error. The effects of the errors, float and the bearing stiffness on power splitting were studied. The study provides a useful theoretical guideline for the design of star gearing.
基金supported by the National Natural Science Foundation of China (No. 51475226)
文摘The tooth surface friction stiffness and friction torque coefficient equations of cylindrical gear are derived.On the basis of factors such as time varying friction coefficient and mesh stiffness,support stiffness,torsional stiffness and comprehensive error,the dynamic equations of the gear trains with bending torsional coupling are established.Using the Fourier series method,the total response of the system is obtained,and the influence of friction on it is analyzed.The results show that when the spur gear enters the meshing,the frictional amplitude of the tooth surface is larger than that of the gear when it is withdrawn from engagement,and the meshing force fluctuates greatly.The frictional force and dynamic meshing force of the herringbone gear tooth surface are relatively stable,and the fluctuation amplitude is much smaller than that of the spur gear.The amplitude of the bearing vibration is not affected by the friction,but the friction has a certain influence on the bearing force of the output shaft.The first order natural frequency of the split stage and the power confluence stage has a large influence on the vibration of the bearing force.In general,the natural frequency of the power confluence stage has a large proportion of influence.
