Modeling And Dynamic Characteristics Of Two Stage Transmission Split Torque-combine Power On Gear System

With the advantages of high reduction ratio,less gear series,high reliability and low noise,the two-stage transmission split torque parallel gear system has a wide application prospect in the transmission system of aviation and ships.The free vibration characteristics and nonlinear characteristics of the two-stage transmission split torsion parallel gear transmission system are studied.The research results can provide guidance for its design and manufacture,and also have important significance for its development and engineering application.Firstly,the lumped mass method is used to establish the pure torsional dynamic model of the system,in which the dynamic excitation factors such as time-varying meshing stiffness,backlash and error are considered.According to the established physical model,the dynamic model diagram with spring and damping is drawn,and the system dynamic differential equation is derived.Then,the dimension of the system dynamic differential equation is normalized,and the influence of coincidence degree on time-varying meshing is analyzed At the same time,with the help of Runge Kutta method with variable step size,the dynamic equations of the system are solved,and the dimensionless displacements of the meshing pairs are obtained.Secondly,the free vibration characteristics of the system are analyzed.By solving the free vibration equation of the undamped system,the natural frequencies and modes of the system are obtained,and the effects of meshing stiffness,torsional stiffness and base circle helix angle on the natural characteristics of the system are discussed.The results show that: on the cylindrical spur gear,with the increase of the coincidence degree,the meshing area of the two teeth is extended;the vibration displacement in the direction of meshing line is larger;there are two kinds of vibration forms in the free vibration of the system,one is that each gear in the two-stage transmission has vibration,the other is that the amplitude of the input gear and the output gear is zero;the smaller meshing stiffness will lead to the repetition frequency phenomenon The results show that the change of meshing stiffness has little effect on the amplitude of spur gear in the divided torsion stage,but obvious effect on the amplitude of helical gear in the parallel stage;the increase of torsional stiffness will increase the vibration of each gear in the two-stage transmission;the change of helix angle of base circle only makes the phase change of each mode.Finally,the dynamic meshing force and dynamic load coefficient of the system are solved;the influences of input parameters,stiffness,damping ratio,backlash and integrated transmission error on the dynamic characteristics of the system are analyzed;and the meshing vibration test design and analysis of the system’s multi-stage torsional transmission are carried out;at the same time,from the point of view of overall parameters,the multi-stage torsional transmission under the excitation of angular frequency,damping and backlash are discussed Combined with time history diagram,FFT spectrum diagram,phase diagram and Poincar é section,the dynamic response of the torsional stage under angular velocity excitation,damping ratio change and backlash excitation is analyzed.It is found that: with the increase of meshing damping ratio,the dynamic load coefficient of each meshing pair decreases;with the increase of backlash,the dynamic load coefficient of two-stage transmission presents an upward trend,in which the dynamic load coefficient of parallel stage fluctuates greatly,and too large backlash is not conducive to improving the stability of the system;when the comprehensive error increases in a certain range,the dynamic load coefficient of sub torsional stage rises slowly,The results show that when the dynamic load coefficient of the parallel stage increases,the slope is large;the torsional transmission of the system shows the alternating motion between period and chaos under the excitation of angular frequency,damping and backlash;when the angular frequency is high,the torsional transmission can still show the periodic motion,which indicates that the system can meet the working requirements of high speed;larger damping helps to improve the stability of the system;reasonable backlash can improve the stability of the system Reduce the impact of tooth surface.