Study On Dynamic Modeling And Dynamic Characteristics Of Herringbone Gear And Power-split Transmission System

The herringbone gear and power-split transmission are widely used in the high speed and heavy load transmission system,especially in the aviation,vessel and rolling industry.With the development of the aviation and vessel technology in the past few years,vibration and noise analysis of gears transmission system were facing more stringent requirements.Accordingly,carrying out the dynamic characteristic research of the herringbone gear and power-split transmission will provide theoretical basis,and has an important application value for the design and research of the high power density drive for our country in the future.This paper studied on dynamic modeling,inherent property analysis,dynamic equation solving,linear and nonlinear vibration characteristics analysis,and vibration test of the herringbone gear transmission.The main focuses and innovations of this paper are summarized as follows:1.Dynamic modeling methods of the herringbone gear and power-split transmission were proposed,and the linear time-varying and nonlinear time-varying dynamic equations of the herringbone gear and power-split transmission were deduced.The herringbone gear was divided into two helical gears whose helix angles were in the opposite directions and the connecting shaft.The connecting shaft of the herringbone gear was deemed as Timoshenko-type beam elements,which couple with the bilateral nodes created by the lumped-mass method.Based on of this,the bending-torsion-axial-swing coupling dynamic model of herringbone gear pair was established.And then,the bending-torsion-axial-swing coupling dynamic equations of herringbone gear power-split transmission can be educed according to the structural features of the power-split transmission.The modeling method can be extended to different forms of herringbone gear transmission systems.The torsion dynamic models and equations of the herringbone gear and power-split transmission were presented.2.The linear time-varying dynamical characteristics of bending-torsion-axial-swing coupling dynamic model of the herringbone gear transmission,and the torsional nonlinear dynamical characteristics of the herringbone gear transmission were studied.The linear time-varying dynamic equations of the herringbone gear transmission which consider the time-varying mesh stiffness,the time-varying support stiffness,and the static transmission error were solved by using Runge-Kutta method under different input rotating speeds and input torque.The torsional nonlinear time-varying dynamic equations which considering the time-varying mesh stiffness,the time-varying support stiffness,the static transmission error and the backlash were solved by using incremental harmonic balance method(IHB).In order to settle the matters of that the initial iteration value of traditional IHB is difficult to choosed,and traditional IHB cannot operate continuously at the singular points of nonlinear dynamic response curve,an modified IHB algorithm was improved by using improved backlash piecewise function,the extrapolation algorithm and arclength continuation algorithm.Finally,the high efficiency of the modified IHB is verified by comparing the modified IHB and the traditional IHB.3.The inherent characteristic of the herringbone gear power-split transmission torsion dynamic model was analyzed,and then the mode transition and natural frequency sensitivity of the transmission system were studied.The torsion free vibration differential equations were deduced from the herringbone gear power-split transmission torsion dynamic mode,and the natural frequencies and modal shapes were solved.And then,by means of the summary of the natural frequencies and modal shapes from the herringbone gear power-split transmission under a variety of dynamic parameters,the mode shapes of free torsional vibration were categorized to two categories: the branch vibration mode and the coupled mode.At last,the mode transition and natural frequency sensitivity of the torsional vibration of the herringbone gear power-split transmission were studied,and the results showed that the inherent characteristic changed following the dynamic parameter from the perspective of mode energy.4.The dynamic characteristics of bending-torsion-axial-swing coupling dynamic equations of the herringbone gear power-split transmission were analyzed.The linear time-varying dynamic equations of the herringbone gear power-split transmission were derived which consider the time-varying mesh stiffness,the time-varying support stiffness and the static transmission error.After eliminating the rigid body displacement and dimensional normalization,the dynamic equations were solved by using Runge-Kutta method.The effects and mapping relationships of the dynamic parameters,such as the separate angle,the support stiffness,the average mesh stiffness,the torsional stiffness and the static transmission error,to the herringbone gear power-split transmission dynamic characteristics were revealed.5.The dynamic characteristic experiments of the herringbone gear transmission were carried on.A gear vibration test rig of closed power circuit was founded for the in-depth experimental measurements and model validation.The dynamic responses were tested under a series of operating conditions of rotating speeds and input torques,and then the dynamic load coefficients were calculated.By comparing the theoretical dynamic load coefficients acquired through the Timoshenko-type beam elements model with the experimental dynamic load coefficients,the Timoshenko-type beam elements modeling method of the herringbone gear proposed in this paper were verified.