| Gear system is widely used in mechanical equipment because of its compact structure,high efficiency and constant transmission ratio.The bifurcation,tooth surface meshing impact and non-meshing of gear transmission system with clearance seriously affect the motion stability of the system,fatigue life and reliability.The internal relation and transfer law among the bifurcation of the dynamical system,tooth surface meshing impact,non-meshing and dynamic load are studied,which has important engineering value and scientific significance for reducing the vibration and noise,and prolonging the operation life of mechanical equipment.In this dissertation,the dimensionless dynamic model of spur gear pair,3-DOF single-stage gear transmission system and multi-stage mixed gear transmission system with planetary are established with considering the nonlinear factors such as tooth backlash and time-varying mesh stiffness.The dynamics characteristics of gear transmission system such as the bifurcation of tooth surface meshing impact and periodic motion,the coexistence of periodic attractor,frequency response characteristics and periodic motion stability are analyzed by CPNF method and harmonic balance method.The correlation matching mechanism and transfer law of the bifurcation,tooth surface non-meshing,tooth back meshing and dynamic load characteristics of the 3-DOF gear transmission system are clarified.The dynamic characteristics of multi-stage mixed gear system under multi-frequency excitation are analyzed by Runge-Kutta numerical simulation.The improved OGY control theory is used to study the chaos control method of high-dimensional gear transmission system.The research results provide a theoretical basis for the reasonable parameter matching for the design.of gear structure.The main contents are as follows.Firstly,an improved CPNF algorithm is proposed for tracking and determining the stability of periodic motion in piecewise smooth dynamical system based on the pseudo-fixed point method.The numerical ansysis of the stability of periodic motion for the gear transmission system with clearance is realized with CPNF method.The OGY control algorithm is improved to realize the chaos control of 3-DOF single-stage gear system.Based on the improved harmonic balance method,the numerical calculation of frequency response characteristics of 3-DOF single-stage gear system and multi-stage mixed gear system are realized.The torsional vibration dynamics model of a 1-DOF gear pair is established by considering the excitation factors such as time-varying meshing stiffness,backlash,damping,comprehensive error and so on.In two-parameter plane with speed parameter,the transfer law of the bifurcation characteristics of the tooth surface meshing impact and periodic motion and the correlation between the bifurcation characteristics and the tooth surface non-meshing,tooth back meshing and dynamic load coefficient of the system are analyzed by several tools such as Poincaré map,bifurcation diagram of the tooth surface meshing impact and periodic motion,FFT spectrum,displacements-time map and bifurcation map,etc.The parameter matching rule of the system is obtained.The tooth surface meshing impact,the periodic bifurcation and vibration strength stability of the system are analyzed.In the global parameter space,the cell mapping theory is used to analyze the transition law of saddle-node bifuraction,doubling periodic bifuraction and grazing ammplitude jump bifurcation,the coextistence of multi-periodic attractor and the stability of periodic motion attractor domain.Based on the H.Blok flash temperature theory and Hertz contact theory,the quantitative relationship between tooth surface flash temperature and nonlinear excitation parameters are studied.The dynamics model of single-stage spur gear pair with tooth surface flash temperature is established,and the effects of tooth surface flash temperature on system bifurcation,tooth surface meshing impact,tooth surface non-meshing and tooth back meshing are analyzed.A 3-DOF single-stage spur gear transmission system with bearing support clearance,tooth backlash,time-varying meshing stiffness and other factors studied,CPNF method is used to analyze periodic motion stability of the doubling periodic bifurcation,Hopf bifurcation and saddle bifurcation of the system.The coexistence of attractors during stable and unstable periods are obtained and the way of entering chaotic motion is predicted.The correlation mechanism and transfer law between the bifurcation of tooth surface meshing impact and periodic motion,tooth non-meshing,tooth back meshing and load coefficient of the system are analyzed.The improved OGY control algorithm is used to control the chaotic motion of the system periodically and good control effect is obtained.Based on the improved 1-order harmonic balance method and quasi-arc continuation algorithm,the effects of dynamic parameters on the multi-value solution,jump characteristics for the system’s amplitude-frequency are obtained.So,the frequency response characteristics transition law and the two-parameter correlation law of single periodic motion and non-impact state are found in the two-parameter plane.A dynamics model of multi-stage mixed gear transmission system composed of planetary train and two-stage fixed axle gear train,which including time-varying meshing stiffness,damping,multi-backlash strong nonlinearity,joint shaft torsion,comprehensive transmission error,multi-meshing-frequency excitation etc.,is established.The influence of nonlinear parameters such as backlash,time-varying meshing stiffness,damping,torsional stiffness of joint shaft and so on for the bifurcation of tooth surface meshing impact and periodic motion,non-meshing duty cycle ratio and tooth back meshing ratio of different gear meshing transmission is analyzed by Runge-Kutta method.As a result,it is found that the bifurcation of tooth surface meshing impact and periodic motion,non-meshing duty ratio and tooth back contact ratio are out of sync in the system.In addition to clearance,time-varying mesh stiffness and damping factors,the torsional stiffness of the connecting shaft and multi-frequency excitation also have important influences on the dynamics characteristics of the system.The influence of system parameters on the amplitude jump and multi-value of the displacement response of the mixed gear train system are analyzed by using the multi-fundamental harmonic balance method.It is found that the nonlinear jump is the strongest in planetary gear system with multi-clearance and the torsion response of the connecting shaft also shows the nonlinear jump due to the influence of tooth meshing backlash in mixed gear system.The study finds that the pseudo-color map can clearly outline the transition law and parameter correlation relation of the dynamics characteristics in the two-parameter plane.The bifurcation characteristics of the gear systems tooth surface meshing impact and periodic motion are mainly affected by parameters such as rotational speed,backlash,time-varying stiffness and flash temperature.The periodic motion and tooth surface meshing impact transfer law are the main factors which affect the tooth non-meshing duty ratio,back contact ratio and dynamic load coefficient.The dynamics characteristics reaches the extreme value in the parameter space of multi-period,quasi-period and chaotic motion.The bifurcation,tooth surface meshing impact and non-meshing characteristics of the multi-stage mixed gear transmission system are more complicated than those of the single-stage gear due to the multi-frequency and multi-clearance nonlinearity.Multi-meshing frequency excitation leads to the characteristics of bifurcation,tooth non-meshing and tooth surface meshing impact of all levels of gear transmission are not synchronous.The smaller the rigidity of the connecting shafts is,the stronger the inhibition of the nonlinear characteristics of the front stage gear transmission is.The amplitude-frequency characteristics of multi-stage gear transmission indicate that the nonlinear amplitude-jump characteristics of planetary gear train are stronger than that of fixed shaft gear train,and the response of connecting shaft is nearly linear.The results of the study on the transition law and the correlation relation of system dynamics parameters have certain reference value and theoretical significance for the selection of gear design parameters and structural optimization. |
PDF Full Text Request