Multi-state Dynamic Model And Dynamic Analysis Of Single-stage Gear Transmission System

Gear transmission system is one of the widely used transmission devices in mechanical equipment.The vibration of the gear system affects the stability,reliability and fatigue life of the machinery.Studying the mechanism of gear vibration generation and its influence factors and laws has important scientific significance and engineering value for the vibration and noise reduction of mechanical equipment and the improvement of the service life and reliability of mechanical equipment.In this paper,the single-stage spur gear transmission system is taken as the research object,taking into account factors such as time-varying stiffness,backlash,tooth surface friction,integrated transmission error,meshing damping and load distribution rate during gear meshing.From simple to complex,the multi-working states nonlinear dynamic models of single-stage gear system with ratio of contact 1 and greater than 1 are established respectively,and its nonlinear dynamic characteristics are studied.The safety domains for a single-stage gear system are established and the safety basin and safety features are studied.The main research contents are as follows:The multi-states nonlinear dynamic models of single-stage gear system with ratio of contact 1 and greater than 1 are established.The multi-working states of the gear teeth such as the tooth-surface meshing,the disengagement and the tooth-back meshing of the gear single and double tooth engagement are considered in the models.The time-varying meshing stiffness and load distribution rate of the gear pair is calculated.The nonlinear terms such as time-varying meshing stiffness and comprehensive transmission error are approximated by Fourier series,and the backlash,tooth surface friction,load distribution rate and time variation are obtained.The dynamic equation of the gear transmission system with factors such as meshing stiffness,integrated transmission error and meshing damping is obtained.According to the tooth multi-working states such as tooth-surface meshing,disengagement and tooth-back meshing when the gears are single and double tooth engagement,the judgment basis of the gear tooth multi-working states is obtained.The system is numerically solved by the fourth-order variable-step Runge-kutta method,and the influence of nonlinear factors on the dynamic behavior of the single-stage gear system is studied.The influence of different parameter changes on system dynamic characteristics and meshing states are analysised by numerical calculating system meshing force cycle change diagram,bifurcation diagram,maximum Lyapunov exponent,phase diagram and dynamic meshing force diagram with time varying.The formation process of the tooth-surface impact,tooth-back impact and the edge contact(edge collision)when entered the meshing were studied.According to the bearing capacity of the surface fatigue pitting and the broken state of the gear teeth during the gear transmission process,the normal force,the tangential force,the contact stress and the bending stress of the gear teeth change with the meshing position are calculated respectively,and the safety conditions are obtained.The safety domains of the single-stage gear system are established according to the safety conditions of the surface fatigue pitting and the broken state during gear transmission.The erosion phenomenon of the safety basin and the influence of parameters on the safety characteristics of the system with the change of parameters are studied by numerically calculating the safety basin of the single-stage gear transmission system under the change of parameters.