Nonlinear Dynamic Analysis Of A Planetary Gear Train Including Tooth Friction

Tooth surface friction is a key and complex factors influencing on the the vibration and noise in planetary gear transmission system.Hence,it is necessary to study the tooth friction between the gear meshing pairs in the planetary gear system.Above all,a new transverse-torsional nonlinear model is established by taking account of the tooth friction,time-varying meshing stiffness,backlash,damping and transmission error.Then stability state response of the model are solved by the four-stage Runge-kutta method,and further investigated the influence of the gear tooth friction on the stability state response.Furthermore,the parameter influence comparison analysis is studied including tooth friction and no including.Firstly,the detail mathematical descriptions of the time-varying meshing stiffness,transmission errors,backlashes and tooth surface friction in the planetary gear system is completed,then established a transverse-torsional nonlinear dynamics mathematical equations of planetary gear train by the lumped parameter method base on the Newton's second law.Secondly,the identical dimensionless is carried out for the equations and solved by four-stage Runge-kutta method,and the stability response of the sun,carrier and ring are investigated by numerical method,and the influence of the gear tooth friction on the stability state response are further investigated.The studies indicated that the response is tooth frictionFinally,the effects of the tooth friction on the nonlinear dynamics characteristic based on the model were studied,and the influence of the mesh frequency,damping and backlashes on the nonlinear dynamics are investigated and the comparison analysis of the situation with tooth friction and without friction ar e studied.Afterwards,the effects of the time-varying meshing stiffness and the transmission errors on the nonlinear dynamics are investigated.The tooth friction changed the boundary conditions from chaos state to the period state under the mesh frequency,the mesh damping and the backlashes parameters induced.The studies indicated that the nonlinear response from periodic state to chaos state by the tooth friction coefficient increasing.