Elastic Dynamics Model And Analysis Of A Gear-Rotor-Bearing System With Tooth Friction

Nowadays,with the rapid rise of new energy automobile,the opening of low-altitude flying area and the rapid increase of high speed rail,the demand for high performance gear drives grows sharply.Gear vibration becomes one of the most important factors restricting the development of high-performance gear in China,beacause it does not match with the high comfort that people pursues increasingly and also shortens the service life of gear drives.Lubrication is a principal means to reduce the friction and wear and improve the dynamic performance.Lubrication failure leads to the large friction and serve wear of meshing teeth,which increases the gear backlash and profile error,and even causes degradation of gear service performance and accelerates gear failure.It has important theoretical significance and application value to investigate the interaction between gear dynamics and tribology.An elastic dynamics model for the gear-rotor-bearing system was established in this work by considering the flexibility of the gear shaft,gyroscopic effect of the rotor,the dynamic supporting stiffness of the bearing and the internal excitations like backlash,modification and time-varying mesh stiffness.The dynamics and tribology of gear drives were studied by coupling the gear dynamics and elastohydrodynamic lubrication(EHL)theory.The tribo-dynamic performance of the gear-rotor-bearing system under dry running condition was analyzed by considering the surface wear and the thermal deformation at high temperature.It is expected that these works can be of benefit to the design of vibration and noise reduction and lubrication system in gear drives,and also be important references in extending the service life of gears and decreasing the power loss of drives.The primary research contents and important conclusions are summarized as follows.1.An elastic dynamics model for the gear-rotor system was established based on finite element method,which was implemented and experimentally verified in a valve train system.The dynamics equation of flexible shaft element was derived by combining pure torsional shaft,tension-compression bar with Timoshenko beam.In this model,the flexible shaft,gear contact model and rotor dynamic model were included.The presented method was applied in a valve train system which consists of a gear drive,cam and link mechanism to verify its validity.A coordinate compatible matrix was built to pick up the necessary degree-of-freedom,which can made the flexible shaft element be applied to the beam,shaft and bar,and the composite structure including them.Then,a test rig of the valve train system was established,and the dynamic stresses of pushrod and the vibration of engine box were measured.The proposed model was verified by comparing the predicted stress and vibration with the measured ones.2.An elastic dynamics model for the gear-rotor-bearing system was established by introducing varying supporting stiffness of bearing.The dynamic supporting stiffness of the deep groove ball bearing was calculated by considering the inertial force and gyroscopic couple of rolling balls.According to the proposed model,the effect of the varying supporting stiffness on the natural frequency and dynamic transmission error(DTE)of this system were analyzed.Both bearing stiffness and gyroscopic effect result in that the natural frequency of the system in forward whirling increases with the rise in the rotation speed.However,the bearing stiffness weakened the effect of backward whirling on natural frequency.The bearing supporting stiffness has negligible effect on DTE of the gear system at middle-and low-speed,but significantly affect the DTE at high-speed.The bifurcation behaviors of the gear-rotor-bearing system with constant and varying supporting stiffness were investigated.The model with two kinds of the supporting stiffness predicted different bifurcation behaviors at high-speed,which results in the considerable difference of the DTE at high-speed.3.The Time-varying mesh stiffness model including oil film stiffness and the elastic tribo-dynamics model for the gear-rotor-bearing system were proposed via coupling the gear dynamics with EHL theory in line contact.The gearbox vibration was measured and the validity of the proposed model was verified by an electrical feedback gear test rig.According to the proposed model,the effect of the lubrication on the mesh stiffness and load distributing factor between teeth was analyzed,and the interaction between gear dynamics and tribology was investigated.The oil film increases the contact area between meshing teeth,thereby intensifying the mesh stiffness,and the mesh stiffness under EHL decreases with an increase in the rotation speed.However,the oil film has negligible influence on the load distributing factor between teeth.Gear vibration leads to the fluctuation of the pressure,thickness,and friction force of oil film,and the amplitude of the fluctuation becomes large with an increase in the rotation speed.In addition,the gyroscopic effect of the rotors and the flexibility of the shaft and bearing obviously affect the DTE,especially at high speed.4.An elastic tribo-dynamics model for the gear drives with modification were proposed under EHL in point contact.The Time-varying mesh stiffness model with tooth modification was established.By coupling the gear dynamics with thermal EHL theory in point contact,the effects of the rotation speed and modification on the mesh stiffness,load distributing factor,tribo-dynamic property were investigated.The profile modification can mitigate the jumping of mesh stiffness caused by the changes of number of teeth pairs.However,unreasonable modification leads to nonuniform distribution of load between teeth,thereby weakening the load capacity of gear.The pressure and temperature rise of oil film becomes large with an increase in the rotation speed,and the profile modification also considerably affect the pressure,thickness and temperature of oil film.The friction coefficient between teeth decreases obviously with a rise of the rotation speed.The friction coefficient generates drastic fluctuation due to gear vibration,but the profile modification has little effect on it.The modification can avoid the meshing teeth separation or back-side contact in a certain range of speed.However,inappropriate modification can also cause subharmonic vibration at high speed,thereby aggravating gear vibration.5.As for the gear-rotor-bearing system under dry running condition,the friction coefficient between meshing teeth was predicted based on a computational inverse technique,and an elastic tribo-dynamics model considering thermal deformation and wear between tooth surfaces was proposed.In this model,the nonuniform temperature field of the system under steady state was predicted by using thermal resistance network method,and the thermal deformation of gear profile was further obtained in the predicted temperature filed.The wear on teeth surfaces was calculated by applying Archard's wear equation.Combining the wear and thermal deformation,the tribological and dynamic properties of the gear-rotor-bearing system under dry running condition were investigated.The gear friction coefficient under dry running condition is three times as large as that under EHL.Due to the loss of antifriction and refrigerant effects,the friction heat increases and heat dissipation becomes bad,thereby leading to a large temperature rise at high speed.Likewise,the wear depth on tooth surfaces generates fluctuation at middle and low high speed because of the gear vibration.However,the discontinuous wear occurs on tooth surfaces at high speed due to the meshing teeth separation and back-side contact.The vibration of the gear-rotor-bearing system becomes large with the continued accumulation of tooth wear.The drastic vibration further aggravates the tooth wear,thereby accelerating the degeneration of dynamic performance of the system.In conclusion,this paper studied the tribo-dynamic property of the gear-rotor-bearing system under EHL and dry running condition,by coupling the EHL theory and gear dynamics.According to the presented method,the coupling mechanism between gear dynamics and tribology was studied preliminarily.These research methods and conclusions can provide important reference in the integrated design of gear dynamics and tribology,and also be of benefit to the optimization of gear vibration and lubrication performance.