Calculation Of Mesh Stiffness With Root Crack And Bearing Stiffness And Dynamic Simulation Of Gear System

The gear system is widely used in engineering as a typical power transmission mechanism.The vibration of the gears affects the bearing characteristics as well as the dynamic characteristics of the whole gear system.During the actual mesh process of the gear pair,the tooth contact positions of the pinion and gear teeth change with time,and the mesh stiffness of the gear pair changes with time as the single and double teeth of the gear pair mesh alternately.The change of mesh stiffness will cause the loaded gear to vibrate,and the bearing will be affected by the gear vibration,resulting in a change in the contact conditions between the rolling element and the raceway,which in turn leads to a periodic change in the bearing stiffness.Bearing is an indispensable component in gear transmission,its role is to support the gear shaft and avoid large vibration caused by direct contact between the shaft and the case of the gear system,therefore,bearing plays an important role in the gear system.Tooth root crack is a relatively common gear failure,because the gear is extremely complex structure and often in complex and harsh working conditions,which greatly increases the chances of gear failure and in turn leads to the failure of the transmission system of mechanical equipment.Therefore,how to effectively and accurately calculate the mesh stiffness and bearing stiffness of healthy gears and faulty gears with root cracks is of great significance to the study of gear fault identification and diagnosis.The dynamic characteristics of the gear system are investigated with the spur gear pair and the rolling bearing in this paper.Based on the consideration of the overall coupling effect between the gear body and gear teeth,the effect of cracks on the gear body and gear teeth,and the offset of bearing inner ring center due to gear vibration,an analytical model of mesh stiffness of healthy gears and faulty gears with tooth root cracks and an analytical model of rolling bearing stiffness are established,and the dynamic characteristics under the action of mesh stiffness excitation and bearing stiffness excitation are discussed.The main research contents of this paper are as follows:(1)Based on the traditional potential energy method,the formula for calculating the mesh stiffness of gear pairs of healthy gears and gears with root crack defects considering the effect of the overall coupling effect between the gear body and gear teeth and the effect of cracks on the gear body and gear teeth is derived,and the accuracy of the method is verified by the finite element method.The effects of different crack depths,crack inclination angles and the angle between the tangent line of the crack initiation position and the center line of the gear teeth on the mesh stiffness of gear pairs are studied based on this analytical model.(2)The improved calculation method of the contact deformation of the rolling bearing considering the influence of the inner ring center offset is proposed in this paper based on the Hertzian contact theory considering that the vibration of the gear system will lead to the influence of the inner ring center offset on the contact deformation of the rolling bearing,and the time-varying bearing stiffness considering the influence of the inner ring center offset is obtained by this method,and compared with the bearing stiffness obtained by the traditional method.(3)The key parameters of dynamic mesh force,mesh damping,friction force and friction arm of the dynamics model are derived,and a 6-DOF dynamics model of the spur gear pair is established by considering the mutual coupling of time-varying mesh stiffness and time-varying bearing stiffness as well as the influence of tooth surface friction.(4)The effects of rotational speed,single-tooth and multi-tooth cracking on the dynamics characteristics of the gear system and the effects of bearing clearance and number of rolling elements on bearing stiffness are investigated based on the 6-DOF dynamics model considering the mutual coupling of time-varying mesh stiffness and time-varying bearing stiffness as well as the effect of tooth surface friction.The effect of time-varying bearing stiffness on the vibration characteristics of the gear system is analyzed considering that the bearing stiffness is influenced by the vibration of the gear system and the number of rolling elements.