Study On Linear Complementary Dynamic Modeling And Vibration Characteristics Of Rolling Bearing Rotor System

As the important part of transmission system and the core part of rotating machinery,the rolling bearing-rotor system is widely used in high-end equipment.The rotor system vibration characteristics have profound impact on the safety and stability of high-end equipment.Therefore,it is of great significance for improving the performance of high-end equipment to study the effect of the rotor system key parameters on its vibration characteristics.In this paper,the linear complementary dynamic model of rolling bearing-rotor system and the solution method of contact constraint are established by coupling the rolling bearing and the rotor through contact constraints,which improves the computational efficiency of joint dynamics simulation.And the influence of geometrical error on the vibration characteristics of rolling bearing and rotor system is studied.The main research methods and contents are as follows:(1)The linear complementary solution method for the contact problem of rolling body and raceway is established.The dynamic motion equation of the rolling body and raceway contact vibration is derived.Newmark scheme is introduced to transform the dynamic motion equation into algebraic equation.And simple mathematical transformation is done to convert the algebraic equation into linear complementary equation.Lemke algorithm and Newton Raphson iteration algorithm are employed to solve the contact vibration of rolling body and raceway.(2)The cylindrical roller bearing and angular contact ball bearing dynamic models with considering bearing geometric error is established based on the linear complementary solution method for the contact problem.The rolling bearing geometric error is described by the gap between rolling body and raceway.Then,the bearing clearance-displacement-deformation compatibility equation was deduced.And the contact force between the rolling body and raceway can be calculated by the Hertz contact formula.According to the Newton's second law,rolling bearing dynamic motion equation is deduced.The bearing dynamic motion equation is transformed into the linear complementary equation.And the bearing nonlinear vibration is solved.(3)An joint simulation dynamic model of rotor system is established by coupling the dynamic model of rolling bearing and rotor.Based on the Lagrange energy method,the dynamic motion equation of the turntable is derived.The Timoshenko beam is used to simulate the elasticity of the shaft.And the dynamic motion equation of the shaft is obtained.Whit considering the box as rigid,the dynamic motion equation of the rolling bearing rotor system can be obtained by adding the dynamic motion equations of the bearing,the turntable and the shaft together on the corresponding degree of freedom.The system dynamic motion equation also is transformed into a linear complementary equation.And the rotor system vibration can be solved by the Lemke algorithm and Newton Raphson iterative algorithm.(4)Based on the dynamic model of rolling bearing and rotor system,the vibration characteristics of cylindrical roller bearing,angular contact ball bearing and rotor system under geometric error are simulated and analyzed.The effects of radial clearance,roller diameter error and rolling element waviness on the cylindrical roller bearing vibration characteristics is studied.And the effects of axial clearance and rolling element waviness on the vibration characteristics of angular contact ball bearing and unbalance rotor systems is investigated.The dynamic modeling method and the joint dynamic simulation model of the rolling bearing-rotor system in this paper improve the efficiency of the rotor system joint dynamic simulation,which lay a foundation for the further study of the system vibration characteristics.