Study Research On Vibration Characteristics Of Complex Shaft Systems Based On Finite Element Method

The rotor-bearing system is one of the main components of rotating machinery,which is widely used in various fields of life and production.There is an urgent need to assure the safe and stable functioning of rotor-bearing systems in various industries,given the rapid development of large-scale machinery manufacturing and the upgrading of safety equipment specifications.The critical speed is an important reference indicator to assess when the rotor system has reached resonance,which is usually one of the main factors impacting stable operation.Therefore,the rotor-bearing system needs to be thoroughly studied and effectively analyzed,and the finite element method（FEM）is one of the more effective methods to study the vibration problems of rotating machinery.The generalized coordinate system and rotor coordinate system are established based on rotor dynamics theory,and the local coordinate system is expanded to the global coordinate system via coordinate transformation to construct the coordinate vector of any point,as well as the velocity vector and acceleration vector of that point,and the kinetic energy and potential energy of the rotor system are expressed.By introducing the equations of kinetic energy and potential energy into the Lagrange equation,the energy equations of the rotor-bearing system are obtained,and the total mass matrix,total stiffness matrix,and total gyroscopic matrix of the rotor are obtained,respectively.Combining the bearing stiffness matrix and considering the excitation matrix constructed by parametric excitation,the vibration differential equations of the specific rotor-bearing system are finally determined.For the mechanical characteristics of variable-section beams,the FEM is applied to derive the coefficient matrices of the bending-torsional-axial vibration of the variable-section shaft system and the geometric matrix constructed by the axial load,and the differential equations of motion of the variable-section shaft system as a whole are constructed by combining the bearing characteristics,assuming the Timoshenko beam theoretical model.The frequencies of singlestage and multi-stage beams under different boundary conditions are investigated separately,thus verifying the validity of the method.The analysis idea of rotating shaft system is proposed,and the vibration characteristics of rotating variable-section shaft system and rotating stepped shaft system are analyzed and compared,and the vibration diagram of the shaft system under different axial loads is studied,and the unbalanced response characteristics of the rotating shaft system are obtained.According to the geometric characteristics of the simplified model of the cross-shaft universal joint,we derive the transmission relationship equations of the transmission input angle versus output angle,acceleration and output torque.Furthermore,we analyze the dynamic characteristics of the transmission at a certain installation angle through numerical programming,and then study the modal analysis of the transmission tandem variable-section shaft system.The results can be used to guide the design of the arrangement of the variable-section shaft system for the output angle.This provides a new idea for the subsequent parametric excitation response analysis of large-parameter,multi-span shaft systems.