Research On Nonlinear Dynamic Behavior And Vibration Characteristics Of Elastic Beam In Large Overall Rotation Considering Rotor Eccentricity Effect

With the modern application of light and flexible mechanism working speed and smoothness requirements.Large range rotating rigid-flexible coupling systems with light and flexible components have been developed.The eccentricity effect of electrically driven rotors at high speeds is becoming more and more important to the stability and accuracy of flexible machinery operation.There are different degrees of dynamic eccentricity and static eccentricity in the processing and manufacturing process of motors,and the resulting mutual coupling between mechanical unbalance forces and unbalanced magnetic tension leads to complex nonlinear dynamics response of flexible mechanisms such as intermittent or sudden vibration.In this dissertation,we explore the coupling relationship and mechanism between the rotor eccentricity effect and the nonlinear dynamic behavior of the elastic beam is applicable to the flexible mechanism of the elastic beam with large rotation,and compare and analyze the effects of dynamic and static eccentricity and dynamic and static eccentricity coupling effect on the vibration characteristics of the rotating beam at different rotational speeds,and then analyze the evolution law and complex dynamic mechanism.By means of flexible dynamics theory,the flexible dynamics model of the elastic beam is established by applying the Galerkin modal truncation method and Hamilton’s principle;and the nonlinear dynamics model of the rotor-elastic beam system under the rotor eccentricity constraint is constructed by using the rotor dynamics theory and the traveling wave superposition principle.The study of the behavior and vibration mechanism of the rotor-elastic beam system under the eccentric constraint of the rotor is carried out by the high-order Runge-Kutta method.The main research contents and results of this paper are as follows.(1)The rotor-elastic beam is used as the research object,the coupling relationship and mechanism between rotor dynamic eccentricity and vibration characteristics of rotating beam are analyzed and discussed.The results show that the dynamic eccentricity of the rotor has a strong coupling relationship with the dynamic response of the system,and the dynamic model of the system can be simplified by neglecting the static eccentricity factor under the working conditions with low accuracy requirements.In addition,with the increase of rotational speed,the dynamic eccentricity effect is more significant.When the speed goes up to 150 rad/s,the elastic beam vibration changes from periodic to non-periodic under the action of dynamic rotor eccentricity,which is also one of the main reasons for the sudden or intermittent vibration of this type of mechanism at high speed.(2)The nonlinear dynamical behavior of a large-range rotating elastic beam with rotor eccentricity constraint is studied.Based on the established kinematic differential equations of the system under the combined action of external excitation and fixed-axis rotation,the stability of the system under different operating conditions of the external excitation and the rotating beam is analyzed.The numerical simulation results show that the rotor eccentricity effect generates 1-frequency harmonic components,and the number and amplitude of the harmonics increase with the speed and gradually approach the main vibration pattern,and then the vibration rapidly changes from periodic to nonperiodic.In addition,the excitation response will further derive new low-frequency harmonic components based on the rotor eccentricity effect,when the speed and excitation amplitude increases will lead to several low-frequency harmonic components in the frequency domain higher than the main vibration,triggering intermittent vibration of different degrees.(3)The coupling mechanism between rigid and flexible coupling effects of elastic beam itself is discussed,the rotor eccentricity effect and the external excitation effect by using the time domain and frequency domain analysis strategies,and to effectively analyze the mechanism of intermittent or sudden uncertain vibration of this kind of flexible machinery.The findings of this study can provide an important theoretical basis and data support for the optimal design of the dynamics and the formulation of the vibration suppression strategy of a large range of rotating flexible machinery.