Nonlinear Vibration Characteristics Of Eccentric Rotor-bearing System Under Unbalanced Magnetic Pull

Rotor-bearing systems is often subjected to a variety of non-linear forces,including unbalanced magnetic pull and non-linear oil film.These non-linear forces are coupled with each other,which seriously affects the vibration characteristics of the system.In the manufacturing pr ocess of rotor,due to the existence of errors,mass eccentricity(dynamic eccentricity)often exists in the systems.As two basic vibration forms of the system,bending vibration and torsional vibration will interact with each other under the premise of the mass eccentricity,which makes the rotor-bearing system show complex nonlinear dynamic response.Especially when the static eccentricity is considered simultaneously,that is to say,nonlinear dynamic behavior of rotor-bearing system will become more complex under the condition of mixed air-gap eccentricity.In order to analyze the bending vibration characteristics and the bending-torsion coupling vibration characteristics of rotor-bearing system under unbalanced magnetic pull at dynam,ic eccentricity and mixed eccentricity,the dynamic models and differential equations of system are established in this paper.The higher order Runge-Kutta method is selected to solve the differential equation,and the bifurcation diagram,cascade spectrum,time history,phase portrait,Poincare section and power spectrum under different variables of rotor are obtained.The bending vibration characteristics and the bending-torsion coupling vibration characteristics under dynamic eccentricity and mixed eccentricity are analyzed synthetically by using the above-mentioned vibration characteristic charts of the rotor.The main research contents and results are as follows:(1)Based on the non-linear relationship between mass eccentricity,static eccentricity and unbalanced magnetic pull,electromagnetic torque,the non-linear analytical expressions of unbalanced magnetic pull and electromagnetic torque of the system under dynamic eccentricity and mixed eccentricity of air gap are deduced in detail by energy method.At the same time,the system is established under the above two unbalanced magnetic pull force models.Dynamic model and differential equation of motion(2)The bending vibration characteristics and the bending-torsion coupling vibration characteristics of system under the dynamic eccentricity of air gap are studied.The effects of rotational speed,mass eccentricity and electromagnetic stiffness on the nonlinear vibration characteristics of the system are analyzed.The analysis results show that the existence of electromagnetic stiffness is beneficial to the stable operation of system in the low and middle speed region without considering the bending-torsion coupling motion.In the process of mass eccentricity change,the system presents the alternating motion law of doubling periodic motion and quasi-periodic motion,and with the increase of mass eccentricity,bending amplitude increases gradually;after considering the bending-torsion coupling motion,system appears chaotic motion,and mainly occurs in the high-speed region(3)In view of the existence of mass eccentricity and static eccentricity,the fourth-order Runge-Kutta method is used to solve the differential equation at mixed eccentricity.The bending vibration characteristics and the bending-torsion coupling vibration characteristics with mixed air-gap eccentricity are analyzed by numerical simulation.The effects of rotational speed,mass eccentricity,static eccentricity,static eccentricity angle and electromagnetic stiffness on the vibration characteristics of system are analyzed.The results show that the magnitude of the static eccentricity and the angle between the static eccentricity and the gravity direction of rotor have significant influence on the nonlinear vibration characteristics of system.When the static eccentricity direction coincides with the gravity direction of the rotor,the vibration is strengthened,and the safe and stable operation of system is threatened.With the increasing of the angle between the static eccentricity and the gravity of rotor,the strengthening effect is weakened gradually.The system tends to run steadily.(4)Aiming at the bending-torsion coupling motion of the system,the influence of electromagnetic stiffness on the non-linear vibration characteristics is analyzed.The results show that the bending electromagnetic stiffness has a great influence on the bending amplitude,and has little effect on the torsional amplitude,while the torsional electromagnetic stiffness has little effect on the bending amplitude,but has a significant effect on the torsional amplitude,making its amplitude increase obviously.When the two kinds of electromagnetic stiffness exist at the same time,the bending-torsion coupling becomes strongerIn summary,the non-linear vibration characteristics of rotor-bearing system under unbalanced magnetic tension are analyzed in this paper.The conclusions can provide a theoretical basis for the fault mechanism and vibration control of the rotating machinery shafting,and provide a new reference for its optimal design.