Nonlinear Dynamics And Performance Optimization Of Two Degree-of-freedom Vibration Isolation System With Quasi-zero Stiffness

Owing to the rapid development of industrial technology,the demands for the load capacity,machining accuracy and operational stability of mechanical devices are improved gradually.It’s also more urgent and important for the vibration control of mechanical equipment.Considering the traditional linear vibration isolation system which has disadvantages in low frequency vibration isolation performance in the field of precision machinery and shipboard equipment,based on the anti-resonance characteristics of the multi-degree of freedom system,the research work concerning on two degree-of-freedom(DOF)quasi-zero stiffness(QZS)nonlinear dynamics and performance optimization of isolation system is conducted so that the vibration isolation performance is able to be further enhanced.It mainly includes the establishment of dynamic model,static characteristics analysis,dynamic characteristics,vibration isolation performance analysis and experimental research of the two DOF QZS vibration isolator.The main research contents are as follows:(1)Establishment of dynamic model and static characteristics analysis of the two DOF QZS vibration isolation system.A negative stiffness structure which contains nonlinear inclined springs is respectively introduced into the upper and lower layers of the traditional linear vibration isolation system to form a two DOF QZS vibration isolator.The effect of nonlinear transverse damping is also considered.First,through the static characteristic analysis,the relation between the parameters of the system is derived on the premise that the system meets the QZS condition.In order to explore the optimal combination of structural and mechanical parameters,the impacts of parameters on the system stiffness characteristics are studied.Taylor series is used to expand the expression of the restoring force,and the approximate expression is obtained.The error between the approximate and exact expression is analyzed quantitatively,and the result shows that the error rate is less than 0.53% in a small displacement range.(2)Nonlinear dynamic characteristics of the system.The nonlinear dynamic equations are established respectively,and the dynamic characteristics are discussed under the excitation of harmonic force and displacement.Harmonic balance method is adopted to achieve the dynamic equation expression.Combined with numerical analysis method,the dynamic response characteristics under different vertical damping ratio,transverse damping ratio,vertical stiffness ratio,mass ratio,force excitation amplitude and displacement excitation amplitude are analyzed.(3)Analysis and optimization of vibration isolation performance of the system.Assuming that the force and displacement transmissibility are taken as the evaluation indexes of the vibration isolation performance,the influences of vertical damping ratio,transverse damping ratio,vertical stiffness ratio,mass ratio,force excitation amplitude and displacement excitation amplitude on the vibration isolation performance are discussed.What’s more,the vibration isolation performance is specially compared with single DOF system with QZS,two DOF QZS isolation system with the linear inclined springs and two DOF QZS isolation system with the upper linear oblique spring and lower nonlinear oblique spring.The optimal combinations of parameters are sought so as to further optimize the vibration isolation performance.(4)Experimental study on the two DOF QZS isolator model.The physical model of the two DOF QZS isolator is designed,and the experimental platform is set up,which mainly includes the excitation system,the vibration isolation system and the signal acquisition and processing system.The response acceleration and acceleration transmissibility of the system are analyzed by frequency sweep experiment,fixed frequency experiment and impact experiment.The results show that the initial vibration isolation frequency decreases with the diminution of the excitation acceleration,which leads to the broadening of the low frequency vibration isolation band.It is feasible to ignore the higher harmonic term when utilizing the harmonic balance method to solve the equation.The excitation acceleration and pulse width have great effects on the vibration isolation and cushioning performance.