Design And Research Of Positive And Negative Stiffness Parallel Vibration Isolation System

Based on the research of the National Natural Science Foundation of China's "Energy Damping Control System for Flexible Parallel Precision Positioning Platform Based on Energy Characteristics" and the quasi-zero stiffness vibration isolation at home and abroad,it is difficult to meet the requirements of general linear isolators in low frequency and ultra low frequency.With good vibration isolation characteristics and wide vibration isolation frequency,a variable load positive and negative stiffness parallel vibration isolator based on quasi-zero stiffness is proposed and designed.Based on the approximate analytical method and numerical method of nonlinear vibration,the static characteristics of the designed quasi-zero stiffness isolator and the dynamic characteristics and vibration isolation performance of the quasi-zero stiffness isolator system are studied.The transmission rate characteristics of the vibration isolation system under light load and overload conditions and the change of load carrying capacity are explored respectively.The validity and correctness of the theory are verified by simulation.The main work and conclusions are as follows:The mathematical model of the positive and negative stiffness parallel vibration isolation system is established by the influence of the tilting spring negative stiffness structure and the vertical spring positive stiffness structure in the system.Firstly,through the study of static characteristics,the expressions of the restoring force and stiffness of the negative stiffness mechanism and the positive stiffness spring are established respectively.Secondly,the system structural parameters and the influence of the sliding rod displacement on the dimensionless force and stiffness of the system are discussed.Finally,Taylor is used.The expansion type approximates the force and stiffness.The results show that the geometrical parameters of the mechanism(the cosine of the horizontal plane when the tilting spring is in the uncompressed state)play an important role,and at this time,the vibration isolation frequency of the system reaches the maximum and the vibration isolation effect is the best.In the case of adjusting the displacement of the slider,the dimension of the dimensionless stiffness is-0.4~0.42,which has a smaller natural frequency and better low-frequency vibration isolation performance.Based on the dynamic characteristics of the system under quasi-zero stiffness state,the dynamic characteristics of the system under harmonic force and harmonic displacement excitation are analyzed.The nonlinear differential equation of the system is established.The steady state method is used to solve the steady state of the system.The equation is used to analyze the influence of excitation amplitude,damping ratio and nonlinear term on the system's frequency response curve.The stability criterion boundary condition of the steady state response of the system is obtained by Mathieu method.The research results show that the vibration isolation system is a nonlinear system with stiff stiffness,and there are unstable regions and jumping phenomena.By reducing the excitation amplitude and nonlinearity or increasing the damping ratio,the unstable region of the system and the vibration isolation starting frequency can be reduced.Combined with the practical considerations of the light load and overload conditions that are easy to appear in the actual application,the nonlinear motion differential equations of the light load and overload systems under harmonic excitation and harmonic displacement excitation are established through the study of dynamic characteristics.The approximate solution of the steady-state response of the overload system is obtained by the harmonic balance method.The effects of the offset displacement and the excitation amplitude on the frequency response curve and vibration isolation performance of the overload system are studied and compared with the ideal system.The results show that with the increase of the excitation amplitude,the stiffness characteristics of the overload system change continuously,which is linear,soft,and hard.The smaller the offset displacement and the excitation amplitude,the smaller the vibration isolation starting frequency of the overload system and the larger the vibration isolation frequency range.By adjusting the initial angle of the negative stiffness mechanism,the overall stiffness at the equilibrium position of the system is changed,and the same load under the load and overload conditions is analyzed.Compared with the transmission rate curve of the overload system,it is found that the overall stiffness of the system is adjusted.After that,under the condition of small excitation amplitude,the system transfer rate at this time is obviously better than the system transfer rate under overload condition,which further validates the effectiveness of the positive and negative stiffness parallel vibration isolation system for variable load low-frequency vibration isolation.Finally,the fourth-order Runge-Kutta method is used to simulate the positivenegative stiffness parallel vibration isolation system.The system is in the quasi-zero stiffness state,under the light overload condition and after adjusting the inclined guide mechanism,under the same load.The response curve and the result are compared with the linear system,indicating that the positive and negative stiffness parallel isolators have excellent performance of low frequency vibration isolation and load rejection with respect to the linear isolator and the quasi-zero stiffness isolator.