Dynamic Design And Analysis Of X-Shaped Quasi-Zero Stiffness Isolator

With the improvement of science and technology,high precision machinery’s increasing demand for micro amplitude and low frequency vibration isolation is on and on.In zero-gravity environment,the micro low frequency perturbation of the satellite,such as gyroscope rotation,attitude adjustment and solar board stretching are unfavorable,which interfere in the stability and function of the spacecraft.Ground test under gravity is a key link to verify its performance in orbit,so the isolator is necessarily able to work regardless of gravity.In order to realize low frequency vibration,reducing the stiffness of traditional linear isolators isolation will deteriorate the stability and bearing capacity of the system.In recent years,it has been a hot topic in this field to widen the vibration isolation frequency band and maintain a better bearing capacity by introducing nonlinear stiffness.There are three kinds of high static and low dynamic vibration isolators that are X-Shaped Structure,Quasi-Zero-Stiffness Structure(QZS)and Roller-Type Structure.Each of them has its unique advantages and disadvantages.The QZS is simple and the linear stiffness can be reduced to 0,but its cubic stiffness term is large.Roller-type structure can be flexibly designed to get desired nonlinear force.X-shaped structure’s relative stiffness is low but its linear stiffness is hard to offset.This dissertation focuses on inventing a new quasi-zero-stiffness isolator whose resonant frequency is in the altra-low frequency range by using a variety of nonlinear stiffness systems.The contents are as follows:An X-shaped nonlinear structure is designed,which is with linear stiffness spring(X-LS)and suitable for weightless environment.Its static and dynamic characteristic analyzed to obtain the advantages over LS.The dynamic equation of X-LS is solved by energy method after establishing the mechanical model.The frequency response of displacement transmissibility under harmonic displacement excitation is obtained by harmonic balance method,which are verified by Runge-Kutta method,and the influence of structural parameters on vibration isolation performance is studied.Runge-Kutta method is used to calculate and compare the time domain responses of systems with different parameters under shock excitation.The results show that X-LS has negative stiffness and beneficial nonlinear stiffness.Adjusting the system parameters can get a wider vibration isolation band than LS,and effectively reduce the severe vibration after impact.An X-shaped structure that is with QZS and used in zero gravity environment is designed.Its dynamic characteristic is analyzed and compared with QZS and X-LS.The static analysis on its mechanical model shows that the stiffness of the structure is asymmetric and quasi-zero.The dynamic response of the system is approximated by the harmonic balance method and verified by numerical method.Taylor expand the nonlinear terms of the dynamic equation and expand the relative displacements into the first harmonic solution.The influences of spring stiffness,spring length,spring precompression,loading angle and displacement excitation amplitude on the dynamic characteristics are compared.The research results show that the vibration isolation performance of X-QZS structure is better than that of QZS and X-LS structure under certain parameters,the resonance frequency is reduced to a lower order of magnitude,and the shock resistance is improved.The nonlinear stiffness of roller-type structure is designed to counteract the negative stiffness of X-QZS structure in gravity environment,and the response of XShaped Isolator with Quasi-Zero-Stiffness and Roller(X-QZS-R)under harmonic displacement excitation is analyzed,which is compared with the performance of X-LS in gravity environment.The design method of roller trajectory is put forward.The relationship between force and displacement is obtained through force analysis.Static analysis shows that designing trajectory can expand the quasi-zero stiffness range.The energy method and harmonic balance method are used to solve the system response under different system parameters of harmonic displacement excitation.Compared with X-LS structure,its range of quasi-zero stiffness is wider and there is no bearing capacity limitation caused by negative stiffness.The system can achieve ultra-low frequency vibration isolation that are lower than 1Hz,which is similar to XQZS.In this dissertation,a design method combining X-shaped structure and quasizero stiffness structure is proposed to achieve superior ultra-low frequency vibration isolation in a no-gravity environment,and an asymmetrical concave track roller structure is used to offset the negative stiffness of X-QZS structure in a gravity environment.It achieves better bearing capacity and wide vibration isolation band similar to the X-QZS structure in gravity free environment.The proposed new quasi zero stiffness isolator provides a new idea for the performance improvement of nonlinear isolator.