Design,Analysis And Testing Of A Parabolic Cam-roller Quasi-zero-stiffness Vibration Isolator

Quasi-zero-stiffness isolators are usually obtained by connecting positive and negative stiffness components in parallel,which combine high load carrying capacity with low frequency vibration isolation,and have attraced much atteneion from industry and academia.Circular cam-roller(CCR)quasi-zero-stiffness(QZS)vibration isolators have been extensively studied,but CCR QZS isolators can only achieve low stiffness in a very small range and cannot withstand excitation with large amplitude.By improving the static performance of the QZS isolator,enabling the QZS isolator is able to to provide lower stiffness in a larger displacement range,resulting in lower initial isolation frequency and peak transmissibility of the isolator.Firstly,based on the CCR QZS isolator,the parabolic cam-roller(PCR)QZS isolator was designed;then based on the PCR QZS isolator,the PCR dual quasi-zero stiffness(DQZS)isolator was proposed;finally,the optimal design of the PCR DQZS isolator was carried out,and the PCR branched quasi-zero-stiffness(BQZS)isolator was proposed.The static performance analyses of PCR QZS vibration isolator,PCR DQZS vibration isolator and PCR BQZS vibration isolator were carried out,and the dynamic performance and vibration isolation performance of PCR QZS vibration isolator and PCR BQZS vibration isolator were investigated.The main research works are as follows:(1)The static model of PCR QZS vibration isolator was developed and the static performance analysis was conducted.The parameter condition for the PCR QZS isolator to achieve zero stiffness at the static equilibrium position was obtained.The restoring force expression for the PCR QZS isolator is a cubic polynomial,which does not need to be simplified and avoid introducing unnecessary errors.The static performance of the PCR QZS isolator and the CCR QZS isolator were compared to obtain the parameter conditions that make the stiffness of the PCR QZS isolator lower than that of the CCR QZS isolator near the static equilibrium position.(2)The dynamic performances of the PCR QZS vibration isolator under harmonic force and harmonic diaplacement excitions were analyzed.The dynamic responses of the PCR QZS vibration isolator under harmonic force and harmonic displacement excitation were analyzed using the harmonic balance method and verified using the 4th order Runge-Kutta method.The effects of parabolic coefficient b,stiffness ratio a damping ratio z,and excitation amplitude on the vibration isolation performance were analyzed,and the effect of parabolic coefficient b on the load carrying capacity of the PCR QZS isolator in the QZS region for the excitation amplitude was analyzed.(3)The experimental study of PCR QZS vibration isolators.An experimental platform was built to test the static and dynamic performances of the PCR QZS vibration isolator,the CCR QZS vibration isolator and the linear vibration isolator.The experimental results verify the theoretical analysis and show that the vibration isolation performance of the proposed PCR QZS vibration isolator is much better than that of the CCR QZS vibration isolator and the corresponding linear vibration isolator.Compared with the CCR QZS isolator,the PCR QZS isolator has a lower stiffness in a wider region near the equilibrium position,and the PCR QZS also has a lower initial isolation frequency and peak transmissibility.(4)Based on the PCR QZS isolator,the PCR DQZS isolator was proposed using a three-spring horizontal force mechanism with quasi-zero stiffness characteristics to replace the linear spring.The static model of PCR DQZS isolator was established,the quasi-zero stiffness parameter condition of PCR DQZS isolator was determined,and the restoring force-displacement relationship and stiffness-displacement relationship of PCR DQZS isolator were obtained.(5)An innovative PCR BQZS vibration isolator was proposed based on the optimized design of the PCR DQZS vibration isolator.The static model of PCR BQZS vibration isolator was established,and the quasi-zero-stiffness parameter condition of PCR BQZS vibration isolator was obtained.The restoring force expression of the PCR BQZS vibration isolator was expanded using Taylor series,and the error quantification analysis resulted in an error ratio of less than 3% using the approximate expression instead of the exact expression in the range of x(?)[-1.58,1.58].A test prototype of the PCR BQZS vibration isolator was fabricated,and the static performance tests were carried out.The restoring force-displacement relationship curves measured from the tests were able to match that predicted by the theory,which verified the theoretical analysis.(6)Dynamic performance analyses of the PCR BQZS vibration isolator under harmonic and shock excitation.The dynamic response of the PCR QZS isolator under harmonic force and base harmonic displacement excitation was analyzed using the averaging method and verified using the 4th order Runge-Kutta method.The dynamic responses of PCR BQZS isolators,PCR QZS isolators and linear isolators under the impact excitation were analyzed using the 4th order Runge-Kutta method,and the impact displacement ratio,impact velocity ratio and impact acceleration ratio were used as the evaluation indexes for the impact isolation performance.