Research On Quasi-zero-stiffness Low-frequency Vibration Reduction And Regulation Methods

Vibration is a common problem in industrial equipments,such as marine engineering,aerospace,transportation,electrical machinery and communication equipment.With the development of large-scale industrial equipments,the lowfrequency vibration problem has gradually become prominent.For industrial equipments that have been designed or built up,vibration reduction and isolation technology is a very effective method to control the vibration of industrial equipments.However,due to the inherent contradiction between vibration isolation frequency and bearing capacity,traditional linear vibration isolation methods cannot be used to control low-frequency vibration.By introducing a negative stiffness mechanism,the quasi-zero-stiffness vibration isolation method realizes the characteristics of high static low dynamic stiffness which significantly reduces the system dynamic stiffness under the premise of heavy load.This provides a new way to solve the problem of low-frequency vibration control.However,the quasi-zero-stiffness vibration isolation method is sensitive to both load and excitation conditions,and how to realize the regulation of low-frequency vibration isolation is still a big challenge.This paper intends to develop quasi-zero-stiffness low-frequency vibration isolation and control methods from two approaches of low-frequency vibration isolation and low-frequency vibration suppression,laying theoretical and technical foundations for low-frequency vibration control of industrial equipment.Firstly,by combining quasi-zero-stiffness and dynamic vibration absorption,a quasizero-stiffness low-frequency vibration absorption method is firstly proposed to achieve low-frequency vibration suppression.Secondly,based on the electromagnetic regulation mechanism,the semi-active and active quasi-zerostiffness low-frequency vibration absorption methods are proposed to broaden and regulate the low-frequency vibration reduction frequency bands.Thirdly,aiming at the problem of low-frequency vibration control of heavy-duty industrial equipments,a heavy-duty quasi-zero-stiffness low-frequency vibration isolation method is developed.Finally,an automatic compensation method for quasi-zero-stiffness low-frequency vibration isolation load mismatch is proposed,which solves the performance degradation problem of lowfrequency vibration isolation caused by load mismatch.The main research contents of the paper are as follows:(1)By combining the quasi-zero-stiffness mechanism with the theory of dynamic vibration absorption,a passive quasi-zero-stiffness vibration reduction method is proposed.Firstly,the design scheme of the quasi-zero-stiffness absorber is given,the restoring force and stiffness of the quasi-zero-stiffness absorber are deduced,and the static characteristics of the quasi-zero-stiffness absorber are analyzed.Secondly,the dynamic model of the quasi-zero-stiffness vibration reduction system is established,and the dynamic response of the system is solved by using the Harmonic Balance Method(HBM).The lowfrequency vibration reduction characteristics of the quasi-zero-stiffness vibration absorber are studied.Furthermore,the effects of the structural parameters on the vibration reduction performance and nonlinear dynamic characteristics are discussed.The vibration reduction characteristics of the quasi-zero-stiffness vibration absorber under different excitations are evaluated.Finally,an experimental prototype of a quasi-zero-stiffness vibration absorber is fabricated to verify the low-frequency vibration reduction performance of the quasi-zero-stiffness low-frequency vibration absorption method and the effects of excitation amplitude on the vibration reduction characteristics.The results show that the low-frequency vibration reduction performance of the quasi-zerostiffness vibration reduction method is obviously better than that of the linear vibration absorption method.(2)Aiming at the problems of the passive quasi-zero-stiffness vibration absorption method,mainly including a single vibration absorption frequency and a narrow vibration reduction frequency band,based on the electromagnetic regulation mechanism,a semi-active quasi-zero-stiffness vibration reduction method is proposed.Firstly,the static characteristics of the semi-active quasizero-stiffness vibration absorber are deduced using the electromagnetic force calculation formulas,and the adjustment range of the stiffness of the semiactive quasi-zero-stiffness vibration absorber is analyzed.Secondly,the dynamic model of the semi-active quasi-zero-stiffness vibration reduction system is established,then,the dynamic response of the system is deduced by the averaging method.Moreover,the vibration reduction frequency band of the semi-active quasi-zero-stiffness vibration reduction system is obtained and the regulation effect of electromagnetic mechanism on vibration reduction frequency band is analyzed.Finally,an experimental prototype of the semiactive quasi-zero-stiffness vibration absorber is prepared,and the ability of the electromagnetic adjustment mechanism to control the vibration reduction frequency,reduction frequency band and reduction performance is verified by experiments.The results show that the semi-active quasi-zero-stiffness vibration reduction method can effectively broaden the low-frequency vibration reduction frequency band.(3)In order to further improve the vibration reduction performance of the quasi-zero-stiffness vibration reduction method,an active quasi-zero-stiffness vibration reduction method is developed based on the sliding mode nonlinear control strategy.Firstly,taking quadratic integral as the objective function,LQR method is used to calculate the optimal sliding mode surface,and the control force required in the control process of the active quasi-zero-stiffness vibration absorber is deduced.Then,the feasibility of the nonlinear sliding mode-based control strategy of the active quasi-zero-stiffness vibration reduction method is verified by numerical simulation.The influences of the system parameters and excitation conditions on the vibration reduction characteristics are explored.Finally,an experimental prototype of the active quasi-zero-stiffness vibration absorber is prepared,a nonlinear sliding mode control system is built up,and vibration control experiments are carried out to verify the feasibility of the sliding mode nonlinear control strategy and the lowfrequency vibration reduction performance of the active quasi-zero-stiffness vibration absorption method.(4)Based on the inclined spring mechanism,a heavy-duty quasi-zerostiffness vibration isolator with high static low dynamic stiffness is developed.Firstly,the static characteristics of the inclined spring quasi-zero-stiffness vibration isolator are theoretically analyzed,and the structural parameters are designed to satisfy the quasi-zero-stiffness characteristics.Secondly,the dynamic model of the quasi-zero-stiffness vibration isolation system is established,and the approximate analytical expressions of the force transmissibility and displacement transmissibility of the quasi-zero-stiffness vibration isolation system are deduced by using the Harmonic Balance Method.The influence of the system parameters on the transmissibility of the vibration system is analyzed.Finally,an experimental prototype of the heavy-duty quasizero-stiffness vibration isolation system is developed,and the static characteristics of the prototype are tested.Furthermore,the vibration isolation performance of the heavy-duty quasi-zero-stiffness vibration isolation system is tested through dynamic experiments.Compared to linear vibration isolators,the experimental results show that the heavy-duty quasi-zero-stiffness vibration isolator can effectively isolate the low-frequency vibration of heavy-duty industrial equipments,and the vibration isolation performance is much better than that of the linear vibration isolator.(5)Aiming at the problem that the low-frequency vibration isolation performance is reduced due to the load mismatch,an automatic compensation method for load mismatch of the quasi-zero-stiffness vibration isolation is proposed.Firstly,a quasi-zero-stiffness vibration isolator is constructed by using a permanent magnet ring and a linear spring in parallel.And,an automatic compensation system for load mismatch is designed based on a programmable logic controller and a stepper motor.Secondly,the static analysis of the quasizero-stiffness vibration isolator is carried out,and the structure parameters of magnetic ring are designed to satisfy the quasi-zero-stiffness characteristic.ing Then,the negative impact of load mismatch on the vibration isolation performance is analyzed,and the automatic compensation strategy for load mismatch of the quasi-zero-stiffness vibration isolation is given.Finally,an experimental prototype of automatic compensation system for load mismatch is developed,and the automatic compensation performance and vibration isolation effect of the system under load mismatch are tested.The automatic compensation system for load mismatch of quasi-zero-stiffness vibration isolation is verified.The results show that the developed compensation system can effectively compensate for load mismatch and assembly errors,so that the vibration isolation system is always in a state of quasi-zero-stiffness,thereby maintaining good low-frequency vibration isolation performance.