Design And Optimization Of Electromagnetic Negative Stiffness Mechanism For Low Frequency Vibration Isolation

With the continuous improvement in the accuracy of processing,measurement and operation of advanced equipment such as lithography machines and robots,and the increasingly complex working environment,the interference of low-frequency vibration has become one of the key factors that limit the performance of equipment.The isolation of low-frequency vibration requires a low-stiffness vibration isolation system,but directly reducing the stiffness will increase the static displacement of the system and reduce the bearing stability.By introducing the negative stiffness mechanism in parallel with the vibration isolation system,high static stiffness and low dynamic stiffness can be achieved,which breaks through the limitation of the effective isolation frequency band caused by the bearing capacity in the traditional technology and realizes low-frequency vibration isolation.The electromagnetic negative stiffness mechanism has the advantages of tunable stiffness,compact structure and non-contact force,so it has great development potential.However,there are still some problems in the existing mechanisms:the nonlinear stiffness produces nonlinear response under large excitation,leading to performance deterioration;the low negative stiffness is not enough to offset the positive stiffness required by the load;and the energy consumption of maintaining the electromagnetic negative stiffness is high.In this study,aiming at the great demand of national advanced equipment for vibration isolation system,based on the principle of the vibration isolator constructed by the parallel connection of positive and negative stiffness,the optimal design of electromagnetic negative stiffness mechanism is studied,and three performance indexes of linear stroke,tunable range and energy efficiency are put forward.Through the combination of mechanism analysis,configuration design,parameter optimization and experimental verification,the application of electromagnetic negative stiffness mechanism in vibration isolation environment such as strong excitation,large weight and low power consumption is extended.So as to improve the low-frequency vibration isolation performance and ensure the stable operation of equipment.The main research contents are as follows:The two formation mechanisms of electromagnetic negative stiffness of magnetic element configuration and magnetic circuit air gap are expounded,and the analysis models are established based on the current-carrying loop equivalent method and the virtual displacement method respectively.Furthermore,the configuration design of magnets and coils and the design of ferromagnetic circuit are innovated.By analyzing the influence of parameters and configuration on stiffness characteristics,the law is summarized and the optimal design flow is put forward.Achieved that:(1)The linear electromagnetic negative stiffness mechanism is proposed,which couples the attractive configuration and the repulsive configuration.By the mutual cancellation of softening nonlinearity and hardening nonlinearity,the non-linearity of the negative stiffness in the 10mm stroke is less than 1%,which can be used in the intense vibration environment.(2)The multi-layer electromagnetic negative stiffness mechanism is proposed,in which several repulsive electromagnetic negative stiffness units are coupled axially.The stroke of negative stiffness is proportional to the number of units configured in the same direction,and the tunable range is proportional to the number of units configured in the opposite direction.It breaks through the performance limitation of the traditional single-layer electromagnetic negative stiffness mechanism.The 6-layer electromagnetic negative stiffness mechanism with opposite configuration achieves a negative stiffness tunable range of±10⁴ N/m in a compact volume of 10^-4m³.(3)The energy-efficient electromagnetic negative stiffness mechanism based on Maxwell's normal force is proposed.By placing the coil on the trunk and reducing the air gaps,the utilization of magnetic field is improved and the magnetoresistance is reduced,thus the energy efficiency of negative stiffness generation is improved.The highest negative stiffness value reaches-10⁵ N/m,and the energy efficiency reaches-5000(N/m)/W.Finally,the designed electromagnetic negative stiffness mechanisms and the positive stiffness mechanism are connected in parallel at the equilibrium position to make a high-static-low-dynamic stiffness vibration isolator.The vibration isolation experiments show that they break through the limitation of bearing capacity and expands the effective isolation frequency band.A semi-active control system based on the cross frequency is introduced,and the natural frequency of the isolator is adjusted to avoid resonance through adaptive frequency tracking and current control.The isolator with electromagnetic negative stiffness improves the ranging accuracy of lidar by 10 times and improves its environmental modeling performance in the vehicle systems.