Study On Static And Dynamic Modeling Of Compliant Amplification Mechanism Based On Flexure Hinge

With the development of modern machinery towards high speed,high precision,and miniaturization,compliant mechanisms are widely used in optical fiber alignment equipment,aerospace,and micro-electromechanical systems(MEMS).The Flexure hinge is the most important component of the compliant mechanism and its static and dynamic performance determines the overall performance of the mechanism.The different notch shape of the flexure hinge has different static and dynamic performance.To improve the comprehensive performance of the flexure hinge,it is necessary to study the design and modeling of the new notch shape.However,the traditional modeling method needs to be solved by integration,which makes it difficult to model the flexure hinge whose notch function cannot be directly integrated.To reduce the difficulty of static and dynamic modeling of flexure hinges,it is necessary to explore more general static and dynamic modeling methods of flexure hinges.Generally,piezoelectric ceramic actuators must be equipped with compliant amplification mechanisms to meet the requirements of a large-stroke precision positioning platform.How to understand and improving the static and dynamic performance of the compliant amplification mechanisms requires modeling research.The static and dynamic modeling of flexure hinges is complicated because of their nonlinear deformation.Therefore,three different compliant amplification mechanisms were studied,and the finite element method,transfer matrix method and dynamic stiffness matrix method were used to model the three mechanisms.The research contents are as follows:A sinusoidal flexure hinge is designed.Based on the bending theory of a beam with a variable section in material mechanics and the Gauss-Legendre quadrature formula,its compliance equation is established.Considering the drift of the rotation center,the calculation formula of the precision factor is derived.The natural frequency model of the flexure hinge is established by the transfer matrix method.The effects of hinge structure parameters on the compliance,precision,compliance precision ratio,and first natural frequency were analyzed.The results show that the minimum thickness of the hinge has the greatest influence on the above four properties,and the width of the hinge has the least influence on the above four properties.The performance was compared with conic flexure hinges.The results show that the sinusoidal flexure hinge has higher precision and natural frequency.Both simulation and experimental results verify the effectiveness of the sinusoidal flexure hinge model.A modeling method based on the transfer matrix method is proposed to solve the compliance and precision factor of the flexure hinge.A new sinc flexure hinge is designed.Firstly,the flexure hinge is discretized into several flexure beam elements in series.Then based on the transfer matrix method,a theoretical model of the compliance and precision factor of the sinc flexure hinge is established.The finite element simulation results are compared with the modeling results.The results show that the error between simulation results and modeling results in this paper is less than 7.0%.Secondly,the influence of structural parameters on compliance,precision factor,and compliance accuracy ratio is analyzed.The analysis results show that the compliance and precision factor are opposite,and the minimum thickness has the most significant influence on the three properties.The compliance,precision,and compliance precision ratio of the conic flexure hinge are compared.Sinc flexure hinge has higher precision and greater compliance precision ratio.Finally,the flexure hinge is machined to measure its compliance.The experimental results show that the error between experimental and theoretical values is less than 7.6%.The effectiveness of the method and the accuracy of the theoretical model are verified by simulation and experiment.A three-stage symmetrical compliant amplification mechanism is designed by combining a two-stage lever mechanism and a half-bridge mechanism.Based on the superposition principle of mechanical deformation of materials and the form function of beam element,the stiffness matrix and the mass matrix of straight circular flexure hinge are derived respectively.On this basis,the static and dynamic model of the compliant amplification mechanism is established by the finite element method.The displacement amplification ratio,input stiffness,maximum hinge stress,and first natural frequency of the mechanism are obtained.The modeling results are compared with the finite element simulation results to verify the effectiveness of the method.The influence of structural parameters on the displacement amplification ratio of the mechanism is also analyzed.The maximum displacement amplification ratio of the mechanism is used to optimize the target.Considering the structure size,input stiffness,maximum stress,and natural frequency as constraints,the optimal design of the mechanism was carried out.Based on the free vibration differential equation of the Euler-Bernoulli beam,the dynamic stiffness matrix of the beam element is derived.The transfer matrix of flexure hinge is derived based on the superposition principle of material mechanical deformation.Then the static and dynamic model of the sinusoidal flexure hinge bridge mechanism is established by using the dynamic stiffness matrix method and transfer matrix method.The effectiveness of the two modeling methods is verified by finite element simulation,and the modeling errors are analyzed.Meanwhile,the displacement amplification ratio,input stiffness,and natural frequency of the bridge mechanism based on the elliptic flexure hinge are compared.The results show that the bridge mechanism based on a sinusoidal flexure hinge has better dynamic performance.A spatial bridge displacement amplifying mechanism is designed by combining the bridge mechanism and the diamond mechanism.The compliance matrix method is used to establish the compliance of flexure hinge in six degrees of freedom directions.The stiffness matrices of different connection forms of space flexure hinge are derived.Based on the dynamic stiffness matrix method,the displacement amplification ratio,input stiffness,and natural frequency models of the spatial bridge displacement amplification mechanism are established.By comparing the modeling results with the finite element simulation results,the validity of the theoretical model is verified.