Modeling And Simulation Of A Class Of Piezoelectric Bimorph Cantilever Beams

Piezoelectric materials are that materials which exhibit the relation between the mechanical and electrical actions.When the mechanical force or stress is loaded into the system,it will generate the electricity,or when the electric field is loaded into the system and in contrast,it produces the strain.In most industrial applications,high speed and precision are the important performance requirements.Piezoelectric ceramics actuators,of these characters,have been widely used in aeronautics and astronautics,engineering,micro-electro-mechanical/optomechanical systems and intelligent systems.Thus,various types of piezoelectric ceramics actuators have been designed,namely piezoelectric single crystal actuator,piezoelectric bimorph actuator,S type piezoelectric actuator and hot piezoelectric actuator.The piezoelectric single crystal beam has been paid wide attention due to its good positioning ability,simple preparation,and low cost.Among them,piezoelectric single crystal beam gains much attention for its capacity of positioning.However,its matrix layer prevents the deformation of the piezoelectric layer,which reduces the delivery stroke.To overcome the shortcoming,in this thesis,a piezoelectric bimorph cantilever which consists of two PZT layers is studied.Firstly,static analysis is studied.based on the d31 mode of piezoelectric material.The existing model of the piezoelectric beam or piezoelectric actuator is established by Euler beam theory.However,the error of the piezoelectric actuator change,when the parameters of the piezoelectric actuator change.For example,when the length of the piezoelectric actuator is gradually increased,the relative error between the theoretical calculation value and the simulation value of the piezoelectric actuator changes.The theoretical model established by Euler-Bernoulli theory is no longer accurate when the length increases gradually and exceeds a certain size.For the limitations of the scope of application of the current theories,in this paper,the MPFM(Modified Pin Force Model)theory is used to enhance the piezoelectric bimorph model to describe the performance of piezoelectric bimorph under the equilibrium of force and moment and boundary conditions.The effect on the bending characteristics of different length and thickness of piezoelectric bimorph is also discussed.Secondly,based on Euler-Bernoulli theory,the dynamic model of PZT bimorph beam is established.The natural frequency of piezoelectric beam is calculated.The influence of different size parameters of piezoelectric bimorph beam on its natural frequency response is analyzed.And the theoretical model of piezoelectric bimorph beam is verified by finite element software simulation.Finally,the experimental system of piezoelectric bimorph beam is built.By loading the same parameters of the ANSYS software on both sides of the piezoelectric bimorph,the end deflection parameters of the piezoelectric bimorph beam are obtained.Then the theoretical value of the mathematical model of the piezoelectric bimorph beam,the value of the ANSYS simulation and the experimental value of the experimental detection system are compared.It is found that using the MPFM(Modified Pin Force Model)theory to establish the piezoelectric bimorph beam model;the calculated values are basically consistent with the simulation values and experimental values.The conclusion is that the bending theory of piezoelectric bimorph beam based on the improved MPFM theory can accurately predict the bending characteristics under different electric loads.It is proved that MPFM theory is more applicable for modeling of long piezoelectric beam or actuator than Euler beam theory.This method can effectively simplify theoretical analysis of piezoelectric beams and has specific practical application value.