Analytical modelling and free vibration analysis of piezoelectric bimorphs

An efficient and accurate analytical model for piezoelectric bimorph based on the improved first-order shear deformation theory （FSDT） is developed in this work. The model combines the equivalent single-layer approach for mechanical displacements and a layerwise-type modelling of the electric potential. Particular attention is devoted to the boundary conditions on the outside faces and to the interface continuity conditions of the bimorphs for the electromechanical variables. Shear correction factor （k） is introduced to modilfy both the shear stress and the electric displacement of each layer. And the detailed mathematical derivations are presented. Free vibration problem of simply supported piezoelectric bimorphs with series or parallel arrangement is investigated for the closed circuit condition, and the results for different length-to-thickness ratios are compared with those obtained from the exact 2D solution. Excellent agreements between the present model prediction with k=-8/9 and the exact solutions are observed for the resonant frequencies.

A 2-dimensional impact driven precise actuator using piezoelectric bimorphs

A new precise actuator is proposed,which is ac-tuated by the impact force of an end-loaded piezoelectric bimorph cantilever,and bears two degrees of freedom for translation and rotation.The dynamic characteristics of the piezoelectric bimorph were analyzed by FEM,and are fur-ther proved by experimental tests.A new control system for the actuator was put forward and tested,which is called the fixed-frequency with adjustable voltage.In addition,the actuator’s performance of translation and rotation were both measured.The results demonstrate that the actuator is char-acterized by a simple structure,large movement range,strong driving ability and high positioning resolution.Its cost is estimated at only 1%of the traditional impact actuators.

Bimorph变形镜10.6μm薄膜研究

基于压电驱动器的Bimorph变形镜是10.6μm系统的一个重要元件。为了镀制薄膜,本文首先利用有限元软件对两种镀膜夹持方式与沉积温度进行了计算,对热应力产生的热变形进行了分析,选择了合适的镀膜夹持方式。为了预测bimorph变形镜受激光辐照后的温升,对单晶硅与石英玻璃制作的bimorph变形镜有限元模型进行了计算与分析。最后,利用光度计对镀制的薄膜进行了反射率测量。试验结果显示反射率测量值大于99.5%,满足实际系统的需要。

电热驱动Bimorph微执行器对流系数估算方法研究

随着电热驱动MEMS器件尺寸进一步缩小,传统热对流系数的取值已无法满足微系统分析建模需求。针对电热型Bimorph结构的MEMS微镜驱动器,通过分析其温度分布,并以其平均温度为参考指标建立简单热阻和对流热阻分段模型,推算出微尺度下精确的对流系数,提高了微执行器设计模型的驱动性能。经理论计算和实验测试验证,对流系数值的误差在8.1%以内,满足实际设计需求,验证了该方法的合理性和可行性。

Bimorph结构微热执行器的节点分析方法

MEMS系统设计的节点分析法已成功应用于机电耦合器件的仿真,且已表明是一种简单实用的方法。本文在已有静态模型的基础上,通过对传热行为的分解以及引入等效质量,建立了Bimorph结构热执行器的动态节点模型。同时选取在电子行业得到普遍应用的电路仿真软件SPICE作为模型仿真平台,并将建立的节点分析模型应用于电路仿真平台。此模型数值实验证明,此方法和有限元分析软件ANSYS的仿真结果吻合较好,而且计算效率高,可在实际器件设计中作为参考。

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.

Thermal stability test and analysis of a 20-actuator bimorph deformable mirror

One of the important characteristic of adaptive mirrors is the thermal stability of surface flatness. In this paper, the thermal stability from 13℃ to 25℃ of a 20-actuator bimorph deformable mirror is tested by a Shack-Hartmann wavefront sensor. Experimental results show that, the surface P-V of bimorph increases nearly linearly with ambient temperature. The ratio is 0.11 μm/℃ and the major component of surface displacement is defocused, compared with which, astigmatism, coma and spherical aberration contribute very small. Besides, a finite element model is built up to analyse the influence of thickness, thermal expansion coefficient and Young＇s modulus of materials on thermal stability. Calculated results show that bimorph has the best thermal stability when the materials have the same thermal expansion coefficient. And when the thickness ratio of glass to PZT is 3 and Young＇s modulus ratio is approximately 0.4, the surface instability behaviour of the bimorph manifests itself most severely.

Interaction between bending and mobile charges in a piezoelectric semiconductor bimorph

We study the bending of a two-layer piezoelectric semiconductor plate(bimorph).The macroscopic theory of piezoelectric semiconductors is employed.A set of two-dimensional plate equations is derived from the three-dimensional equations.The plate equations exhibit direct couplings among bending,electric polarization along the plate thickness,and mobile charges.In the case of pure bending,a combination of physical and geometric parameters is identified which characterizes the strength of the interaction between the mechanical load and the distribution of mobile charges.In the bending of a rectangular plate under a distributed transverse mechanical load,it is shown that mobile charge distributions and potential barriers/wells develop in the plate.When the mechanical load is local and self-balanced,the induced carrier distributions and potential barriers/wells are also localized near the loading area.The results are fundamentally useful for mechanically manipulating mobile charges in piezoelectric semiconductor devices.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.

Research on an inertial piezoelectric actuator for a micro in-pipe robot

A new kind of inertial piezoelectric actuator for a micro in-pipe robot is proposed and studied. The actuator is composed of a body, corresponding to a mass rod, and four elastic legs. Each leg is a composite piezoelectric bimorph beam, made up of a middle metal element, an upper and lower piezoelectric elements. The mechanism is driven by an asymmetric waveform voltage, such as saw-toothed waveform, and utilizes the dynamic relationship between the maximum static friction force and the inertial force. To study the actuator, firstly, the constituent equation of a composite piezoelectric bimorph under both applied voltage and external force was inferred by thermodynamics. Secondly, the dvnamic model of the actuator was established analyzing the relationship between the locomotive states, viz. displacement and velocity, and design parameters, such as piezoelectric strain constant, elastic modulus,length, width and thickness of the piezoelectric element, actuator mass, and driving vohage. At last, the dynamic equation was solved and the theoretical calculation of the inherent frequency was more consistent with the experimental data, which proved the rationality of the model. All these lay a theoretical foundation of the micro actuator parameter optimization and more research on a micro robot.

Piezoelectric bimorph MEMS speakers

One of the key requirements for MEMS speakers is to increase the sound pressure level(SPL)while keeping the size as small as possible.In this paper we present a MEMS speaker based on piezoelectric bimorph cantilevers that produces a higher SPL than conventional unimorph cantilever speakers.The active diaphragm size is 1.4×1.4 mm^(2).The bimorph cantilevers are connected in parallel to make full use of the actuation voltage.At 1 kHz,the measured SPL reached 73 dB and the peak SPL reached 102 dB at the resonance frequency of 10 kHz in a 711 ear simulator under a driving voltage of 10 V_(rms).The total harmonic distortion of the MEMS speaker was less than 3%in the range from 100 Hz to 20 kHz.Although the absolute SPL was not the highest,this work provides a better SPL for all piezoelectric MEMS speakers.

A Hybrid Silicon-PDMS Micropump Actuated by PZT Bimorph

The fabrication and characterization of a hybrid Silicon-PDMS micropump based on MEMS technology is presented. The micropump consists of one chamber,two passive valves and one PDMS diaphragm.A PZT bimorph working as the actuator is mounted on the PDMS diaphragm.The use of the PDMS diaphragm and the PZT bimorph can give rise to large displacements of the pump diaphragm,making the micropump more efficient and easier to be fabricated.The flow rate of the micropump is a function to the voltage and frequency of the applied square wave.When a square wave of 100V is applied,a maximum flow rate of 317μL/min and a back-pressure of 2 kPa are achieved at 20 Hz.

Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror

A theoretical model of a circular flexure-mode piezoelectric bimorph ac- tuator is established. The circular bimorph structure, consisting of two flexible layers of piezoelectric material and a layer of metallic material in the middle, is powered to the flexural deformation. The analytical solutions including the statics solution and the dynamics solution are derived from the 3D equations of the linear theory of piezoelectric- ity. Numerical results are included to show the circular bimorph piezoelectric actuator （CBPA） performance, depending on the physical parameters.

基于MEMS技术的太赫兹可调波导带阻滤波器

本文提出了一种基于双层弯曲热微执行器的新颖的调谐方式,太赫兹带阻滤波器采用波导加载金属块的形式。双层弯曲热微执行器驱动金属膜片移动,利用可动金属膜片改变波导中加载金属块周围的电磁场分布达到调谐的目的。设计了一款中心频率为275.1 GHz的可调带阻滤波器,仿真结果显示,双层弯曲热微执行器产生180μm位移时,滤波器实现了中心频率23.2 GHz的调谐范围,反射衰减由24.7 d B变化到15.9 d B。

Disk Bimorph-Type Piezoelectric Energy Harvester

The study of the experimental investigation of a disk-type piezoelectric energy harvester presented. The harvester contains disk bimorph piezoceramic element of the umbrella form and contains two disk PZT plates. The element is excited at the base point at its center. The element is supplied by a loading ring mass to decrease its resonance frequency. The dependences of the vibration displacement along the radii of the bimorph and the ring mass from the frequency of excitation are presented and the output voltage frequency response is also presented as well. The idle mode and the load duty are investigated. The value of the internal resistance of the harvester is obtained using the load characteristic. The piezoelectric specific power is estimated experimentally.

A New Motor of Stick Type with Coupled Mechanical Vibration of Bimorph Beam and Frictional Force

This paper proposes a new non-magnetic motor with a rotor rotated by using the resonance energy of a bimorph cantilever beam excited by electrostatic force. The use of flexible material enables conversion of translational vibration to rotary movement in one direction. Basic characteristics of a prototype motor with two bimorph cantilever beams, such as rotational speed, output torque, and efficiency were determined experimentally. Results show that a maximum rotational speed of 2800 rpm was obtained without a load torque. It is also observed that this motor produces the output torque of 98 μNm when the rotational speed was 980 rpm. The maximum efficiency was 24% when the input power was 0.065 W.

FABRICATION OF PIEZOELECTRIC BIMORPH USING LEAD ZIRCONATE TITANATE THIN FILM DEPOSITED BY HYDROTHERMAL METHOD

In order to describe the characteristics of piezoelectric bimorph, properties of lead zirconate titanate （LZT） film are studied by X-ray diffraction （XRD） and scanning eletron microscope （SEM）. The ratio of PbTiOJPbZrO3 in LZT is 53/47, which is around morphotropic phase boundary （MPB）. LZT film is composed of cubic particles with the average size of 5 ~ma. Density of thin film is figured out through the datum measured in experiments. The displacement model used to analyze the driving ability of bimorph is set up, and the effect of elastic intermediate layer is taken into account. Piezoelectric coefficient of LZT film is worked out by using the displacement model. Experiments of driving ability show that deformation of bimorph free end does not increase with times of crystal growth processes and the maximum deformation is obtained after two times crystal growth processes. Finally, the ferroelectric property of the bimorph is investigated and coercive voltage of the bimorph is obtained.

A low frequency piezoelectric power harvester using a spiral-shaped bimorph

We propose a spiral-shaped piezoelectric bimorph power harvester operating with coupled flexural and extensional vibration modes for applications to low frequency energy sources. A theoretical analysis is performed and the computational results show that the spiral structure has relatively low operating frequency compared to beam power harvesters of the same size. It is found that to optimize the performance of a piezoelectric spiral-shaped harvester careful design is needed.

Theoretical analysis and simulation of thermoelastic deformation of bimorph microbeams

In this paper, a purely mechanical model for the thermoelastic behavior of a bimorph microbeam is presented. The thermoelastic coupling problem of the microbeam is converted to a mechanical problem by simply replacing the thermal stress in the beam with a bulk force and a surface force. Thermoelastic deformation of the bimorph microbeams with constraints frequently used in micro-electro-mechanical systems (MEMS) devices has been derived based on this model and is characterized by FEA simulation. Coincidence of the results from theory and simulation demonstrates the validity of the model. The analysis shows that a bimorph microbeam with a soft constraint and a uniform temperature field has a larger thermoelastic deformation than that with a hard constraint and a linear temperature field. In addition to the adoption of materials with large CTE mismatch,thickness ratio and length ratio of the two layers need to be optimized to get a large thermoelastic deformation.

Bimorph deformable mirror based adaptive optics scanning laser ophthalmoscope for retina imaging in vivo

A bimorph deformable mirror （DM） with a large stroke of more than 30 μm using 35 actuators is presented and characterized for an adaptive optics （AO） confocal scanning laser ophthalmoscope application. Facilitated with a Shack-Hartmann wavefront sensor, the bimorph DM-based AO operates closed-loop AO corrections for hu- man eyes and reduces wavefront aberrations in most eyes to below 0.1 μm rms. Results from living eyes, including one exhibiting ~5D of myopia and ~2D of astigmatism along with notable high-order aberrations, reveal a prac- tical efficient aberration correction and demonstrate a great benefit for retina imaging, including improving resolution, increasing brightness, and enhancing the contrast of images.