L-shaped piezoelectric motor--part I: design and experimental analysis

This paper proposes an L-shaped piezoelectric motor consisting of two piezoelectric bimorphs of different lengths arranged perpendicularly to each other. The coupling of the bending vibration mode of the bimorphs results in an elliptical motion at the tip. A detailed finite element model was developed to optimize the dimensions of bimorph to achieve an effective coupling at the resonance frequency of 246 Hz. The motor was characterized by developing rotational and linear stages. The linear stage was tested with different friction contact surfaces and the maximum velocity was measured to be 12 mm/s. The rotational stage was used to obtain additional performance characteristics from the motor: maximum velocity of 120 rad/s, mechanical torque of 4.7 × 10-(5) N·m, and efficiency of 8.55%.     

Electric energy generator

This study reports an extremely cost-effective mechanism for converting wind energy into electric energy using piezoelectric bimorph actuators at small scale. The total dimensions of the electric energy generator are 5.08 x 11.6 x 7.7 cm3. The rectangular, box-shaped body of the overall structure is made using 3.2-mm thick plastic. Slits are made on two opposite faces of the box so that two columns and six rows of bimorph actuators can be inserted. Each row of bimorph actuators is separated from each other by a gap of 6 mm, and the two columns of bimorphs are separated from each other by a gap of 6.35 mm. In between the two columns, a cylindrical rod is inserted consisting of six rectangular hooks. The hooks are positioned in such a way that each of them just touches the two bimorphs on either side in a particular row. As the wind flows across the generator, it creates a rotary motion on the attached fan that is converted into vertical motion of the cylindrical rod using the cam-shaft mechanism. This vertical motion of the cylindrical rod creates oscillating stress on the bimorphs due to attached hooks. The bimorphs produce output voltage proportional to the applied oscillating stress through piezoelectric effect. The prototype fabricated in this study was found to generate 1.2 mW power at a wind speed of 12 mph across the load of 1.7 komega.     

Approximate equations for the flexure of thin,incomplete, piezoelectric bimorphs

Summary In this paper the linear, three-dimensional, piezoelectric equations for a body in equilibrium are reduced to approximate, two-dimensional ones, treating the flexure of thin bimorphs, partly coated by electrodes (incomplete bimorphs). For that purpose two-dimensional equations are derived for piezoelectric plates and for bimorphs with completely coated faces. An assumption about the charge distribution on the inner electrode is given, stating that the charge vanishes on those parts where the outer faces are free of electrodes. This assumption allows the application of the mentioned, approximate equations for plates and bimorphs to the parts of incomplete bimorphs. By stating edge and continuity conditions, the approximate theory ls completed. The solution for a circular, incomplete, piezoceramic bimorph, loaded by a singular force in the centre, is given and compared with experimental results.     

Benchmark analysis of piezoelectric bimorph energy harvesters composed of laminated composite beam substrates

This paper is concerned with the derivation of exact solutions for the responses of piezoelectric bimorph energy harvesters composed of laminated composite beam substrates. An electro-elastic finite element model is also developed based on the layer wise first order shear deformation theory for computing the responses of the bimorphs under general boundary and loading conditions. Both series and parallel connections of the piezoelectric layers of the bimorphs are considered. The responses computed by the finite element model excellently match with that obtained by the exact solutions. The induced electric potential in case of the bimorph in which the piezoelectric layers are connected in series is significantly larger than that in case of the bimorph with piezoelectric layers connected in parallel. If the thickness of the piezoelectric layers and the substrate remain same, the piezoelectric bimorph composed of antisymmetric angle-ply substrate beam is capable of inducing more electric potential than the bimorphs with cross-ply substrate beams. Also, if the bimorph is cantilever, it induces significantly more electric potential than when it is simply supported. Optimum thickness of the piezoelectric layers of the bimorph and unimorph harvesters has been determined. Most importantly, it is found that the bimorph with its piezoelectric layers connected in series performs significantly better than the unimorph if the mass and volume of the piezoelectric layers and the substrates remain same. The results presented here may serve as the benchmark results for verifying experimental and numerical models.

     

Resonance and antiresonance of symmetric and asymmetric cantilevered piezoelectric flexors

The resonances of dynamically excited symmetric piezoelectric bimorphs have been determined from the equations of state. Under the effect of sinusoidal stimuli: a moment exerted at the tip M, a force exerted perpendicular to the plane of the bimorph also applied at the tip F, a uniformly applied pressure p, and an electrode voltage V, they respond with a sinusoidal tip rotation alpha, tip deflection delta, volume displacement nu, and electrode charge Q. All of the former are related to all of the latter through a dynamic admittance matrix B. The antiresonance frequency of the capacitance C have been found while also antiresonance in off-diagonal elements have been determined. The latter indicate that at these frequencies the bimorph does not work as an actuator or sensor in the particular domain of the off-diagonal. The mode shape at these antiresonance frequencies has been determined. The antiresonance of b(14) determines that for this frequency the tip has deflection but no rotation, while the antiresonance of b(24 ) indicates that the tip has rotation but no deflection. No antiresonance in the volume displacement is found, indicating that the bimorph is a pressure converter (microphone) at all frequencies. Micromachined piezoelectric heterogeneous bimorphs have been fabricated using the techniques of I.C. fabrication. Their deflections have been measured as a function of frequency and applied voltage, while these have been compared with the theoretical predictions. An anomalously large quadratic deflection has been found, superimposed on the linear piezoelectric behavior. The agreement between the linear part of the experimental deflection and the theory was quite good.     

Vibrations and static responses of asymmetric bimorph disks of piezoelectric ceramics

In an earlier article, the flexural vibrations in bimorph disks and extensional vibrations in homogeneous disks of piezoelectric ceramics were studied. In the present paper, the coupled flexural and extensional vibrations and static responses in an asymmetric bimorph disk, which is formed by bonding together two piezoelectric ceramic disks of unequal thickness and opposite polarization, are investigated. Governing equations of coupled motions for asymmetric bimorphs are deduced from the recently derived 2-D, first-order equations for piezoelectric crystal plates with thickness-graded material properties. Then, closed form solutions of these equations for circular disks are obtained for free vibrations, piezoelectrically forced vibrations, and responses under static voltage difference. Resonance frequencies, distribution of displacements and surface charges, impedances, and static responses are calculated for asymmetric bimorph disks of various thickness ratios and diameter-to-thickness ratios. Experimental data on resonances and impedances are obtained for asymmetric bimorph disks of PZT-857 for different thickness ratios. Comparisons of predicted and measured results show that the agreements are close.     

Efficient charge recovery method for driving piezoelectric actuators with quasi-square waves

In this paper, an efficient charge recovery method for driving piezoelectric actuators with low frequency square waves in low-power applications such as mobile microrobots is investigated. Efficiency issues related to periodic mechanical work of the actuators and the relationship among the driving electronics efficiency, the piezoelectric coupling factor, and the actuator energy transmission coefficient are discussed. The proposed charge recovery method exploiting the energy transfer between an inductor and a general capacitive load is compared with existing techniques that lead to inherent inefficiencies. A charge recovery method is then applied to piezoelectric actuators, especially to bimorph ones. Unitary efficiency can be obtained theoretically for purely capacitive loads while intrinsic losses such as hysteresis necessarily lower the efficiency. In order to show the validity of the method, a prototype driving electronics consisting of an extended H-bridge is constructed and tested by experiments and simulations. Preliminary results show that 75% of charge (i.e., more than 56% of energy) can be recovered for bending actuators such as bimorphs without any component optimization at low fields.     

Design and fabrication of bimorph transducer for optimal vibration energy harvesting

High energy density piezoelectric composition corresponding to 0.9Pb(Zr0.56Ti0.44)O3–0.1Pb[(Zn0.8/3Ni0.2/3) Nb2/3]O3 + 2 mol% MnO2 (PZTZNN) and 0.8[Pb(Zr0.52Ti0.48) O3]-0.2[Pb(Zn1/3Nb2/3)O3] (PZTPZN) were synthesized by conventional ceramic processing technique using three different sintering profiles. Plates of the sintered samples were used to fabricate the piezoelectric bimorphs with optimized dimensions to exhibit resonance in the loaded condition in the range of ~200 Hz. An analytical model for energy harvesting from bimorph transducer was developed which was confirmed by experimental measurements. The results of this study clearly show that power density of bimorph transducer can be enhanced by increasing the magnitude of product (d ? g), where d is the piezoelectric strain constant and g is the piezoelectric voltage constant.     

Polymeric nanolayers as actuators for ultrasensitive thermal bimorphs

Polymeric nanolayers are introduced here as active, thermal-stress mediating structures facilitating extremely sensitive thermal detection based upon the thermomechanical response of a bimaterial polymer-silicon microcantilever. To maximize the bimaterial bending effect, the microcantilever bimorph is composed of stiff polysilicon, with a strongly adhered polymer deposited via plasma-enhanced chemical vapor deposition. The polymer layers with thickness ranging from 20 to 200 nm possess a rapid and pronounced response to temperature fluctuations due to intrinsic sensitive thermal behavior. We show that by taking advantage of the thermal stresses generated by the huge mismatch of material properties in the polymer-silicon bimorph, unprecedented thermal sensitivities can be achieved. In fact, the temperature resolution of our bimaterial microcantilevers approaches 0.2 mK with thermal sensitivity reaching 2 nm/mK; both parameters are more than an order of magnitude better than the current metal-ceramic design. This new hybrid platform overcomes the inherently limited sensitivity of current sensor designs and provides the basis to develop the ultimate uncooled IR microsensor with unsurpassable sensitivity.     

A Low-Cost Experimental Setup to Characterize Piezoelectric Cantilever Bimorphs

Hysteresis is a common phenomenon in nonlinear systems. Piezoelectric bimorphs show hysteretic behavior when operating as actuators. Tools that produce the characterization of these devices are available; they use high-cost setups that measure deformations with resolutions on the order of nanometers. In this paper, a new low-cost experimental setup that uses coupled infrared detectors to investigate the behavior of piezoelectric actuators is discussed. The tool, providing deformation measurements with a resolution on the order of 10 , is intended to produce a rough estimation of the device behavior and is of interest for research and educational purposes. Low cost, easy reproducibility in research and educational laboratories, a contactless measurement strategy, an inset calibration facility, and a suitable user interface are the main features of the tool developed. Notes on the uncertainty introduced by the tool when estimating bimorph deformations are given. Moreover, a case study that concerns the characterization of a piezoelectric bimorph actuator is discussed to illustrate the performance of the system developed in a real case.     

A nonlinear electromechanical model for ferroelectric materials: application to soft-PZT thick films screen-printed on alumina substrate

Motivated by experimental observations made on soft-PZT/alumina cantilever bimorphs, a nonlinear electromechanical model is presented describing the characteristic phenomena of ferroelectricity: the dielectric hysteresis, the butterfly loop, and the ferroelastic hysteresis. This model uses a phenomenological formulation, written within the general framework of thermodynamics of irreversible processes. The one-dimensional formulation of the model is successfully validated using experimental data from the literature. The model is used to predict the electromechanical behavior of a PZT/alumina cantilever bimorph. The results of the simulations are very promising.     

Design and fabrication of a high performance multilayer piezoelectric actuator with bending deformation

A new bending mode multimorph actuator was designed and fabricated successfully by a multiple screen printing process. Unlike the conventional bimorph actuator in which the bend occurs in the thickness direction, the bend in the multimorph actuator occurs in the widthwise direction because of synchronistical deformation of each single monolithic layer in the multilayer structure. The theoretical analysis and experimental measurements were conducted to study the performance of this type of actuator, and a comparison was made with the conventional bimorph actuator. Larger displacement, higher resonance frequency, and much larger blocking force could be achieved with the multimorph actuator than with a bimorph actuator of similar dimensions. The multimorph actuator presented in this paper provides a valuable alternative for actuator applications beyond those available with the popular bimorph and longitudinal multilayer actuators.     

Governing equations for a piezoelectric plate with graded properties across the thickness

Two-dimensional first-order governing equations for electroded piezoelectric crystal plates with general symmetry and thickness-graded material properties are deduced from the three-dimensional equations of linear piezoelectricity by Mindlin's general procedure of series expansion. Mechanical displacements and thickness-graded material properties, i.e., the elastic stiffnesses, piezoelectric coefficients, dielectric permittivities, and mass density, are expanded in powers of the thickness coordinate, while electric potential is expanded in a special series in order to accommodate the specified electric potentials at electroded faces of the plate. The effects of graded material properties on the piezoelectrically induced stresses or deformations by the applied surface potentials are clearly exhibited in these newly derived equations which reduce to Mindlin's first-order equations of elastic anisotropic plates when the material properties are homogeneous. Closed form solutions are obtained from the three-dimensional equations of piezoelectricity and from the present two-dimensional equations for both homogeneous plates and bimorphs of piezoelectric ceramics. Dispersion curves for homogeneous plates and bimorphs and resonance frequencies for bimorph strips with finite width are computed from the solutions of three-dimensional and two-dimensional equations. Comparison of the results shows that predictions from the two-dimensional equations are very close to those from the three-dimensional equations.     

Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs

Three experimental techniques are used in this study to access the resonant characteristics of piezoceramic bimorphs in parallel and series connections. These experimental methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, point-wise displacement, and electric impedance, respectively. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time by the AF-ESPI method. LDV-DSA is used to determine the resonant frequencies of the vibration mode for out-of-plane motion. The impedance analysis is used to measure the resonant and antiresonant frequencies for in-plane motion. Although the out-of-plane mode is the dominant motion of piezoceramic bimorphs, it is found in this study that the amount of displacement for the in-plane motion in parallel connection is large enough to be measured by AF-ESPI and impedance. It is interesting to note that resonant frequencies of the specimen in parallel connection for the out-of-plane motion determined by LDV-DSA are the same as that for the in-plane motion obtained by impedance. Furthermore, both in-plane and out-of-plane mode shapes for the specimen in parallel connection are obtained in the same resonant frequency from the AF-ESPI method. It is concluded in this study that the particle motions of piezoceramic bimorphs for parallel connection in resonance are essentially three-dimensional. However, it is found that only out-of-plane vibration modes can be excited for the specimen in series connection. Numerical computations based on the finite-element method are presented, and the theoretical predicted results are compared with the experimental measurements. Good agreements between the experimental measured data and numerical calculated results are found for resonant frequencies and mode shapes of the piezoceramic bimorph.     

双迭片压电振子的振动研究

利用压电方程和小挠度弯振理论,推导了边界自由压电陶瓷双迭片薄板小挠度条件下弯曲振动位移的一般解及振型频率方程。由频率方程计算得到的各阶振型频率与用有限元方法计算的结果基本相符,并基本得到实验结果的验证。所得结论对边界自由双迭片压电振子弯曲振动的设计提供了理论参考。     

Electromechanical coupling and output efficiency of piezoelectric bending actuators

Electromechanical coupling mechanisms in piezoelectric bending actuators are discussed in this paper based on the constitutive equations of cantilever bimorph and unimorph actuators. Three actuator characteristic parameters, (e.g., electromechanical coupling coefficient, maximum energy transmission coefficient, and maximum mechanical output energy) are discussed for cantilever bimorph and unimorph actuators. In the case of the bimorph actuator, if the effect of the bonding layer is negligible, these parameters are directly related to the transverse coupling factor lest. In the case of the unimorph actuator, these parameters also depend on the Young's modulus and the thickness of the elastic layer. Maximum values for these parameters can be obtained by choosing proper thickness ratio and Young's modulus ratio of elastic and piezoelectric layers. Calculation results on four unimorph actuators indicate that the use of stiffer elastic material is preferred to increase electromechanical coupling and output mechanical energy in unimorph actuators.     

Bimorph变形镜10.6μm薄膜研究

基于压电驱动器的Bimorph变形镜是10.6 μm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.     

High-frequency resonant characteristics of triple-layered piezoceramic bimorphs determined using experimental measurements and theoretical analysis

This is an experimental, theoretical, and numerical investigation of vibration characteristics in high-frequency resonance, which are studied for parallel- and series-type piezoelectric bimorphs. In the experimental measurements, the full-field optical technique known as electronic speckle pattern interferometry (ESPI) is used to measure the transverse (out-of-plane) and planar (in-plane) resonant frequencies and corresponding mode shapes for piezoelectric bimorphs. In addition, in-plane resonant frequencies are obtained from impedance analysis and the response curves of the frequency spectra show different vibration characteristics of the piezoelectric bimorphs with different electrical connections. Piezoelectric bimorphs with normal connections have three-dimensional coupled vibration characteristics and the out-of-plane vibration dominates the motion. However, only in-plane vibration motions can be excited in the high-frequency range for abnormal connections, and the resonant characteristics are similar to the single-layered piezoelectric plate. The triple-layered piezoelectric bimorphs with abnormal connection are also analyzed using theoretical analysis. The resonant frequencies, mode shapes, and normalized displacements are calculated based on the analytical solution. The experimental results and the theoretical analysis are in good agreement with the numerical calculations using the finite element method. From the discussion of the results for the parallel- and series-type piezoelectric bimorphs with normal and abnormal connections, the vibration characteristics at high frequencies are completely analyzed in this study.     

Piezoelectric micromotor based on the structure of serial bending arms

This paper presents a new piezoelectric micromotor based on the structure of serial bending arms. Serial bending arms are composed of two piezoelectric bimorphs with one end fixed and the other end free, driven by two signals of a biased square wave with a phase difference of /spl pi//2. The free end of a cantilever arm will move along an elliptic orbit so that the cantilever is used to drive a cylinder rotor. The rotor's end surface contacts the free end of the cantilever, resulting in the rotor's rotation. There are six serial bending arms anchored on the base. The driving mechanism of the micromotor is proposed and analyzed. A new micromotor prototype, 5 mm in diameter, has been fabricated and characterized. The maximum rotational speed reaches 325 rpm, and the output torque is about 36.5 /spl mu/Nm.     

Factors affecting the performance of piezoelectric bending actuators for advanced applications: an overview

The behaviors of piezoelectric bending actuators both in static and dynamic conditions driven by a high electric field were investigated and are summarized in this paper. In the static condition, the polarization and the displacement were measured and analyzed. It was found that the displacement hysteresis loop is the superposition of displacement loop induced by each layer of the actuator. The shape variation of the hysteresis loop is affected by the actuator configuration, i.e., the arrangement of electric field and poling direction. When the poling direction is parallel to an even electric field, such as parallel bimorph, the domain turns to switch at the exact coercive field of the piezoelectric material. However, when the poling direction is antiparallel to the electric field, such as series bimorph, the effect of electric field redistribution will take place during the domain reorientation, which reduces the actual electric field in the electric field–poling direction antiparallel layer, therefore prohibiting further domain reorientation. As a result, the series bimorph is noted to be more resistant to domain reorientation than the parallel bimorph. In the dynamic condition, the functions and relations of vibration velocity, heat generation, stress, and frequency were examined both theoretically and experimentally. It was found that the stress effect dominates at low frequency. At low frequency the failure mode of the actuator is often the physical fracture of the material. However, at high frequency, the failure modes mainly resulted from heat generation, unstable operation, depoling, and domain reorientation of the actuators. The vibration velocity will also decrease accordingly at the high frequency range due to more losses and heat generation.