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.     

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.

     

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.     

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.     

含压电片复合材料层合板的高阶计算模型

给出了一种分析含任意内埋压电片复合材料层合板的高阶耦合模型, 板的位移场采用三阶剪切理论, 并提出了压电片中电势场在厚度方向的三次分布模式, 可以更精确地描述力、电耦合作用下电场的非均匀分布。在平面应力的假设下给出了简化的压电材料本构方程, 推导了基于该模型的压电层合板有限元计算公式, 并对双压电片梁的弯曲和层合板的变形控制进行了计算, 压电梁的弯曲计算结果与解析结果吻合良好, 表明本文的模型和公式是精确有效的。     

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.     

Traveling-wave piezoelectric linear motor. I. The stator design

A new type of piezoelectric linear motor incorporating a traveling wave has been developed. The linear motor is comprised of a stator and a carriage. The stator design, which consists of a meander-line structure and gear teeth mounted on the meander-line structure, is the focus of this article. The meander-line structure is constructed with bimorph actuators arranged in a line. These actuators are driven by two phased sets of alternating current (ac) in order to generate a traveling wave. The traveling wave is transferred to the gear teeth, by which the carriage is driven. Modeling of the stator is derived by use of a strain energy method. The performance of various materials is evaluated by analytical and experimental methods. The analytical and the experimental results are quite approximate. Modal analysis is investigated using ANSYS. Appropriate modes associated with ultrasonic levels of resonant frequency are selected to obtain desired motion and to enhance the output performance. Surface speed for various applied input voltage are studied and indicate a nearly linear relationship. The stator in combination with the carriage makes up the linear motor     

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.     

Traveling-wave piezoelectric linear motor Part I: the stator design.

A new type of piezoelectric linear motor incorporating a traveling wave has been developed. The linear motor is comprised of a stator and a carriage. The stator design, which consists of a meander-line structure and gear teeth mounted on the meander-line structure, is the focus of this article. The meander-line structure is constructed with bimorph actuators arranged in a line. These actuators are driven by two phased sets of alternating current (ac) in order to generate a traveling wave. The traveling wave is transferred to the gear teeth, by which the carriage is driven. Modeling of the stator is derived by use of a strain energy method. The performance of various materials is evaluated by analytical and experimental methods. The analytical and the experimental results are quite approximate. Modal analysis is investigated using ANSYS. Appropriate modes associated with ultrasonic levels of resonant frequency are selected to obtain desired motion and to enhance the output performance. Surface speed for various applied input voltage are studied and indicate a nearly linear relationship. The stator in combination with the carriage makes up the linear motor.     

Thin-Film Piezoelectric Actuators of Nonuniform Thickness and Nonhomogeneous Material Properties for Modulating Actuation Stress

The effects of the thickness variation and the material property variation of thin-film piezoelectric actuators on the actuation shear stress when the actuators are attached to an elastic plate are studied. A system of 2D equations for the flexure and shear of an elastic plate with symmetric piezoelectric actuators on the plate surfaces is derived. The equations are reduced to the case of elementary flexure without shear as a special case. The effects of the actuator thickness variation and material property variation on the actuation stress are examined using the equations obtained. It is shown that the distribution of the actuation stress depends on the thickness and material property variations of the actuators, and that actuators with varying thickness or varying material properties can be used to make modal actuators for producing a particular deformation or exciting a particular vibration mode.     

Composite piezoelectric transducer with truncated conical endcaps“cymbal”

This paper presents original results obtained in the development of the moonie-type transducers for actuator applications. The moonie-type actuators fill the gap between multilayer and bimorph actuators, but its position-dependent displacement and low generative force are unacceptable for certain applications. The moonie transducers were modified systematically by using finite element analysis combined with experimental techniques. A new transducer design, named “cymbal transducer”, was developed with larger displacement, larger generative forces, and more cost-effective manufacturing. The cymbal transducers consist of a cylindrical ceramic element sandwiched between two truncated conical metal endcaps and can be used as both sensors and actuators. The cymbal actuator exhibits almost 40 times higher displacement than the same size of ceramic element. Effective piezoelectric charge coefficient, Eff. d₃₃, of cymbal is roughly 40 times higher than PZT itself     

Numerical modelling of piezoelectric actuators exposed to hydrogen

Modern fuel injectors have been developed based on piezoelectric stack actuators. Performance and durability of actuators in a hydrogen environment are important considerations in the development of hydrogen injectors. 2D plane stress and 3D models for analysis of coupled diffusion and thermo-electromechanical response of actuators are presented. Chemical potential, electric field and temperature gradients are taken as driving forces for hydrogen transport. The explicit Euler finite difference method is used to solve the nonlinear diffusion governing equation. The finite element method is used for time-dependent analysis of fully coupled mechanical, electric and thermal fields. The diffusion process and thermo-electromechanical deformations are coupled through the dependence of piezoelectric properties on hydrogen concentration. Experimental results for the piezoelectric coefficient d ₃₃ of PZT ceramics exposed to different hydrogen concentrations are used. A comparison of a fully coupled 2D model with 2D and 3D models with reduced coupling is made to examine the significance of coupling and computational efficiency. Selected numerical results are presented for time histories of hydrogen concentration, temperature and stroke of an idealized actuator unit cell to obtain a preliminary understanding of the performance of actuators exposed to hydrogen.     

New applications of photostrictive ferroics

 Photostriction in ferroelectrics arises from a superposition of photovoltaic and inverse piezoelectric effects. (Pb,La)(Zr,Ti)O₃ ceramics doped with WO₃ exhibit large photostriction under irradiation of near-ultraviolet light, and are applicable to remote control actuators and photoacoustic devices. Using a bimorph configuration, a photo-driven relay and a micro walking device have been developed, which are designed to start moving as a result from the irradiation, having neither electric lead wires nor electric circuits. The mechanical resonance of the bimorph was also induced by an intermittent illumination of purple-color light; this verified the feasibility of applying photostriction for ”photophone” applications. Received: 10 September 1997/Accepted: 9 October 1997     

Experimental study on control fins of a small flying vehicle using piezo-composite actuators

A camber morphing control fin design and an all-moving control fin design using piezo-composite unimorph actuators are presented in this paper. The control fin of a small flying object is usually actuated using a servo motor system with an electromagnetic motor. Much research has been conducted to solve the structural complexity of servo actuation systems to convert the rotation of a servo motor to a linear actuation motion. To simplify this structural complexity, several types of smart actuators have been developed, such as bimorph or unimorph actuators with piezoelectric material layers and shape memory alloy actuators. In this study, a camber morphing type control fin and an all-moving type control fin actuated using piezo-composite actuators are designed to evaluate their ability to simplify the structural complexity of the gear transmission and electromagnetic servo motor system or hydraulic actuator system. Within the skin of the control fin, a piezo-composite actuator is mounted and the other end inserted in a slot of the control fin. As the piezo-composite actuator is excited by an electric field, the pitch angle of the control fin is changed. Experimental testing for the pitch rotation angle of a control fin in a 450 V electric field showed the deflection angle of the camber morphing control fin was 1.4° and the rotational angle of the all-moving control fin was 5.4°, which is obtained from the rotation angle magnification linkage structural system.     

Finite element analysis of a multilayer piezoelectric actuator taking into account the ferroelectric and ferroelastic behaviors

Ferroelasticity and ferroelectricity are the non-linear behaviors exhibited by piezoceramics, especially in the case of high electric field or stress. Many studies have focused on the role of ferroelastic and ferroelectric switching in fracture of actuators. However, engineering reliability analyzes are carried out with tools like finite element software that do not take into account these non-linear phenomena. To overcome such a problem, a simplified phenomenological constitutive law describing the non-linear behavior of piezoceramics has been developed and implemented in the commercial software ABAQUS. This finite element tool is used to study the effects of applied voltage on the electroelastic field concentrations ahead of electrodes in a multilayer piezoelectric actuator. The study lies on the experimental observations made by Shindo et al. [Y. Shindo, M. Yoshida, F. Narita, K. Horiguchi, Electroelastic field concentrations ahead of electrodes in multilayer piezoelectric actuators: experiment and finite element simulation, J. Mech. Phys. Solids 52 (2004) 1109–1124]. Electroelastic analysis on piezoceramics with surface electrode showed that high values of stress and electric displacement arose in the neighborhood of the electrode tip. Thus, the strain, stress and electric displacement concentrations were calculated and the numerical results showed that ferroelectric switching arose in the area of the electrode tip, causing a change in remnant polarization and remnant strain.     

考虑外部阻抗的压电叠层作动器机电耦合模型

压电叠层作动器在结构振动控制及其它场合表现出良好应用前景,建立能够反映其物理本质的数学模型非常重要。以压电材料的本构关系以及杆的纵向振动方程为基础,考虑外部阻抗的影响,推导了短路机械阻抗、电阻抗以及转换系数的表达式,并构造了转换方程,从而建立了能够描述压电叠层作动器与主体结构之间机电耦合特性的阻抗模型。理论分析和数值模拟结果表明外部阻抗对这些参数有重要影响：当两端的外部阻抗完全相同时,作动器的电阻抗和转换系数有最高的共振频率,作动器可看成两个具有固定-自由边界条件的作动器的串联。其它情况下则均有不同程度的降低。因此,为实现更好的控制效果需要考虑阻抗匹配问题。     

Electromechanical modeling and analytical investigation of nonlinearities in energy harvesting piezoelectric beams

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester implementing constitutive relations of nonlinear piezoelectricity together with nonlinear curvature and shortening effect relations, is investigated. To achieve this goal first of all a comprehensive fully-coupled electromechanical nonlinear model is presented through a variational approach. The governing nonlinear partial differential equations of the proposed model are order reduced and solved by means of the perturbation method of multiple scales. Results are presented for a PZT/Silicon/PZT laminated beam as a case study. Findings indicate that material nonlinearities of the PZT layer has the dominant effect leading to softening behavior of the frequency response. At the primary resonance, different frequency responses of the extracted power can be distinguished according to the excitation amplitude, which is due to harmonic generation as a result of piezoelectric nonlinearity. The extracted power is analytically computed and validated with a good agreement by a numerical solution.     

Optimal shapes of PZT actuators for laminated structures subjected to displacement or eigenfrequency constraints

In this paper, dynamics, electromechanical couplings, and control of piezoelectric laminated cylindrical shells and rectangular plates are investigated. It is assumed that the piezoelectric layers are distributed on the top and bottom surfaces of the structures. First of all the governing equations and boundary conditions including elastic and piezoelectric couplings are formulated and solutions are derived. Then control of the plate/shells deflections and natural frequencies using high control voltages are studied in order to optimize the structural response. The present formulation of optimal design introduces boundaries of piezoelectric patches as new class of design variables. In addition, classical design variables in the form of ply orientation angles of orthotropic layers are also taken into account. For the actuator/actuator configuration, it was shown that the piezoelectric actuators can significantly reduce deformations/eigenfrequencies of the composite plate. Those effects were dependent on the value of the applied voltage. It was demonstrated that the proper choice of the actuator area is more efficient in reducing deflections/eigenfrequencies. The accuracy of optimal design are verified both with the aid of the FE package ABAQUS and using the standard Rayleigh-Ritz method. The results concerning active vibration control for axisymmetric cylindrical shells are also discussed.     

Fabrication and experimental characterization of d31 telescopic piezoelectric actuators

A popular and useful piezoelectric actuator is the stack. Unfortunately with this type of actuation architecture the long lengths normally required to obtain necessary displacements can pose packaging and buckling problems. To overcome these limitations, a new architecture for piezoelectric actuators has been developed called telescopic. The basic design consists of concentric shells interconnected by end-caps which alternate in placement between the two axial ends of the shells. This leads to a linear displacement amplification at the cost of force; yet the force remains at the same magnitude as a stack and significantly higher than bender type architectures. This paper describes the fabrication and experimental characterization of three different telescopic prototypes. The actuator prototypes discussed in this paper mark a definitive step forward in fabrication techniques for complex piezoceramic structures. Materials Systems, Inc. has adapted injection molding for the fabrication of net shape piezoceramic actuators. Injection molding provides several advantages over conventional fabrication techniques, including: high production rate, uniform part dimensions, uniform piezoelectric properties, and reduced fabrication and assembly costs. Acrylate polymerization, developed at the University of Michigan, is similar to gelcasting, but uses a nonaqueous slurry which facilitates the production of large, tall, complex components such as the telescopic actuator, and is ideal for the rapid manufacture of unique or small batch structures. To demonstrate these fabrication processes a five tube telescopic actuator was injection molded along with a very tall three tube actuator that was cast using the acrylate polymerization method. As a benchmark, a third actuator was built from off-the-shelf tubes that were joined with aluminum end-caps. Each prototype's free deflection behavior was experimentally characterized and the results of the testing are presented within this paper.