强离心场下旋转型行波超声电机定子动力学分析与试验

研究了强离心场下旋转型行波超声电机定子的动力学特性,分析了离心刚化效应对定子的影响。通过计算离心力做的功(或称为离心势能)推导出因离心刚化效应引起的附加刚度矩阵,进而得到强离心场下定子的特性矩阵(包括质量矩阵和刚度矩阵),求解得到定子的模态参数;并根据压电陶瓷的孤极区反馈的电压信号,确定了高旋环境下定子的固有频率;总结了强离心场下超声电机定子动力学特性变化规律,给出了高旋环境下超声电机的驱动控制应对策略,为高旋环境下超声电机的应用奠定基础。     

Design and performance testing of an ultrasonic linear motor with dual piezoelectric actuators

In this work, design and performance testing of an ultrasonic linear motor with dual piezoelectric actuator patches are studied. The motor system consists of a linear stator, a pre-load weight, and two piezoelectric actuator patches. The piezoelectric actuators are bonded with the linear elastic stator at specific locations. The stator generates propagating waves when the piezoelectric actuators are subjected to harmonic excitations. Vibration characteristics of the linear stator are analyzed and compared with finite element and experimental results. The analytical, finite element, and experimental results show agreement. In the experiments, performance of the ultrasonic linear motor is tested. Relationships between velocity and pre-load weight, velocity and applied voltage, driving force and applied voltage, and velocity and driving force are reported. The design of the dual piezoelectric actuators yields a simpler structure with a smaller number of actuators and lower stator stiffness compared with a conventional design of an ultrasonic linear motor with fully laminated piezoelectric actuators.     

A torque estimator for a traveling wave ultrasonic motor--application to an active claw

Depending on its electrical-to-mechanical energy conversion process, the torque on a traveling wave ultrasonic motor (TWUM)'s shaft is not directly proportional to a measurable electrical variable, such as current or voltage. But it is derived from a complicated process at the stator/rotor interface. The load torque is thus quite unknown, and this can be a disadvantage in applications in which a torque limitation is required or a torque measurement is needed. The aim of this article is to come up with a straightforward torque estimator on a TWUM. For that purpose, the motor is modeled; this modeling leads to different estimator strategies. More specifically, we chose a strategy for which a speed sensor is useless, relying only on the stator's resonant behavior. The parameters of the motor needed for the estimator are measured afterward, and some nonlinearities are identified and taken into account. Several experimental trials then are carried out to check the performance of the estimator. A claw actuated by a TWUM is presented because this is a typical application in which the knowledge of the torque helps guarantee the safety of the device.     

A Field-Network Model of a Linear Oscillating Motor and Its Dynamics Characteristics

We describe a method of modeling of the dynamics characteristics for linear oscillating motors. We used electromagnetic finite-element analysis in the network model, which contains the electric circuit and mechanical equations. We compared the integral parameters of the electromagnetic field with the measured ones. We also compared the calculated and measured waves of the stator current for two values of supply voltage. The comparison yields a good agreement.     

Modified Eshelby tensor for an ellipsoidal inclusion imperfectly embedded in an infinite piezoelectric medium

The modified Eshelby tensor for predicting the effective moduli of particle-reinforced piezoelectric composites is derived for the problem of an ellipsoidal inclusion which is imperfectly bonded to the matrix. A linear interface relation is adopted, which involves discontinuities of the mechanical displacements and electric potential across the interface, and assumes that the corresponding jumps are proportional to the continuous stresses and electric displacements at the interface. The piezoelectric field induced by a uniform eigenstrain given only in the inclusion is deduced analytically. As the induced piezoelectric field is no longer uniform, the average strains and electric displacements are calculated, and the modified piezoelectric Eshelby tensor is evaluated by both an iterative method and a direct method. By comparison, it is shown that the iterative method yields rapidly convergent results.     

Micromechanics models for the effective nonlinear electro-mechanical responses of piezoelectric composites

The nonlinear behavior of piezoelectric composites becomes prominent when the composites are subjected to high electric fields, which is often the case in actuator applications. Understanding the nonlinear behavior of piezoelectric composites is crucial in designing structures comprising of these materials. This study presents micromechanics models for predicting nonlinear electro-mechanical responses of polarized piezoelectric composites, comprising of a linear non-piezoelectric homogeneous medium (matrix) reinforced by either nonlinear piezoelectric fibers or particles, subjected to high electric fields. The maximum electric field applied is within the coercive electric field limit. The constitutive relations for the polarized piezoelectric inclusions consist of the third- and fourth-order electro-mechanical coupling tensors and the second- and third-order electric permeability tensors. The Mori–Tanaka micromechanics and simplified unit-cell micromechanics models are formulated to predict the effective nonlinear electro-mechanical responses of piezoelectric fiber reinforced and particle reinforced composites, respectively. Linearized micromechanical relations are first used to provide trial solutions followed by iterative schemes in order to correct errors from linearizing the nonlinear responses. Numerical results are presented to illustrate the performance of each micromechanics model.     

Dynamic strength around two interacting piezoelectric nano-fibers with surfaces/interfaces in solid under electro-elastic waves

Considerable efforts have been devoted to the characterization of the strength at the surfaces/interfaces of piezoelectric nanocomposites. In this paper, the multiple scattering of electro-elastic waves from two piezoelectric nano-fibers in piezoelectric matrix is considered and the dynamic stress at the interface is obtained. A decoupling function is introduced to solve the governing equation in piezoelectric materials. The displacement and electric potential are described by a wave function expansion method. The addition theorem for cylindrical wave function is used to obtain the total coupling wave field. The conventional surface/interface model of Gurtin and Murdoch is extended to the case of coupling stress and electric displacement. The dynamic stress concentration factor around two nano-fibers is obtained. Through numerical analysis, it is found that the interaction between the two nano-fibers has a significant effect on the coupling of stress and electric displacement at the interface, especially in the region of high frequency. The interacting effect of the two piezoelectric interfaces is also related to the properties of the nano-fibers and interface. To show the validity of the dynamic model, comparison with existing results is also given.     

Linear electro-elastic fracture mechanics of piezoelectric materials

The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials. The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads. The energy-release rate expressions show that the electric fields generally tend to slow the crack growth. It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account. The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field.     

Subsonic slip waves along the interface between two piezoelectric solids in sliding contact with local separation

The Stroh formalism of piezoelectric crystals and singular integral equation technique are applied to study the propagation of possible slip waves in presence of local separation at the interface between two frictionless contact piezoelectric solids, which are pressed together by uniaxial pressure and laid in the electric field. The problem is cast into a set of singular integral equations of which the closed solutions are obtained. Discussion on the existence of such slip waves is presented. The results show that such slip waves, which have square-root singularities at both ends of the local separation zones, can propagate in some special material combinations. And the existence of such slip waves is related with the applied mechanical and electric fields.     

Electromechanical analysis of piezoelectric bimorph actuator in static state considering the nonlinearity at high electric field

This article contains electromechanical analysis of a piezoelectric bimorph actuator at high electric field by incorporating second-order constitutive equations of piezoelectric material. Tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically derived for the actuator at high electric field. The analysis shows that output energy and energy density increase more rapidly at high electric field, compared to the prediction by the linear model. The analysis shows energy efficiency depends on electric field. Some analytical results are validated with the published experimental results.     

Messung des piezoelektrischen Effektes an stoßbelasteten Gesteinsstäben

Measurements of the piezoelectric effect of impact loaded rock bars The piezoelectric effect, which causes electric charge at the surface of impact loaded rock bars, is shown by measurements using electrodes. Moreover, electric field of this charge leads to measuring with antenna. The one-dimensional theory of elastic waves in bars is the theoretical basis of computation. The comparison of all the experimentally and numerically determined data has proven a good agreement of typical features of mechanical waves measured by used methods. The electric charge and the antenna signal are measurable on the front surface and on the lateral surfaces of samples. For using later measuring points needs a certain relation between wave length and sensor length. With respect of material of used granite samples the essential requirements are piezoelectrically active rocks. These properties dont depend on quartz content alone. So the piezoelectric effect enables to measure mechanical stress waves by transducer(antenna)which is not physically in contact with the appropriated rock sample.     

车用永磁同步电机电磁噪声分析研究

以电动汽车驱动用永磁同步电机为研究对象,从作用于电机定子表面的电磁力波和电机定子结构的动态特性两个方面对电动汽车驱动用永磁同步电机空载工况的电磁噪声展开研究.通过研究永磁同步电机产生电磁力波的机理,推导了空载工况电磁力波的解析分析方法,结合电磁仿真的手段,精确计算了电机在空载工况下电磁力波的波次、频率和幅值;通过建立电机定子结构的有限元仿真模型及有限元模态仿真计算,得到了定子结构的模态频率和振型.发现：电机定子结构的前6阶模态频率较低,电机空载工况在调速过程中所激发的电磁力容易引起电机定子结构的共振.该研究为电动汽车驱动用永磁同步电机的减振降噪提供了指导.     

Dynamic stress from a cylindrical inclusion buried in a functionally graded piezoelectric material layer under electro-elastic waves

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and dynamic stress around a subsurface cylindrical inclusion in a functionally graded piezoelectric material layer bonded to homogeneous piezoelectric materials. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the inclusion. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. Through the numerical solutions of dynamic stress concentration factors around the inclusion, it is found that when the cylindrical inclusion possesses higher rigidity and greater piezoelectric constant than the two phases of functionally graded materials, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion possesses lower rigidity and smaller piezoelectric constant than the two phases of functionally graded materials, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater. The effect of the properties of the inclusion on the dynamic stress around the inclusion is greater than that on the electric field. The effects of wave frequency on the dynamic stress and electric field are also examined.     

压电复合梁热机电耦合有限元模型

压电材料应用于航天结构形状或振动控制时,可能会受到热场、力场和电场的共同作用。为分析处于热场、力场和电场共同作用下的压电复合结构,文中基于高阶剪切变形理论、高阶电势模型和线性温度分布假设,利用虚功原理建立了压电复合梁结构的热-机-电耦合有限元模型。该模型可应用于热机电耦合压电复合结构的形状与振动控制研究。利用本文模型对压电双晶片梁、压电复合悬臂梁进行了数值仿真,仿真结果与文献给出的理论结果和实验值吻合良好,表明本文模型是正确有效的。     

智能板动荷载监测的压电单元模态法

基于对智能层合板结构的模态分析,提出由结构的压电模态响应反演瞬态荷载时间历程的有限元方法。介绍了压电模态传感器的实现原理,并给出了由实测压电单元输出得到结构模态响应的计算公式。采用无条件稳定的精细逐步积分法求解结构的模态动力学微分方程,构造了通过结构的模态响应反求荷载列阵的迭代算法。该方法作为动态激励的压电模态响应易于实时监测,迭代过程简单可靠、计算速度快、识别精度较高,适用于任意形状和边界条件的复杂型智能结构。实例表明了该方法的可行性。     

Wave propagation analysis in inhomogeneous piezo‐composite layer by the thin‐layer method

The thin‐layer method (TLM) is used to study the propagation of waves in inhomogeneous piezo‐composite layered media caused by mechanical loading and electrical excitation. The element is formulated in the time‐wavenumber domain, which drastically reduces the cost of computation compared to the finite element (FE) method. Fourier series are used for the spatial representation of the unknown variables. The material properties are allowed to vary in the depthwise direction only. Both linear and exponential variations of elastic and electrical properties are considered. Several numerical examples are presented, which bring out the characteristics of wave propagation in anisotropic and inhomogeneous layered media. The element is useful for modelling ultrasonic transducers (UT) and one such example is given to show the effect of electric actuation in a composite material and the difference in the responses elicited for various ply‐angles. Further, an ultrasonic transducer composed of functionally graded piezoelectric materials (FGPM) is modelled and the effect of gradation on mechanical response is demonstrated. The effect of anisotropy and inhomogeneity is shown in the normal modes for both displacement and electric potential. The element is further utilized to estimate the piezoelectric properties from the measured response using non‐linear optimization, a strategy that is referred to as the pulse propagation technique (PPT). Copyright © 2005 John Wiley & Sons, Ltd.     

Multilayer modal actuator-based piezoelectric transformers

An innovative, multilayer piezoelectric transformer equipped with a full modal filtering input electrode is reported herein. This modal-shaped electrode, based on the orthogonal property of structural vibration modes, is characterized by full modal filtering to ensure that only the desired vibration mode is excited during operation. The newly developed piezoelectric transformer is comprised of three layers: a multilayered input layer, an insulation layer, and a single output layer. The electrode shape of the input layer is derived from its structural vibration modal shape, which takes advantage of the orthogonal property of the vibration modes to achieve a full modal filtering effect. The insulation layer possesses two functions: first, to couple the mechanical vibration energy between the input and output, and second, to provide electrical insulation between the two layers. To meet the two functions, a low temperature, co-fired ceramic (LTCC) was used to provide the high mechanical rigidity and high electrical insulation. It can be shown that this newly developed piezoelectric transformer has the advantage of possessing a more efficient energy transfer and a wider optimal working frequency range when compared to traditional piezoelectric transformers. A multilayer piezoelectric, transformer-based inverter applicable for use in LCD monitors or portable displays is presented as well.     

压电智能结构冲击荷载谱的反演方法

基于对智能层合板结构的模态分析，提出由结构的压电模态响应反演瞬态荷载时间历程的有限元方法。介绍了压电模态传感器的实现原理，并给出了由实测压电单元输出得到结构模态响应的计算公式。采用无条件稳定的精细逐步积分法求解结构的模态动力学微分方程，构造了通过结构的模态响应直接反求荷载列阵的迭代算法。该方法迭代过程简单可靠、计算速度快、识别精度高，适用于任意形状和边界条件的复杂智能结构。实例表明了该方法的可行性。     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

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