Vibration of piezoelectric/elastic laminated trimorph ring transducer

This article describes the vibration characteristics of the trimorph ring transducer that consists of an isotropic elastic ring laminated between two identical piezoelectric rings under mechanical traction-free and constant electric voltage boundary conditions. The electro-elasticity theory with Kirchhoff-Love plate theory was applied to formulate the electromechanical solution. The resonance, antiresonance frequencies with corresponding mode shapes were verified by the measured impedance frequency responses. And, the design of maximized electromechanical coupling coefficients (EMCC) is proceeded.     

低Qm压电振子机电耦合系数的标准计算方法的原理误差分析

压电材料的机电耦合系数通常由谐振及反谐振频率之间的相对间隔确定。常用的ＩＥＥＥ标准计算公式,是由描述理想无损压电振子的电行为方程推导得出的。本文结出了压电材料的固有损耗产生的谐振及反谐振频率的偏移及由此引起的标准公式的误差。代替以往分析时常用的等效电路方法,本文采用把损耗考虑在内的严格的压电振子导纳或阻抗模型。分析结果表明：由测得的谐振子及反谐振频率用标准公式得出的耦合系数小于材料的固有耦合系数;     

用于超声清洗复合振动换能器的研究

本文研究了一种由纵向振动夹心式压电超声换能器与弯曲圆盘组成的用于液体中超声处理的复合振动辐射器。推出了恢复合振动系统的共振频率设计方程，分析了各个振动模式的机电转换特性及其声波辐射特性，测量了振动系统的共振频率及其有效机电耦合系数。从实验及理论结果可以看出，振动系统的频率测试值与设计值基本符合。在一定的共振频率上，该振动系统具有最大的有效机电耦合系数，是一种很有前途的功率超声辐射器。     

Efficiency of excitation of piezoceramic transducers at antiresonance frequency

The efficiency of piezoceramic transducers excited at both the resonance and antiresonance frequency was investigated. Losses in piezoceramics are phenomenologically considered to have three coupled mechanisms: dielectric, mechanical, and piezoelectric losses. Expressions for the resonance and antiresonance quality factors, which ultimately determine transducer efficiency, have been received on the basis of complex material constants for both stiffened and unstiffened vibration modes. Comparison of electric and mechanical fields, thermal and electrical losses of power supply, and their distribution in the transducer volume have been made. For a given constant mechanical displacement of the transducer top, the required electric voltage applied to the transducer at the antiresonance frequency is proportional to the resonance quality factor, but the changes in the intrinsic electric and mechanical field characteristics in the common case are not too essential. The requirements on the piezoceramic parameters, types of transducer vibration, and especially on the factor of piezoelectric losses in a range of physically valid values were established to provide maximal quality factors at the antiresonance frequency.     

Analysis of a disk-type piezoelectric ultrasonic motor using impedance matrices

The dynamic behavior and the performance characteristics of the disk-type traveling wave piezoelectric ultrasonic motors (USM) are analyzed using impedance matrices. The stator is divided into three coupled subsystems: an inner metal disk, a piezoelectric annular actuator with segmented electrodes, and an outer metal disk with teeth. The effects of both shear deformation and rotary inertia are taken into account in deriving an impedance matrix for the piezoelectric actuator. The impedance matrices for each subsystem then are combined into a global impedance matrix using continuity conditions at the interfaces. A comparison is made between the impedance matrix model and the three-dimensional finite element model of the piezoelectric stator, obtaining the resonance and antiresonance frequencies and the effective electromechanical coupling factors versus circumferential mode numbers. Using the calculated resonance frequency and the vibration modes for the stator and a brush model with the Coulomb friction for the stator and rotor contact, stall torque, and no-load speed versus excitation frequencies are calculated at different preloads. Performance characteristics such as speed-torque curve and the output efficiency of the USM also are estimated using the current impedance matrix and the contact model. The present impedance model can be shown to be very effective in the design of the USM.     

Modeling for temperature compensation and temperature characterizations of BAW resonators at GHz frequencies

This paper deals with the temperature dependence of electrical and physical features of various kinds of solidly mounted resonators (SMR). The presented bulk acoustic wave (BAW) devices are designed for the 2 GHz application. The temperature coefficient of frequency (TCF) is determined from measurements well above the temperature range defined for wireless telecommunication system specifications. Therefore, evolution of electromechanical coupling factors and quality factors at resonance and antiresonance are also monitored. Results of characterizations show the trend for a subsequent theoretical temperature compensation study by using analytical modeling. To improve accuracy of modeling, an attempt to extract temperature dependence of dielectric permittivity epsilon(33) and piezoelectric coefficient e(33) is made. Finally, a well-known analytical model is modified to take into account the temperature dependence of length, density, stiffness coefficient, dielectric permittivity, and piezoelectric coefficient. Modeling highlights the need to deposit a material with positive temperature coefficient of stiffness on the top electrode. Realistic thickness of such a layer is determined. At the same time, it is necessary to adjust piezoelectric and electrode thin film thicknesses for simultaneously keeping a constant antiresonance frequency, reaching a zero temperature coefficient of frequency for antiresonance, and minimizing the decrease in the coupling factor because of the mass-loading deposition.     

三叠片压电复合换能器弯曲振动的比较研究

用瑞利法对三叠片弯振圆盘换能器在三种不同边界条件下的振动特性进行理论研究,推导了谐振频率及有效机电耦合系数的表达式,通过数值计算分析了复合换能器的谐振频率及有效机电耦合系数随换能器各结构参数的变化规律并进行比较研究,同时将计算结果与有限元模拟结果比较,结果表明不同边界条件下换能器的结构参数对谐振频率和有效机电耦合系数影响不同:在换能器结构参数一定时,自由边界条件下谐振频率最大,简支边界条件下最小,固定边界条件下次之;有效机电耦合系数随着金属片厚度、陶瓷片厚度和陶瓷片半径变化时,分别有一个最大值;其他参数一定时,有效机电耦合系数在简支边界条件下最大,自由边界条件下的值稍大于固定边界条件下的值。上述研究结果可为三叠片弯曲振动换能器的设计和实际应用提供一定的理论支持。     

Elastic, dielectric, and piezoelectric losses in piezoceramics: how it works all together

The quality factor along with electromechanical coupling coefficient (CEMC) is commonly used as a measure of the energy efficiency of a piezoelectric transducer (PT) working as an energy converter. Losses in piezoceramics are phenomenologically considered to have three coupled mechanisms: dielectric, elastic, and piezoelectric. Their cumulative performance first of all determines the PT quality factor characterizing the efficiency of vibrational energy accumulation, and related to it dissipative effects. The extended definition of the PT electromechanical quality factor (EMQ) with permanent energy exchange between electrical source of excitation and PT was proposed. The EMQ analysis has been conducted on the basis of complex material constants for both stiffened and unstiffened canonical vibrational modes. The efficiency of mechanically free and electrically excited piezoceramic transducers in a wide frequency range of PT harmonics, especially between the fundamental resonance and antiresonance frequencies, was investigated, and the effect of piezoelectric loss anomaly with extremely low total losses was predicted. Particularly, optimization of PT excitation with connected reactive (capacitive) element was conducted to provide higher PT mechanical vibrational characteristics with less total losses. The requirements to the piezoceramic material parameters, types of transducer vibrations, and especially to the piezoelectric loss factor in the range of physically valid values were established to provide maximal EMQ.     

Determination of electromechanical coupling factors of low Q piezoelectric resonators operating in stiffened modes

The electromechanical coupling coefficient is usually determined from the relative spacing of the frequencies of resonance and antiresonance. The conventional formula is derived from equations describing the electrical behavior of an ideal piezoelectric resonator in the absence of losses. In this paper, the influence of the intrinsic material losses on the shift of the resonance/antiresonance frequencies, and therefore on the accuracy of the standard formula to determine k, is analyzed. The exact one-dimensional model of the piezoelectric resonator vibrating in a pure stiffened mode, with a rigorous account of the internal mechanical losses, has been taken as a reference, instead of the frequently used lumped approximate equivalent circuit (Butterworth-Van Dyke). It is shown that the coupling coefficient determined from the frequencies f(s) and f(p) is less than the intrinsic coupling coefficient, and that the error increases for highly attenuating materials with weak electromechanical coupling. The error due to the effect of attenuation, which increases with the decrease of the product Q(m)k of the resonator intrinsic parameters, has been systematically evaluated and plotted for 0.5相似文献   

一种超声手术刀推挽激励换能器的研究

设计了一种超声手术刀用的新型推挽激励换能器。它是在夹心式单晶堆压电超声换能器的经典构造基础上,把原先激励一组压电陶瓷晶片堆的方式,改为同时施加反相激励的前后两组晶堆。利用有限元方法,对该推挽激励换能器进行模态分析和频率响应分析。在相同大小的电压激励下,相对单晶堆换能器,推挽激励换能器可以获得更高的工作带宽和机电耦合系数,提高了换能器的电声转换效率。按照仿真结果加工推挽激励换能器,实现良好的动力学和电学特性,满足设计要求。     

A dynamics model for nonlinear electrostrictive actuators

This paper examines the nonlinear vibration of an electrostrictive ceramic rod actuator excited by a harmonic voltage source. A frequency-domain model was developed using the nonlinear constitutive law for electrostriction. The results predict harmonic distortion of the device's displacement due to the ceramic's nonlinear behavior. AC voltage signal and DC voltage bias were studied to determine the optimum power source parameters for minimizing distortion. The calculations show that the rod's resonance frequency and amplitude depend on the electromechanical coupling strength and differ greatly for large AC voltages from the equivalent linear piezoelectric results. The nonlinear analysis relates the device's electromechanical coupling coefficient to the computed resonance and antiresonance frequencies. This important result could provide the basis for future measurement of the electrostrictive coupling coefficient using resonance techniques.     

Resonance acoustoelasticity measurement of stress in thin plates

A computer-driven, swept-frequency measurement technique is developed on the basis of resonance birefringence acoustoelasticity to evaluate the stresses in thin plates. The resonance frequency depends on the thickness and the elastic wave velocity; they change with stress because of the Poisson effect and the acoustoelastic effect. The resonance frequency is obtained from the spectral response curve in the electric impedance of the piezoelectric transducer. The frequency displacement induced by acoustically coupling the transducer can be minimized by employing the resonance peak closest to the transducer fundamental frequency. To illustrate the method, the residual stress is measured in butt-welded aluminum alloy plates and is compared with the results of conventional methods.     

Radiation impedance and equivalent circuit for piezoelectric ultrasonic composite transducers of vibrational mode-conversion

The piezoelectric ultrasonic composite transducer, which can be used in either gas or liquid media, is studied in this paper. The composite transducer is composed of a longitudinal sandwich piezoelectric transducer, a mechanical transformer, and a metal circular plate in flexural vibration. Acoustic radiation is produced by the flexural circular plate, which is excited by the longitudinal sandwich transducer and transformer. Based on the classic flexural theory of plates, the equivalent lumped parameters for a plate in axially symmetric flexural vibration with free boundary conditions are obtained. The radiation impedance of the plate is derived and the relationship between the radiation impedance and the frequency is analyzed. The equivalent circuits for the plate in flexural vibration and the composite transducer are given. The vibrational modes and the harmonic response of the composite piezoelectric transducer are simulated by the numerical method. Based on the theoretical and numerical analysis, two composite piezoelectric ultrasonic transducers are designed and manufactured, their admittance-frequency curves are measured, and the resonance frequency is obtained. The flexural vibrational displacement distribution of the transducer is measured with a laser scanning vibrometer. It is shown that the theoretical results are in good agreement with the measured resonance frequency and the displacement distribution.     

表面波电磁声换能器及电声学特性的研究

电磁超声换能器的非接触、信号重复性好等特点使得其在高温自动检测、材料特性测量等领域有着广泛的应用前景。利用电磁超声技术激发表面波更是行之有效的方法,论文着重于理论分析,对表面波电磁声换能器的物理结构、电声学特性作了较为全面和深入的研究,并用等效电路模型探讨了阻抗匹配的方法。结果表明,电磁声换能器为感性负载,不同于压电器件的容性负载特性,因此对换能器的设计和优化也有着独自的特性;随着提离距离的增大,相应的换能效率也将急剧下降;阻抗匹配对于提高信号的输出强度,抑制谐波分量有着重要的作用,而采用电容并联匹配相比串联匹配,能够提供更高的转换效率。     

DC bias-dependent shift of the resonance frequencies in BST thin film membranes

Direct current (DC) bias-dependent acoustic resonance phenomena have been observed in micromachined tunable thin film capacitors based on Ba(0.3)Sr(0.7)TiO3 (BST) thin films. The antiresonance frequency is only weakly DC bias dependent, and the resonance frequency exhibits a much stronger dependence on the applied DC bias. The resonance frequency shifted by 1.2% for a frequency of about 6.7 GHz and an applied field of 667 KV/cm. At the same time the effective electromechanical coupling constant k(2)(t,eff) increased to 2.0%. The tuning of the resonance frequency depends on the tunability of the film permittivity and on the mechanical load on the piezoactive layer. The experimental observations correlate well with the theoretical predictions derived from the free energy P expansion using Landau theory.     

Calculation and measurement of electromechanical coupling coefficient of capacitive micromachined ultrasonic transducers

The electromechanical coupling coefficient is an important figure of merit of ultrasonic transducers. The transducer bandwidth is determined by the electromechanical coupling efficiency. The coupling coefficient is, by definition, the ratio of delivered mechanical energy to the stored total energy in the transducer. In this paper, we present the calculation and measurement of coupling coefficient for capacitive micromachined ultrasonic transducers (CMUTs). The finite element method (FEM) is used for our calculations, and the FEM results are compared with the analytical results obtained with parallel plate approximation. The effect of series and parallel capacitances in the CMUT also is investigated. The FEM calculations of the CMUT indicate that the electromechanical coupling coefficient is independent of any series capacitance that may exist in the structure. The series capacitance, however, alters the collapse voltage of the membrane. The parallel parasitic capacitance that may exist in a CMUT or is external to the transducer reduces the coupling coefficient at a given bias voltage. At the collapse, regardless of the parasitics, the coupling coefficient reaches unity. Our experimental measurements confirm a coupling coefficient of 0.85 before collapse, and measurements are in agreement with theory.     

面剪切振动模式弛豫铁电单晶换能器

[011]极化方向、zxt-45°切型的PIN-PMT-PT单晶因其高剪切压电应变常数、高机电耦合系数和高柔顺系数等特点,在水声换能器中存在广阔的应用前景.通过设计中间质量块的方法,将单晶产生的剪切振动转换为换能器的纵向振动,并利用辐射头的弯曲振动和圆环尾质量块振动的耦合拓宽工作频带.通过有限元仿真分析,研究了结构参数...     

压电陶瓷圆环与金属圆环复合振动系统的径向振动

对由压电陶瓷圆环与金属圆环组成的复合振动系统的径向振动特性进行了研究。首先分析了压电陶瓷圆环和金属圆环的径向振动,推出了其各自的机电等效电路。在此基础上,得出了压电陶瓷圆环与金属圆环复合振动系统的机电等效电路及其共振频率方程。探讨了系统的共振及反共振频率、有效机电耦合系数与其几何尺寸之间的关系。研究表明,当复合振动系统的壁厚比增大时,其共振及反共振频率升高。对于换能器的第一阶径向振动,其有效机电耦合系数随壁厚比的增大而单调减小;对于换能器的第二阶径向振动,其有效机电耦合系数随壁厚比的增大会出现一个极大值,而且,在一定的壁厚比范围内,换能器第二阶径向振动的有效机电耦合系数大于第一阶径向振动的有效机电耦合系数,这一规律与传统的有关压电换能器的分析理论及结果是有所不同的。     

Radial vibration of the composite ultrasonic transducer of piezoelectric and metal rings

The radial composite ultrasonic transducer of a piezoelectric ceramic ring and a metal ring is studied. The radial vibrations of a piezoelectric ceramic ring polarized in the thickness direction and a metal ring are analyzed and their electromechanical equivalent circuits are obtained. On the basis of the electromechanical equivalent circuits of the piezoelectric and the metal ring and the radial boundary conditions, the total electromechanical equivalent circuit for the composite ultrasonic transducer is also obtained. The resonance frequency and anti-resonance frequency equations of the composite ultrasonic transducer are given. Some radial composite ultrasonic transducers are designed and manufactured and their resonance and anti-resonance frequencies are measured. Experiments show that the measured resonance frequencies are in a good agreement with the theoretical results.     

Analysis of methods for determining electromechanical couplingcoefficients of piezoelectric elements

An important characteristic of piezoelectric elements as energy converters is the energy conversion efficiency. The electromechanical coupling coefficient (EMCC) is commonly used as a measure of a piezoelectric elements' efficiency. The latest Standard on Piezoelectric recommends that EMCC be determined by the use of the Berlincourt et al. formula for a uniform electroelastic state, and the dynamic formula by Mason for near resonance frequencies. This paper is devoted to the analysis of these two formulas along with a third formula. The EMCC of commonly seen piezoelectric elements are formulated and analyzed. The comparison of the numerical results leads us to the following conclusions: 1. The formula of Berlincourt et al. is valid only for a uniform electroelastic state, 2. The dynamic formula of Mason gives the EMCC at a frequency equal to the arithmetic mean of resonance and the corresponding antiresonance frequencies, 3. The third formula for the EMCC is valid for both the static and dynamic electroelastic state of a piezoelement, and its results are in good agreement with those found by using Berlincourt's formula and the dynamic formula of Mason