Optimization of the performance of the sandwich piezoelectric ultrasonic transducer

The resonance and antiresonance frequency, the effective electromechanical coupling coefficient, and the mechanical quality factor of a sandwich piezoelectric ultrasonic transducer are studied and optimized. The effect of the thickness of thick piezoelectric element electrodes on the transducer performance is analyzed. The effect of the length and position of the piezoelectric elements in the transducer is also studied. It is shown that, although using thick electrodes is beneficial for releasing heat produced by the piezoelectric elements, the effective electromechanical coupling coefficient and the mechanical quality factor are reduced. The length and the position of the piezoelectric elements affect the performances of the transducer. Increasing the length of the piezoelectric elements decreases the mechanical quality factor, but the effective electromechanical coupling coefficient increases. When the length reaches a certain value, the effective electromechanical coupling coefficient reaches a maximum value. When the piezoelectric elements are located at the geometrical center or the displacement node, the effective electromechanical coupling coefficient and the mechanical quality factor are maximized.     

声波测井压电振子的有限元分析

压电振子是新一代方位声波测井仪器中相控圆弧阵声波辐射器的重要组成部分。利用有限元法对构成圆弧阵的压电振子进行了设计分析,结果显示了压电振子存在多阶弯曲振动模态,且长度方向一阶弯曲振动能够满足方位声波测井的工作频率要求。针对长度方向一阶弯曲振动模式,数值模拟了几何尺寸对压电振子性能参数的影响。压电振子的谐振频率随着陶瓷片长度、基片或陶瓷片厚度的减小而降低;压电振子的辐射声功率随着陶瓷片长度或压电振子宽度的增加、基片或陶瓷片厚度的减小而增大;合理地选取长度和厚度可使压电振子具有较高的机电耦合系数。数值模拟结果可以对圆弧阵结构优化设计起到良好的指导作用。     

Theoretical analysis and experimental validation of radial cascaded composite ultrasonic transducer

A radial cascaded composite ultrasonic transducer is analyzed.The transducer consists of three short metal tubes and two radially polarized piezoelectric ceramic short tubes arranged alternately along the radial direction.The short metal tubes and the piezoelectric ceramic short tubes are connected in parallel electrically and in series mechanically,which can multiply the input sound power and sound intensity.Based on the theory of plane stress,the electro-mechanical equivalent circuit of radial vibration of the transducer is derived firstly.The resonance/anti-resonance frequency equation and the expression of the effective electromechanical coupling coefficient are obtained.Excellent electromechanical characteristics are determined by changing the radial geometric dimensions.Two prototypes of the transducers are designed and manufactured to support the analytical theory.It is concluded that the theoretical resonance/anti-resonance frequencies are consistent with the numerical and experimental results.When R_2 is at certain values,both the anti-resonance frequency and effective electromechanical coupling coefficient corresponding to the second mode have maximal values.The radial cascaded composite ultrasonic transducer is expected to be used in the fields of ultrasonic water treatment and underwater acoustics.     

复合圆环弯曲振动四极子模态分析

针对压电圆环弯曲振动机电转换性能较差的问题,提出了一种复合圆环弯曲振动换能器,它由一个径向极化的压电陶瓷内圆环和一个金属外圆环复合而成。基于能量原理推导得到了复合圆环弯曲振动的谐振频率和有效机电耦合系数,探讨了弯曲振动四极子模态特性与其结构尺寸间的关系。当压电圆环尺寸不变时,随外侧金属圆环壁厚增加,复合圆环弯曲振动四极子模态谐振频率上升,有效机电耦合系数迅速上升到极大值后缓慢下降。最后,设计制作了圆环换能器并对其谐振频率和有效机电耦合系数进行了实验测试,测试结果与解析结果和数值模拟结果吻合得较好。      

Characteristics of backing impacts on the performance of the thickness mode piezoelectric transducer

The impacts of the thickness, the specific acoustic impedance and the mechanical loss factor of the backing on the performance of the thickness mode piezoelectric transducer are systemically studied, which are focused on the effective electromechanical coupling coefficient and the mechanical quality factor near the center frequency. The results show that with contin?uous increasing of the backing thickness, the effective electromechanical coupling coefficient and the mechanical quality factor are found rapidly declined by oscillation way. With the increase of the difference value of the acoustic impedance between the backing material and the piezoelec?tric material, the effective electromechanical coupling coefficient deceases and the mechanical quality factor increases. Under condition that the thickness of the piezoelectric material is fixed, the effective electromechanical coupling coefficient is found declined with the increase of the mechanical loss factor by monotonous way. The mechanical quality factor has minimum value and the electric characteristic curve tends to be smooth in a given frequency range. The equivalent circuit theory result is in good agreement with the ones by finite element method and the experimental results. The work mentioned above provides a theoretical guidance for the design and experimental fabrication of the thickness mode piezoelectric transducer.     

径向复合圆柱压电超声换能器

提出一种三元径向复合圆柱压电超声换能器,并对其径向振动特性进行了研究。基于弹性力学理论及机电类比原理,导出了柱坐标系中分割处理径向极化压电陶瓷管准厚度模振动及薄壁短圆管径向振动的机电等效电路;利用径向力和振速连续的边界条件,得出了径向复合圆柱压电换能器系统的径向振动机电等效电路及其共振频率方程。探讨了换能器径向共振频率及有效机电耦合系数随其几何尺寸的变化关系。研究表明,换能器的径向共振频率及有效机电耦合系数随其内芯半径和预应力管壁厚度增大而降低。研制了一些径向复合圆柱压电换能器,并对其径向共振频率进行了测试。结果表明,理论与实验结果基本一致。      

背衬参数对厚度模压电换能器特性的影响

系统研究了厚度模压电换能器的背衬厚度、声阻抗率及机械损耗因子对换能器振动性能影响,重点分析了在所关心频率附近的有效机电耦合系数和机械品质因数。计算结果表明,随着背衬厚度增大,换能器的有效机电耦合系数和机械品质因数均震荡减小;背衬声阻抗率与压电片声阻抗率差值增大,换能器有效机电耦合系数减小,机械品质因数增大;保持压电片厚度不变,增大背衬的机械损耗因子,换能器有效机电耦合系数单调减小,机械品质因数有极小值,在给定频率范围内电特性曲线趋于光滑。用有限元方法验证了等效电路计算方法的正确性,并对比了换能器的测试结果和计算结果。计算所得规律为厚度模压电换能器的设计和实验制作提供了理论依据。      

Optimization Design for the Sandwich Piezoelectric Transmitters in Acoustic Logging

An optimized transducer prototype with a sandwich structure vibrated longitudinally is proposed for a transmitter in acoustic logging,especially in acoustic logging while drilling,by taking account of drilling environments with high temperature and pressure,as well as strong collar drilling vibration during the drilling process.Aimed to improve the transmitting performance,numerical and experimental studies for the transducer optimization are conducted.The impact of location and length of the piezoelectric stack on resonance characteristics and effective electromechanical coupling coefficient is calculated and analyzed.Admittance and transmitting performance of the proposed transducer are measured in laboratory experiments,and the results are compared with simulated ones.It is shown that the newly proposed transducer has higher transmitting performance with lower resonance frequencies.This work provides theoretical and experimental bases for transducer designing and acoustic wave measurements in acoustic logging,especially in acoustic logging while drilling.     

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals (PCs), a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper. This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform. Firstly, the vibration of the model is analyzed theoretically, the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established, and the resonance frequency equation is derived. The effects of the length, width, and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method, the effective electromechanical coupling coefficient is also analyzed. The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate. The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method. The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated. The results show that the theoretical results are in good agreement with the simulation results. When the resonance frequency is in the band gap, the decoupling phenomenon occurs, and then the vibration mode in the thickness direction is purer.     

基于2-2型压电复合材料的新型宽频带径向振动超声换能器

本文提出了一种基于2-2型压电复合材料的新型宽频带径向振动超声换能器,它主要由内金属圆环和外压电陶瓷复合材料圆环组成.首先利用Newnham串并联理论和均匀场理论推导了2-2型压电复合材料的等效参数;其次利用解析法得到了金属圆环和径向极化压电复合陶瓷圆环径向振动的机电等效电路;最后得到了换能器的六端机电等效电路,从而得到了换能器的频率方程.接着分析了换能器共振频率和反共振频率以及有效机电耦合系数与几何尺寸、两相体积占比的关系,采用仿真软件对新型换能器的径向振动进行了数值模拟.结果表明,利用解析法得到的共振频率和反共振频率与数值模拟结果吻合较好.此外,对换能器在水下的辐射声场进行了仿真研究,结果表明新型复合材料径向换能器相比传统纯陶瓷径向换能器,发射电压响应幅值更大,工作带宽提高接近一倍,声匹配更佳.     

Effects of coupled vibrations on the parameters of tangentially polarized stripe-electroded piezoelectric cylinders (L)

The effects of coupled vibrations on the piezoelectric properties and electroacoustic transducer performance of radially polarized hollow cylindrical elements as a function of the choice of height-to-diameter ratio have been well documented [J. Acoust. Soc. Am. 120(3), 1374-1380 (2006); J. Acoust. Soc. Am. 122(6), 3419-3427 (2007)]. This letter presents experimental work on the effects of coupled (circumferential, axial, and flexural) vibrations on the resonance frequencies, effective electromechanical coupling coefficient, and acoustical performance of tangentially polarized piezoceramic cylindrical elements. Comparisons are made with analytical predictions of the properties of uniformly circumferentially polarized cylinders.     

阶梯圆环压电超声换能器径向振动性能的理论研究*

提出了一种阶梯圆环径向振动压电超声换能器,根据力电类比原理建立了阶梯圆环及阶梯圆环换能器的径向振动等效电路,推导了阶梯圆环的径向共振频率方程和位移放大系数,在此基础上进一步推导了换能器的径向共振和反共振频率方程。通过理论推导和有限元仿真模拟分析了阶梯圆环压电超声换能器的径向振动性能。结果表明,增大阶梯圆环中内外环的径向厚度之比K1或减小轴向厚度之比K2,阶梯圆环的一阶径向共振频率减小,二阶径向共振频率增大;在二阶径向共振模式下,K1、K2值在一定范围内阶梯圆环可实现由内向外的径向位移振幅放大;随着压电陶瓷圆环的内半径增大,阶梯圆环压电超声换能器的一阶、二阶径向共振和反共振频率减小,二阶径向共振下的有效机电转换系数趋于零;增大阶梯圆环内环的外半径,换能器的一阶径向共振和反共振频率减小,二阶径向共振和反共振频率先增大后减小,理论推导与仿真模拟结果符合良好。本文研究结果为阶梯圆环压电超声换能器的工程应用提供理论参考。     

锥形剖面径向复合超声换能器的机电等效电路

研究了一种锥形剖面径向复合超声换能器。该换能器由一个等截面内金属圆环、一个轴向极化的压电陶瓷圆环和一个锥形剖面外金属圆环沿径向复合而成,且换能器的径向尺寸远大于高度。锥形剖面外金属圆环满足关系式h=h₀r,h₀为厚度变化常数。基于平面应力径向振动理论,推导了换能器的机电等效电路,得到了共振频率方程和反共振频率方程,进而研究了换能器的振动特性。并将理论计算的第1阶、第2阶径向共振频率和反共振频率与数值仿真结果相比较,二者结果一致。研究表明:锥形剖面换能器第1阶、第2阶径向共振频率、反共振频率、有效机电耦合系数不仅与换能器各部分的材料、径向几何尺寸有关,还与h₀有关。h₀越大,第1阶径向共振频率、反共振频率越大,有效机电耦合系数先增大后减小。与等截面相比,锥形剖面换能器沿径向向外辐射声波,辐射面积更大,辐射声功率更高,指向性更好。      

Bender transducer design and operation

An empirical study covering a wide range of bender transducer sizes and operating frequencies is reported. A spherical device model is shown to give good account of bender performance, including interaction effects. A set of empirical rules for scaling equivalent circuit parameters according to the device geometry is identified. An effective spherical radius, approximately half the diaphragm radius, is identified for the typical bender. The effects of pressure and drive voltage on performance are described for particular devices. Sensitivity factors for the equivalent circuit parameters to the operating conditions are determined. These are related to sensitivity factors for the coupling coefficient (Kc) and electromechanical transformer turns ratio (N). Both these parameters are shown to have similar sensitivity responses, decreasing with pressure (planar stress), and increasing with voltage (electric field). The results of high drive tests carried out at Seneca Lake are reported. Values of conventional figures of merit (FOM(V) and FOM(M)), close to the highest claimed for any underwater transducer, are tabled. When allowance for the operating efficiency is included in the figure of merit definitions, the bender appears to be superior to other device types.     

Vibration characteristics of a piezoelectric open-shell transducer

This paper deals with the vibration characteristics of a piezoelectric open-shell transducer which was made by dividing a cylindrical piezoelectric transducer longitudinally into two segments. Two-dimensional governing equations were derived by using the cylindrical membrane theory. Applying mechanical and electrical boundary conditions yielded a characteristic equation for the resonance frequencies of the piezoelectric open-shell transducer. The fundamental frequency and the electromechanical coupling factor were calculated and compared with the results of the finite element analysis and experiment. The fundamental mode shape obtained theoretically was compared with the result of the finite element analysis. The theoretical analysis was verified to provide the vibration characteristics of an open-shell transducer.     

夹心式径向复合压电超声换能器

对夹心式径向复合压电换能器径向振动特性进行了研究。该换能器由弹性内芯、预应力金属管及柱面压电陶瓷晶堆径向复合而成.利用机电类比法,得到了换能器的径向振动等效电路及频率方程。探讨了换能器第1、2阶径向共振频率及有效机电耦合系数与其几何尺寸的关系。研究表明,换能器第1阶径向共振频率随其内芯内径及预应力管壁厚度增大而降低;第2阶共振频率随内芯内径增大存在极小值,但随预应力管壁厚度增大单调下降。此外,采用第2阶径向共振模式能获得较高的有效机电耦合系数,并且压电陶瓷处于位移节线时,换能器有效机电耦合系数达极大值。对换能器共振频率的测试与有限元仿真表明。理论与实验及仿真结果符合较好。      

横波远探测测井换能器研究

为提高偶极子横波远探测反射波的信噪比和增加其探测距离,根据偶极子井孔模式波的激发特性及反射波传播特征分析,研制了基于三叠片的低频大功率偶极子的横波远探测换能器,以降低模式波的相对能量和增加反射波的相对能量。为了得到满足要求的低频大功率偶极换能器,采用有限元方法对现有三叠片进行了优化改进,得到一种符合设计要求的换能器结构,最后制作了样机并对其进行了测试。样机测试结果跟仿真吻合得很好,低频性能得到了极大改善：换能器在谐振频率1.2 kHz附近具有极好的偶极子指向性,谐振频率处的响应比X-MAC同频率段大19 dB。该换能器的研发成功将为偶极子远探测测井仪器性能及成像质量的提高奠定了坚实的基础。     

幂函数型环形聚能器径向振动的等效电路

基于机电类比原理和变厚度薄圆环的平面应力方程,推导了幂函数型环形聚能器径向振动的等效电路、共振频率方程和位移放大系数。讨论了第一、二阶径向共振频率及相应的位移放大系数随圆环半径比的变化关系。结果表明,幂函数型环形聚能器径向振动的等效电路是一种非互易二端口等效网络;一阶和二阶共振频率随圆环内外半径比的增大而增大;一阶径向共振模式下位移放大系数随圆环半径比的增大先降低后升高,二阶径向共振模式下位移放大系数随圆环半径比的增大而降低,但二阶时的位移放大系数整体大于一阶,因此二阶径向共振模式具有更好的径向振动性能。用COMSOL有限元软件对解析理论分析结果进行了验证,仿真模拟结果与解析理论符合良好。根据幂函数型环形聚能器的等效电路模型,进一步设计了一种压电环形换能器,计算了第一、二阶径向共振频率、反共振频率及有效机电耦合系数,通过与COMSOL有限元软件模拟结果对比,符合良好。本文研究结果为幂函数型环形聚能器及压电环形换能器的工程应用提供了简明设计理论,文中研究结论可作为一种径向超声切割刀在超声工程中获得重要应用。      

一种高灵敏压电平面水声换能器

设计并制作了一种高灵敏压电平面水声换能器。该换能器敏感元件是对1-3-2型压电复合材料结构的改进,即在带基底的压电陶瓷小柱阵列间不注入聚合物,并在其上表面直接覆盖金属板,构成“带基底的压电小柱阵列+金属盖板”结构敏感元件(称为“空气填充型”敏感元件)。对“空气填充型”敏感元件的谐振频率进行了理论计算和有限元仿真,与实测结果较吻合。为便于对比性能,同时制作了同尺寸“1-3-2型压电复合材料+金属盖板”结构敏感元件(称为“聚合物填充型”敏感元件)换能器。分别对“空气填充型”和“聚合物填充型”敏感元件换能器的有效机电耦合系数、发送电压响应和接收灵敏度进行有限元仿真和实测,结果均显示,“空气填充型”敏感元件换能器具有较高的接收灵敏度,相较于“聚合物填充型”敏感元件换能器可提高21 dB。该敏感元件换能器能有效提高灵敏度,可为研制高灵敏换能器提供参考。      

换能器前辐射头与轴向相平行方向的弯曲振动

复合棒型换能器前面的变截面组件在工作时常伴有弯曲振动现象，这在一定程度上会影响换能器的工作性能；利用复合棒型换能器的纵向振动基频与前辐射头弯曲振动的恰当耦合，可展宽换能器的频带。本文用有限元法，研究了前辐射头在声换能器组成中的弯曲振动问题，与测试结果相吻合。