Study on the step-type circular ring ultrasonic concentrator in radial vibration

In this paper, the plane radial vibration of an isotropic metal thin circular rings is studied and its equivalent circuit model is obtained. Based on the equivalent circuit model, the step-type circular ring concentrator consisting of two metal thin circular rings in radial vibration is analyzed. Its compound equivalent circuit is derived and the resonance frequency equation is obtained. The relationship between the resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions is analyzed. The resonance frequency of the step-type radial concentrator is calculated based on the resonance frequency equation. For comparison, the resonance frequency of the step-type radial concentrator is also obtained by using numerical method. It is illustrated that the resonance frequencies from these two methods are in a good agreement with each other.     

Radial vibration and ultrasonic field of a long tubular ultrasonic radiator

The radial vibration of a metal long circular tube is studied analytically and its electro-mechanical equivalent circuit is obtained. Based on the equivalent circuit, the radial resonance frequency equation is derived. The theoretical relationship between the radial resonance frequency and the geometrical dimensions is studied. Finite element method is used to simulate the radial vibration and the radiated ultrasonic field and the results are compared with those from the analytical method. It is concluded that the radial resonance frequency for a solid metal rod is larger than that for a metal tube with the same outer radius. The radial resonance frequencies from the analytical method are in good agreement with those from the numerical method. Based on the acoustic field analysis, it is concluded that the long metal tube with small wall thickness is superior to that with large wall thickness in producing radial vibration and ultrasonic radiation. Therefore, it is expected to be used as an effective radial ultrasonic radiator in ultrasonic sewage treatment, ultrasonic antiscale and descaling and other ultrasonic liquid handling applications.     

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。      

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。     

Study on the radial composite piezoelectric ceramic transducer in radial vibration

A new type of radial composite piezoelectric transducer in radial vibration is developed and analyzed. The radial composite transducer consists of a piezoelectric ceramic thin ring polarized in the thickness direction and a metal thin circular ring. They are connected together and excited to vibrate in the radial direction. The radial vibrations of a piezoelectric ceramic thin ring and a metal thin circular ring are analyzed, respectively. Their radial electro-mechanical equivalent circuits are obtained. Based on the electro-mechanical equivalent circuits and using the boundary conditions between the piezoelectric ceramic thin ring and the metal thin circular ring in the radial direction, the electro-mechanical equivalent circuit of the radial composite piezoelectric transducer is derived out and the resonance frequency equation is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. Some radial composite piezoelectric transducers are designed and manufactured. The resonance frequencies and the anti-resonance frequencies, the electro-mechanical equivalent circuit parameters are measured. The effective electro-mechanical coupling coefficient and the mechanical quality factor are calculated. It is illustrated that the measured radial resonance frequencies are in good agreement with the theoretical results from the resonance frequency equation.     

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.     

狭缝式环形超声聚能器的径向振动特性

对一种狭缝式环形超声聚能器的径向振动特性进行了研究。基于机电类比原理,通过引入面积比系数,推出了聚能器的径向振动机电等效电路及频率方程;得出了其径向位移振幅放大系数表达式。通过数值计算,探讨了聚能器第1、2阶径向共振频率及振幅放大系数与其半径比的关系;分析了狭缝长度、角度及数目对聚能器振幅放大系数及共振频率的影响,并进行了有限元仿真。研究表明,聚能器的振幅放大系数随其半径比的变化存在极大值,并随狭缝数量、长度及宽度增加而增大;而其径向共振频率则随三者的增加而减小,理论与有限元仿真及实验结果符合较好。      

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,ho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...     

Radial vibration of a slit-type annular ultrasonic concentrator

The radial vibration characteristic of an annular ultrasonic concentrator with multislits is studied.Based on the electro-mechanical analogy and by introducing an area ratio coefficient,the radial vibrational equivalent circuit and the frequency equation of the concentrator are derived.The radial displacement amplitude magnification factor of it is obtained.By numerical calculating,the relationship between the radial displacement amplitude magnification factor,the resonance frequency of the concentrator at the first and second resonance and its radius ratio are investigated.Also,the relationship between the radial displacement amplitude magnification factor,the resonance frequency of the concentrator and the length,the angle and the number of the silts are analyzed.It is illustrated that a maximum of displacement amplitude magnification factor of the concentrator appears with the increase of the radius ratio,and the amplitude magnification factor increase as the length,the angle and the number of the silts increase,while the radial resonance frequency of the concentrator decreases as the length,the angle and the number of the silts increase.The theoretical resonance frequencies are in good agreement with that of the FEM simulations and measurement.     

Analysis of the sandwich piezoelectric ultrasonic transducer in coupled vibration

The coupled vibration of the sandwich piezoelectric transducer with a large cross-section is analyzed using an approximate analytic method. The resonance frequency equations of the transducer are derived and the effect of the geometrical dimensions on the resonance frequency is studied. It is illustrated that when the radial vibration in the transducer is considered, the vibration of the sandwich transducer becomes more complex. Apart from the longitudinal resonance frequency, the radial resonance frequency can also be obtained. For comparison, numerical methods are also used to simulate the coupled vibration; the resonance frequency and the vibrational displacement distribution are computed. Compared with one-dimensional longitudinal theory, the radial dimensions of the transducer are no longer limited because the coupled vibration is considered. Compared with numerical methods, the physical meaning of the analytic method is concise. It is illustrated that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with those from numerical methods, and they are in better agreement with the measured results than those from one-dimensional theory. Since the radial and the coupled vibration are considered in the analysis, more resonance frequencies can be obtained. Therefore, using the coupled resonance frequency equations, the sandwich transducer with multifrequency or wide frequency bandwidth can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry and other applications.     

A new type of high power composite ultrasonic transducer

A new type of high power composite ultrasonic transducer was proposed and studied. The composite transducer consists of a sandwich longitudinal piezoelectric transducer, an isotropic metal hollow cylinder with large radial dimension, and the front and back metal radiation mass. By means of its special structure and Poisson’s effect, the composite transducer can produce vibrations both in its longitudinal and radial directions, and therefore, it can radiate sound waves in three-dimensional space. The electro-mechanical equivalent circuit of the composite transducer was derived and the resonance frequency equation was obtained analytically. Numerical methods were used to simulate the vibration of the composite transducer, and the vibrational displacement distribution, the resonance frequency and the radiation sound field are given. Some composite transducers are designed and manufactured; their resonance frequencies and the radiation acoustic field are measured and compared with the analytical and numerical results. It can be seen that the measured frequencies and acoustic field contour are in good agreement with the analytical and numerical results. It is expected that this kind of composite ultrasonic transducer can be used in more and more power ultrasonic applications, such as ultrasonic cleaning, ultrasonic extraction, ultrasonic sonochemistry and other ultrasonic liquid processing, where high ultrasonic power and large ultrasonic processing space are needed increasingly.     

径向极化压电陶瓷长圆管复合超声换能器的径向振动

提出了一种圆管式径向复合压电陶瓷换能器,并对其径向振动特性进行了分析。该换能器由径向极化的压电陶瓷圆管以及金属外圆管组成。利用解析法得出了金属圆管以及具有任意壁厚的径向极化压电陶瓷圆管径向振动的机电等效电路。基于金属圆管与压电圆管的机械边界条件,得出了换能器的六端机电等效电路。在此基础上得出了换能器共振及反共振频率方程的解析表达式,给出了换能器的共振及反共振频率与其几何尺寸之间的依赖关系。利用数值方法对换能器的径向振动特性进行了模拟及仿真,并与解析结果进行了比较。最后,设计并加工了一些径向复合管式压电陶瓷换能器,利用精密阻抗分析仪对其共振及反共振频率进行了实验测试。研究结果表明,利用解析理论得出的换能器共振及反共振频率与数值模拟结果以及实验测试结果符合很好。      

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。      

Study on the high power air-coupled ultrasonic compound transducer

The high power air-coupled compound ultrasonic transducer in flexural vibration is studied. The transducer consists of a sandwich longitudinal piezoelectric transducer and a circular thin plate in flexural vibration. The resonance frequency equation and the equivalent circuit of a circular radiator with clamped boundary condition are derived. The resonance frequency equation and the equivalent circuit of the compound transducer are also obtained. The radiated acoustic field of the circular thin plate radiator is analyzed and the directional pattern is calculated. It can be seen that when the vibrational order of the circular thin plate in flexural vibration is increased, the radiated acoustic field becomes complex.     

Axisymmetric vibrations of an isotropic elastic non-homogeneous circular plate of linearly varying thickness

Free axisymmetric vibrations of an isotropic, elastic, non-homogeneous circular plate of linearly varying thickness have been studied on the classical theory of plates. The non-homogeneity of the material of the plate is assumed to arise due to the variation of Young's modulus and density with the radius vector whereas Poisson's ratio is assumed to remain constant. The governing differential equation of motion is solved by the method of Frobenius. The transverse displacement of the plate has been expressed as a power series in terms of the radial co-ordinate. The frequency parameters corresponding to the first two modes of vibration have been computed for different values of the non-homogeneity parameter and taper constant and for clamped and simply supported edge conditions of the plate. A comparison between the numerical results for homogeneous and non-homogeneous material of the plate is also made.     

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。      

模式转换环形耦合振动超声辐射器

提出了一种新型耦合振动环形超声辐射器,辐射器由纵振换能器及变幅杆激励特定尺寸的金属圆环,使其能有效地将纵向振动转化为圆环的径向轴向耦合振动从而向环的径向、轴向辐射超声波,并且在环的中心形成聚焦声场。推导了该辐射器的等效电路,给出了等效电路法和有限元法优化设计环形超声辐射器的详细过程。研究了耦合振动环形超声辐射器的谐振特性及其辐射声场特性,根据理论计算结果加工了相应的环形超声辐射器,实验测试结果与理论计算结果符合得较好。本文提出的模式转换环形耦合超声辐射器可望在声化学等液体处理领域获得应用。      

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.     

一种新型Cymbal换能器的研究

提出并研究了一种新型的Cymbal换能器.与传统的Cymbal换能器相比,该换能器中的压电陶瓷圆盘由一个金属圆环和压电陶瓷圆盘的径向组合体所代替.论文首先探讨了压电陶瓷圆盘和金属圆环组合体的径向振动,用解析方法得出了其径向振动的机电等效电路.在此基础上,得出了新型Cymbal换能器的机电等效电路,并得出了其共振及反共振...     

A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.