纵弯及纵径振动模式转换功率超声换能器的研究
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摘要
随着超声应用的进一步发展,功率超声技术已广泛用于农业、工业、环境保护、医药卫生和国防等领域,尤其在超声焊接、超声清洗、超声化学及超声中草药提取等应用领域,此时单一振动模式的换能器已不能满足一些特定领域的应用要求,非常需要一些辐射面积较大的功率超声换能器。为了提高换能器的功率并增大超声波的辐射面积,往往需要一些模式转换型和耦合振动模式的超声换能器。本文基于模式转换的思想,即,一种振动模态转换为另一种或多种耦合的振动模态,研究了纵弯振动模式转换及纵径耦合振动模式功率超声换能器,其主要内容包含：
(1)介绍了夹心式压电超声换能器各部分(包括压电陶瓷晶堆及变截面棒)的设计理论,并给出了其机电等效电路及频率方程；同时,以夹心式换能器的前端面振动位移振幅为目标,介绍了有限元软件ANSYS优化设计的方法和步骤,给出了优化计算结果,希望该理论及优化方法为本论文后续模式转换功率超声换能器中夹心式压电换能器的设计提供理论基础。
(2)从薄圆盘弯曲复合振动系统或纵弯模式振动系统的优化设计出发,提出了分布参数系统集中参数化的概念,根据一分布参数系统的动能和势能与另一具有集中参数系统的对应动能和势能相等的原则,得出了三种边界条件即自由边界、固定边界和简支边界薄圆盘弯曲振动的集中等效参数：等效质量和等效弹性系数。然后从辐射声功率角度求得了圆盘的辐射声阻抗,画出了薄圆盘弯曲振动时的集中参数等效电路图,并得出了其共振频率方程。对于相同尺寸且振动在相同阶数的圆盘而言,自由边界条件的共振频率大于简支边界条件的共振频率,但小于固定边界的共振频率,不过,三种边界条件下计算的理论值都与模拟值都比较吻合。因此,圆盘的集中参数等效电路对弯曲振动系统的设计提供了理论参考,期望能够用于系统的机电等效电路中,大大简化其求解过程,方便设计最佳工作状态。
(3)对大尺寸的弹性金属柱体及压电陶瓷柱体进行了分析,得出了它们的等效电路或频率方程。首先,基于表观弹性法,分析了大尺寸环状金属柱体的等效电路,为用机电等效电路法设计超声振动系统提供了方便,不过此种情况主要适用于薄壁柱体,即壁厚远小于外半径。其次,基于弹性动力学方程,根据环状柱体两端及内、外两侧的自由边界条件,推导出了半径、厚度及长度任意变化的环状弹性柱体共振频率方程,结果表明,理论结果与数值模拟有很好的一致性,为纵径耦合振动系统的设计提供了一定的理论。最后,在环状弹性柱体分析的基础上,运用相似的分析方法,简单地对大尺寸压电陶瓷柱体进行了理论分析。
(4)根据弯曲振动薄圆盘集中等效参数的分析,提出了一种新型的纵弯模式转换压电超声换能器,包含后盖板、轴向极化的压电陶瓷片及弯曲振动金属圆盘。推导出了该换能器纵弯振动模式的机电等效电路,并得出了其共振频率方程。通过该类换能器频率方程可以看出,其共振频率及反共振频率随其材料参数和几何尺寸的变化而变化。因此可以根据此方程确定频率或几何尺寸等,为设计该类换能器提供了方便。其次利用有限元软件ATILA分析了整个换能器的振动性能及辐射声场的分布情况。最后,设计并加工了相应的模式转换换能器,分别用精密阻抗分析仪Agilent Hp4294测试了该换能器的频率变化特性曲线,用全场扫描式激光测振仪Polytec PSV-400测试了换能器的端面位移振幅分布。通过有限元软件模拟及实验测试结果可以看出,该换能器通过纵向激励单元的纵向振动带动辐射端面产生弯曲振动,并使其整体处于同一共振模式,即纵弯振动模式,从而增大了传统夹心式换能器的辐射面积,为大功率及大辐射面积换能器的设计提供了思路。
(5)根据环形柱体纵径耦合振动的分析,提出了一种新型的纵径耦合振动模式柱状压电超声换能器,包含纵向振动夹心式压电换能器、柱状金属圆管及前后辐射金属盖板。根据传输线理论和梅森机电等效模型,利用柱状换能器各部分连接处边界上力和速度连续的特性,得到了纵径耦合振动模式柱状压电超声换能器的机电等效电路,并得出了其共振频率方程。其次,利用有限元软件分析了整个换能器的振动性能,并用ANSYS软件的参数化优化编程技术对其振动特性进行了优化设计。最后,分析了相同尺寸的换能器在空气中及水中的位移及声场情况,选择了合适尺寸的换能器对其声场进行了分析。该柱状超声换能器通过激励夹心式换能器产生弯曲振动,带动前后辐射盖板做纵向振动的同时,柱状金属圆管做纵径耦合振动,并使其整体处于同一共振模式,即纵径耦合振动模式。能够看出,换能器的两端面振动位移分布基本均匀,同时,在柱状换能器的侧面产生径向振动；且随着换能器的径向尺寸与纵向尺寸比值的增加,径向振动位移逐渐增大。对柱状换能器空气中振动及水中的声场进行比较,可以看出,共振频率与换能器中金属柱体的壁厚有密切的关系。因此,选择合适的尺寸,该类柱状压电超声换能器将能够被用作一个三维超声辐射器,同时第二阶的辐射声压也比较强,也期望该类换能器能够作为多频的超声辐射器。
With the development of ultrasonic application, ultrasonic technology has been widely used in the fields of agriculture, industry, environment protection, medicine and national defense, and so on. Especially in the ultrasonic welding, ultrasonic cleaning, ultrasonic chemistry and ultrasonic extraction of Chinese herbal medicine and other applications, the transducers of single vibration mode cannot meet the requirements of some specific applications, and so, some power transducers with larger radiation area should be urgently needed. In order to improve power and increase ultrasonic radiation area, some mode-conversion ultrasonic transducers are often needed. In this paper, based on the mode-conversion theory, i.e. a vibration mode is converted into the other or more coupled vibration mode, the power ultrasonic transducers for longitudinal-flexural vibration mode-conversion and longitudinal-radial coupled vibration are developed and the main contents include as follows:
(1) The design theory of the sandwich piezoelectric ultrasonic transducer (including the piezoelectric ceramic pile and variable cross section bar) is introduced, and its electro-mechanical equivalent circuit and resonance frequency equation are given. Then, taking vibrational displacement amplitude of the transducer's front end as the goal, the method and step of the optimization design are introduced by using the finite element software ANSYS, and the optimization results are given. It is expected that the theory of the sandwich piezoelectric ultrasonic transducer can provide a theoretical basis for the design of the following mode-conversion power ultrasonic transducers.
(2) From the point of optimization design of flexural composite vibration system and longitudinal-flexural mode vibration system, for the distributed parameter system, the concept of lumped parameter is put forward. According to the equivalent principle of the kinetic energy and the potential energy for a distributed parameter system and another lumped parameter system, we give the lumped parameter equivalent mass and equivalent elasticity coefficient of the flexural vibration plate with the free boundary, and fixed boundary or simply supported boundary. From the point of radiation sound power, the radiation impedance is obtained. Then, the lumped parameter equivalent circuit is drawn and the resonance frequency equation is given. For the same dimension plate in the same order, resonant frequency with free boundary condition is larger than that with the simply supported boundary condition, but smaller than the resonance frequency with the fixed boundary condition. The theoretical values with three kinds of boundary conditions are consistent with the simulated ones. Therefore, these results can serve as a reference for designing flexural vibration systems and the theory is convenient to design the best working state.
(3) The elastic metal cylinder and the piezoelectric ceramic cylinder with larger dimension are analyzed, and their equivalent circuits or frequency equations are obtained. Firstly, based on the apparent elasticity method, the equivalent circuit of metal cylinder is analyzed, which provides convenience for the design of ultrasonic vibration system by using electro-mechanical equivalent circuit method, but this situation is mainly suitable for thin-wall cylinder. Secondly, based on elastic dynamic equation and according to the boundary conditions of free-end annular elastic cylinder, the resonance frequency equation of annular cylinder with arbitrary dimension of longitudinal-radial coupled vibration is derived. The results show that the analytical resonance frequencies are in good agreement with the numerical results. This theory can serve as reference for the design of the longitudinal-radial composite vibrational systems. Finally, based on the analysis of the annular elastic cylinder, using the similar analytical method, the theory of the piezoelectric ceramic cylinder with large dimension is simply analyzed.
(4) A new type of piezoelectric ultrasonic transducer for longitudinal-flexural vibrational mode-conversion is proposed. The mode-conversion transducer has a back metal mass, longitudinally polarized piezoelectric ceramic pile, and a circular metal plate. Based on the equivalent lumped parameters of the thin plate, the equivalent circuit and resonance frequency equation of the mode-conversion transducer are given. It can be seen from the frequency equation that the resonance frequencies and anti-resonance frequencies depend on the material parameters and the geometrical dimensions. This theory provides convenience for the design of this kind of transducer. Then, by using the finite element software ATILA, the vibration properties and sound radiation distribution of the whole transducer are analyzed. Finally, the vibrational mode-conversion transducers with the same simulated parameters and geometric dimensions are manufactured. The frequency characteristics and the amplitude distribution of the end surface of the transducers are measured by using Agilent Hp4294precision impedance analyzer and the scanning laser vibrometer Polytec PSV-400. It can be seen that the longitudinal vibration of the piezoelectric vibrator drives the circular metal plate to produce flexural vibration, i.e. the whole transducer is in longitudinal-flexural vibration mode, which increases the radiation area of the conventional sandwich transducer. The theory provides a design idea for high power transducers with large radiation area.
(5) The longitudinal-radial coupled vibration of a cylindrical piezoelectric ultrasonic transducer with large geometrical dimensions is analyzed. The cylindrical transducer is composed of a longitudinal sandwich transducer, a metal tube and two metal radiation masses. According to the transmission line theory and Mason electro-mechanical equivalent model, by using force and velocity continuity of the transducer boundaries, the electro-mechanical equivalent circuit and the resonance frequency equation of the cylindrical transducer are derived. Then, the vibration performance of the transducer is analyzed and optimized by using the finite element software. Finally, the displacement and the sound pressure are analyzed. The front and the back metal radiation masses are driven to vibrate longitudinally by the inner sandwich longitudinal transducer, which causes the metal tube to produce longitudinal-radial coupled vibration. It can be seen that the axial vibrational displacements on the two end surfaces of the cylindrical transducer are basically uniformly distributed. On the other hand, the radial vibration on the side cylindrical surface is produced. And with the increase of radial-longitudinal ratio of the transducer, radial vibration displacement increases gradually. Compared with vibration distribution in air and sound pressure in water, resonance frequency and wall thickness of the cylindrical transducer have a close relationship. Therefore, if the right dimensions can be chosen, this kind of cylindrical transducer must be used as a three-dimensional ultrasonic radiator. At the same time, the cylindrical transducer can also produce the obvious longitudinal-radial coupled vibration at the second vibrational mode. Therefore, it is expected that the kind of transducer can also be used as a new type of multi-frequency radiator.
(1)介绍了夹心式压电超声换能器各部分(包括压电陶瓷晶堆及变截面棒)的设计理论,并给出了其机电等效电路及频率方程；同时,以夹心式换能器的前端面振动位移振幅为目标,介绍了有限元软件ANSYS优化设计的方法和步骤,给出了优化计算结果,希望该理论及优化方法为本论文后续模式转换功率超声换能器中夹心式压电换能器的设计提供理论基础。
(2)从薄圆盘弯曲复合振动系统或纵弯模式振动系统的优化设计出发,提出了分布参数系统集中参数化的概念,根据一分布参数系统的动能和势能与另一具有集中参数系统的对应动能和势能相等的原则,得出了三种边界条件即自由边界、固定边界和简支边界薄圆盘弯曲振动的集中等效参数：等效质量和等效弹性系数。然后从辐射声功率角度求得了圆盘的辐射声阻抗,画出了薄圆盘弯曲振动时的集中参数等效电路图,并得出了其共振频率方程。对于相同尺寸且振动在相同阶数的圆盘而言,自由边界条件的共振频率大于简支边界条件的共振频率,但小于固定边界的共振频率,不过,三种边界条件下计算的理论值都与模拟值都比较吻合。因此,圆盘的集中参数等效电路对弯曲振动系统的设计提供了理论参考,期望能够用于系统的机电等效电路中,大大简化其求解过程,方便设计最佳工作状态。
(3)对大尺寸的弹性金属柱体及压电陶瓷柱体进行了分析,得出了它们的等效电路或频率方程。首先,基于表观弹性法,分析了大尺寸环状金属柱体的等效电路,为用机电等效电路法设计超声振动系统提供了方便,不过此种情况主要适用于薄壁柱体,即壁厚远小于外半径。其次,基于弹性动力学方程,根据环状柱体两端及内、外两侧的自由边界条件,推导出了半径、厚度及长度任意变化的环状弹性柱体共振频率方程,结果表明,理论结果与数值模拟有很好的一致性,为纵径耦合振动系统的设计提供了一定的理论。最后,在环状弹性柱体分析的基础上,运用相似的分析方法,简单地对大尺寸压电陶瓷柱体进行了理论分析。
(4)根据弯曲振动薄圆盘集中等效参数的分析,提出了一种新型的纵弯模式转换压电超声换能器,包含后盖板、轴向极化的压电陶瓷片及弯曲振动金属圆盘。推导出了该换能器纵弯振动模式的机电等效电路,并得出了其共振频率方程。通过该类换能器频率方程可以看出,其共振频率及反共振频率随其材料参数和几何尺寸的变化而变化。因此可以根据此方程确定频率或几何尺寸等,为设计该类换能器提供了方便。其次利用有限元软件ATILA分析了整个换能器的振动性能及辐射声场的分布情况。最后,设计并加工了相应的模式转换换能器,分别用精密阻抗分析仪Agilent Hp4294测试了该换能器的频率变化特性曲线,用全场扫描式激光测振仪Polytec PSV-400测试了换能器的端面位移振幅分布。通过有限元软件模拟及实验测试结果可以看出,该换能器通过纵向激励单元的纵向振动带动辐射端面产生弯曲振动,并使其整体处于同一共振模式,即纵弯振动模式,从而增大了传统夹心式换能器的辐射面积,为大功率及大辐射面积换能器的设计提供了思路。
(5)根据环形柱体纵径耦合振动的分析,提出了一种新型的纵径耦合振动模式柱状压电超声换能器,包含纵向振动夹心式压电换能器、柱状金属圆管及前后辐射金属盖板。根据传输线理论和梅森机电等效模型,利用柱状换能器各部分连接处边界上力和速度连续的特性,得到了纵径耦合振动模式柱状压电超声换能器的机电等效电路,并得出了其共振频率方程。其次,利用有限元软件分析了整个换能器的振动性能,并用ANSYS软件的参数化优化编程技术对其振动特性进行了优化设计。最后,分析了相同尺寸的换能器在空气中及水中的位移及声场情况,选择了合适尺寸的换能器对其声场进行了分析。该柱状超声换能器通过激励夹心式换能器产生弯曲振动,带动前后辐射盖板做纵向振动的同时,柱状金属圆管做纵径耦合振动,并使其整体处于同一共振模式,即纵径耦合振动模式。能够看出,换能器的两端面振动位移分布基本均匀,同时,在柱状换能器的侧面产生径向振动；且随着换能器的径向尺寸与纵向尺寸比值的增加,径向振动位移逐渐增大。对柱状换能器空气中振动及水中的声场进行比较,可以看出,共振频率与换能器中金属柱体的壁厚有密切的关系。因此,选择合适的尺寸,该类柱状压电超声换能器将能够被用作一个三维超声辐射器,同时第二阶的辐射声压也比较强,也期望该类换能器能够作为多频的超声辐射器。
With the development of ultrasonic application, ultrasonic technology has been widely used in the fields of agriculture, industry, environment protection, medicine and national defense, and so on. Especially in the ultrasonic welding, ultrasonic cleaning, ultrasonic chemistry and ultrasonic extraction of Chinese herbal medicine and other applications, the transducers of single vibration mode cannot meet the requirements of some specific applications, and so, some power transducers with larger radiation area should be urgently needed. In order to improve power and increase ultrasonic radiation area, some mode-conversion ultrasonic transducers are often needed. In this paper, based on the mode-conversion theory, i.e. a vibration mode is converted into the other or more coupled vibration mode, the power ultrasonic transducers for longitudinal-flexural vibration mode-conversion and longitudinal-radial coupled vibration are developed and the main contents include as follows:
(1) The design theory of the sandwich piezoelectric ultrasonic transducer (including the piezoelectric ceramic pile and variable cross section bar) is introduced, and its electro-mechanical equivalent circuit and resonance frequency equation are given. Then, taking vibrational displacement amplitude of the transducer's front end as the goal, the method and step of the optimization design are introduced by using the finite element software ANSYS, and the optimization results are given. It is expected that the theory of the sandwich piezoelectric ultrasonic transducer can provide a theoretical basis for the design of the following mode-conversion power ultrasonic transducers.
(2) From the point of optimization design of flexural composite vibration system and longitudinal-flexural mode vibration system, for the distributed parameter system, the concept of lumped parameter is put forward. According to the equivalent principle of the kinetic energy and the potential energy for a distributed parameter system and another lumped parameter system, we give the lumped parameter equivalent mass and equivalent elasticity coefficient of the flexural vibration plate with the free boundary, and fixed boundary or simply supported boundary. From the point of radiation sound power, the radiation impedance is obtained. Then, the lumped parameter equivalent circuit is drawn and the resonance frequency equation is given. For the same dimension plate in the same order, resonant frequency with free boundary condition is larger than that with the simply supported boundary condition, but smaller than the resonance frequency with the fixed boundary condition. The theoretical values with three kinds of boundary conditions are consistent with the simulated ones. Therefore, these results can serve as a reference for designing flexural vibration systems and the theory is convenient to design the best working state.
(3) The elastic metal cylinder and the piezoelectric ceramic cylinder with larger dimension are analyzed, and their equivalent circuits or frequency equations are obtained. Firstly, based on the apparent elasticity method, the equivalent circuit of metal cylinder is analyzed, which provides convenience for the design of ultrasonic vibration system by using electro-mechanical equivalent circuit method, but this situation is mainly suitable for thin-wall cylinder. Secondly, based on elastic dynamic equation and according to the boundary conditions of free-end annular elastic cylinder, the resonance frequency equation of annular cylinder with arbitrary dimension of longitudinal-radial coupled vibration is derived. The results show that the analytical resonance frequencies are in good agreement with the numerical results. This theory can serve as reference for the design of the longitudinal-radial composite vibrational systems. Finally, based on the analysis of the annular elastic cylinder, using the similar analytical method, the theory of the piezoelectric ceramic cylinder with large dimension is simply analyzed.
(4) A new type of piezoelectric ultrasonic transducer for longitudinal-flexural vibrational mode-conversion is proposed. The mode-conversion transducer has a back metal mass, longitudinally polarized piezoelectric ceramic pile, and a circular metal plate. Based on the equivalent lumped parameters of the thin plate, the equivalent circuit and resonance frequency equation of the mode-conversion transducer are given. It can be seen from the frequency equation that the resonance frequencies and anti-resonance frequencies depend on the material parameters and the geometrical dimensions. This theory provides convenience for the design of this kind of transducer. Then, by using the finite element software ATILA, the vibration properties and sound radiation distribution of the whole transducer are analyzed. Finally, the vibrational mode-conversion transducers with the same simulated parameters and geometric dimensions are manufactured. The frequency characteristics and the amplitude distribution of the end surface of the transducers are measured by using Agilent Hp4294precision impedance analyzer and the scanning laser vibrometer Polytec PSV-400. It can be seen that the longitudinal vibration of the piezoelectric vibrator drives the circular metal plate to produce flexural vibration, i.e. the whole transducer is in longitudinal-flexural vibration mode, which increases the radiation area of the conventional sandwich transducer. The theory provides a design idea for high power transducers with large radiation area.
(5) The longitudinal-radial coupled vibration of a cylindrical piezoelectric ultrasonic transducer with large geometrical dimensions is analyzed. The cylindrical transducer is composed of a longitudinal sandwich transducer, a metal tube and two metal radiation masses. According to the transmission line theory and Mason electro-mechanical equivalent model, by using force and velocity continuity of the transducer boundaries, the electro-mechanical equivalent circuit and the resonance frequency equation of the cylindrical transducer are derived. Then, the vibration performance of the transducer is analyzed and optimized by using the finite element software. Finally, the displacement and the sound pressure are analyzed. The front and the back metal radiation masses are driven to vibrate longitudinally by the inner sandwich longitudinal transducer, which causes the metal tube to produce longitudinal-radial coupled vibration. It can be seen that the axial vibrational displacements on the two end surfaces of the cylindrical transducer are basically uniformly distributed. On the other hand, the radial vibration on the side cylindrical surface is produced. And with the increase of radial-longitudinal ratio of the transducer, radial vibration displacement increases gradually. Compared with vibration distribution in air and sound pressure in water, resonance frequency and wall thickness of the cylindrical transducer have a close relationship. Therefore, if the right dimensions can be chosen, this kind of cylindrical transducer must be used as a three-dimensional ultrasonic radiator. At the same time, the cylindrical transducer can also produce the obvious longitudinal-radial coupled vibration at the second vibrational mode. Therefore, it is expected that the kind of transducer can also be used as a new type of multi-frequency radiator.
引文
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