Multimodal electromechanical model of piezoelectric transformers by Hamilton's principle

This work deals with a general energetic approach to establish an accurate electromechanical model of a piezoelectric transformer (PT). Hamilton's principle is used to obtain the equations of motion for free vibrations. The modal characteristics (mass, stiffness, primary and secondary electromechanical conversion factors) are also deduced. Then, to illustrate this general electromechanical method, the variational principle is applied to both homogeneous and nonhomogeneous Rosen-type PT models. A comparison of modal parameters, mechanical displacements, and electrical potentials are presented for both models. Finally, the validity of the electrodynamical model of nonhomogeneous Rosen-type PT is confirmed by a numerical comparison based on a finite elements method and an experimental identification.     

Finite element simulation of piezoelectric transformers

Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design     

Controlled-source analogous circuits and SPICE models forpiezoelectric transducers

Transmission line analogous circuits for piezoelectric transducers are developed which employ controlled sources rather than the traditional transformer to model the coupling between the electrical and the mechanical systems. A novel method is used to derive each model that consists of adding a term that is equal to zero to one of the device electromechanical equations. When this is done, it is shown that the equations can be cast into the form of the familiar telegraphist's equations for the voltage and current on an electrical transmission line. The circuits are derived for both the thickness-mode piezoelectric transducer and the side-electrode bar piezoelectric transducer. SPICE models of the analogous circuits are presented and an example simulation is given     

压电陶瓷变压器的发展——回顾与展望

文章简要介绍了压电变压器的工作原理 ,给出了压电变压器几个重要工作特性的数学表达式 ,并对压电变压器的发展过程进行了简要的回顾。在此基础上 ,文章着重对压电变压器在研发过程中所涉及的五个方面的问题进行了详细的探讨与说明 ,作者讨论了压电变压器等效电路模型的改进措施及压电变压各个特性的研究状况 ,分析和对比了各种用于制作压电变压器的压电材料的优缺点及其性能的改进方法 ,探讨了各种振动模式作用于压电变压器的效果 ,总结了压电变压器的制作工艺及结构对其特性的影响效果 ,给出了压电变压器的具体应用的例子 ,并指出了压电变压器今后的发展方向及有待解决的问题     

Modeling and analysis on ring-type piezoelectric transformers

This paper presents an electromechanical model for a ring-type piezoelectric transformer (PT). To establish this model, vibration characteristics of the piezoelectric ring with free boundary conditions are analyzed in advance. Based on the vibration analysis of the piezoelectric ring, the operating frequency and vibration mode of the PT are chosen. Then, electromechanical equations of motion for the PT are derived based on Hamilton's principle, which can be used to simulate the coupled electromechanical system for the transformer. Such as voltage stepup ratio, input impedance, output impedance, input power, output power, and efficiency are calculated by the equations. The optimal load resistance and the maximum efficiency for the PT will be presented in this paper. Experiments also were conducted to verify the theoretical analysis, and a good agreement was obtained.     

Modeling of a disk-type piezoelectric transformer

In this paper, an electromechanical model for a disk-type piezoelectric transformer (PT) is proposed. To establish this model, vibration characteristics of the piezoelectric disk with free boundary conditions are analyzed in advance. Based on the vibration analysis results of the piezoelectric disk, the operating frequency and vibration mode of the PT are chosen. Then, electromechanical equations of motion for the PT can be derived based on Hamilton's principle, which can be used to simulate the coupled electromechanical system for the transformer. Voltage step-up ratio, input impedance, output impedance, input power, output power, and efficiency can be calculated by the equations. Thus, the optimal load resistance and the maximum efficiency for the PT are also calculated in this paper. Finally, experiments were conducted to verify the theoretical analysis, and good agreement was obtained.     

Modeling and analysis of circular flexural-vibration-mode piezoelectric transformer

We propose a circular flexural-vibration-mode piezoelectric transformer and perform a theoretical analysis of the transformer. An equivalent circuit is derived from the equations of piezoelectricity and the Hamilton's principle. With this equivalent circuit, the voltage gain ratio, input impedance, and the efficiency of the circular flexural-vibration-mode piezoelectric transformer can be determined. The basic behavior of the transformer is shown by numerical results.     

平面应变轴对称压电圆柱壳的随机响应

提出求解随机激励轴对称压电圆柱壳响应的一种方法，并导出相应的解析表达式。首先给出压电圆柱壳在边界随机激励下的基本方程；然后通过位移与电势的变换，将随机激励变换到运动方程中；再利用Legendre多项式展开位移，应用Galerkin法化偏微分的运动方程为常微分方程组；最后根据随机振动理论，得到压电圆柱壳位移与加速度响应的均方值，由此可计算随机响应、分析有关因素的影响与机电耦合关系等。分析说明了存在的机电耦合项，及由此产生广义刚度的非对称性。     

Identification of material constants for piezoelectric transformers by three-dimensional,finite-element method and a design-sensitivity method

In this paper, an inversion scheme for piezoelectric constants of piezoelectric transformers is proposed. The impedance of piezoelectric transducers is calculated using a three-dimensional finite element method. The validity of this is confirmed experimentally. The effects of material coefficients on piezoelectric transformers are investigated numerically. Six material coefficient variables for piezoelectric transformers were selected, and a design sensitivity method was adopted as an inversion scheme. The validity of the proposed method was confirmed by step-up ratio calculations. The proposed method is applied to the analysis of a sample piezoelectric transformer, and its resonance characteristics are obtained by numerically combined equivalent circuit method.     

球对称压电壳的随机最优控制

分析研究球对称压电壳在边界随机激励下的最优控制问题。给出压电壳的机电动力学方程、应力和电位移表达式,建立其随机最优控制问题方程;通过电势积分转化为机械振动控制方程。通过位移变换和Galerkin法,导出关于模态位移的多自由度振动最优控制方程。根据随机动态规划原理,建立HJB方程,得到压电壳的最优控制电势;并给出受控壳系统的频响函数、响应谱密度和相关函数等表达式,以计算其随机响应。最后给出数值结果,显示压电壳的随机最优控制效果。     

New equivalent lumped electrical circuit for piezoelectric transformers

A new equivalent circuit is proposed for a contour-vibration-mode piezoelectric transformer (PT). It is shown that the usual lumped equivalent circuit derived from the conventional Mason approach is not accurate. The proposed circuit, built on experimental measurements, makes an explicit difference between the elastic energies stored respectively on the primary and secondary parts. The experimental and theoretical resonance frequencies with the secondary in open or short circuit are in good agreement as well as the output "voltage-current" characteristic and the optimum efficiency working point. This circuit can be extended to various PT configurations and appears to be a useful tool for modeling electronic devices that integrate piezoelectric transformers.     

基于系统相似方法的叠堆型压电驱动器非线性动力学建模及实验研究

根据机械系统与电气系统的相似方法,将叠堆型压电驱动器的非线性电-机械耦合模型完全转换到电气域内,建立了其非线性相似电路模型;给出了非线性相似电路模型中迟滞因子的辨识方法,并对某款商用叠堆型压电驱动器进行了迟滞因子的辨识试验;基于非线性相似电路模型和迟滞因子的辨识结果,对该款叠堆型压电驱动器的非线性特性进行了仿真分析,得到了其非线性位移迟滞回线;仿真结果与试验结果吻合,证明了该建模过程与辨识方法的正确性。该建模方法在电气域内对叠堆型压电驱动器电-机械耦合特性及非线性迟滞特性进行描述,建模过程物理意义清晰且简单实用,对于研究压电驱动器的动态特性及控制算法具有实际意义。     

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;     

A Rosen-type piezoelectric transformer employing lead-free K0.5Na0.5NbO3 ceramics

Lead-free K_0.5Na_0.5NbO₃–K_5.4Cu_1.3Ta₁₀O₂₉–MnO₂ (KNN–KCT–Mn) ceramics have been prepared by a conventional ceramic sintering technique. The ceramics show excellent piezoelectric properties for application in power devices, and the optimum properties measured are as follows: piezoelectric constant d ₃₃ = 90 pC/N, planar electromechanical coupling factor k _p = 0.40, mechanical quality factor Q _m = 1900, remanent polarization P _r = 11.8 μC/cm², coercive field E _c = 0.85 kV/mm. A Rosen-type piezoelectric transformer with a dimension of 21 mm × 6 mm × 1.2 mm was fabricated using the KNN–KCT–Mn ceramics. Properties of the piezoelectric transformer operating in the first and second modes have been characterized. For the first mode, the transformer has a maximum output power of 0.7 W with a temperature rise of 14 °C. For the second mode, the maximum output power of the transformer is 1.8 W with a temperature rise of 33 °C. KNN–KCT–Mn ceramics have shown to be a potential lead-free candidate to be used in high-voltage–low-current devices.     

A sub-layer model for a thick piezoelectric patch bonded on elastic substrate

Summary. In this paper, the two-dimensional electromechanical coupling problems that a piezoelectric patch of finite size bonded to an elastic substrate are considered. A subdivision model that the single physical piezoelectric layer is mathematically divided into a number of thinner layers is proposed to analyze the electromechanical responses of the structures. Within each virtual sub-layer of the piezoelectric patch the electric displacement and normal stress in the axial direction are assumed to be linear functions of the thickness coordinate. Hellinger-Reissner variational principle for elasticity is extended to the systems of piezoelectric multi-materials. The governing equations that comprise one-dimensional differential equations and integro-differential equations are rigorously derived from the stationary conditions of the variational functional along with substitution of the assumed electromechanical fields. The subdivision model satisfies all mechanical and electric continuity conditions across the virtual interfaces and the physical interface of piezoelectrics/substrate. The numerical solutions of the governing equations are conducted, and the convergence of the subdivision model is demonstrated.     

Effects of a parallel resistor on electrical characteristics of a piezoelectric transformer in open-circuit transient state

This paper investigates electrical transient characteristics of a Rosen-type piezoelectric transformer (PT), including maximum voltages, time constants, energy losses and average powers, and their improvements immediately after turning OFF. A parallel resistor connected to both input terminals of the PT is needed to improve the transient characteristics. An equivalent circuit for the PT is first given. Then, an open-circuit voltage, involving a direct current (DC) component and an alternating current (AC) component, and its related energy losses are derived from the equivalent circuit with initial conditions. Moreover, an AC power control system, including a DC-to-AC resonant inverter, a control switch and electronic instruments, is constructed to determine the electrical characteristics of the OFF transient state. Furthermore, the effects of the parallel resistor on the transient characteristics at different parallel resistances are measured. The advantages of adding the parallel resistor also are discussed. From the measured results, the DC time constant is greatly decreased from 9 to 0.04 ms by a 10 k(omega) parallel resistance under open output.     

Pulse Shape Improvement in Core-Type High-Voltage Pulse Transformers With Auxiliary Windings

High-voltage pulsed power technologies are rapidly emerging as a key to efficient and flexible use of electrical power for many industrial applications. One of the most important elements in high-voltage pulse-generating circuit technology is the transformer, generally used to further increase the pulse output voltage level. However, its nonideal behavior has significant influence on the output pulse shape. The most attractive winding configuration for high-voltage, the core-type transformer with primary and secondary on different core legs, is seldom used in pulsed applications, because of its weak magnetic coupling between windings, which would result in a slow-rising output voltage pulse. This paper shows that auxiliary windings, suitably positioned and connected, provide a dramatic improvement in the pulse rise time in core-type high-voltage pulse transformers. The paper derives a mathematical model and uses it to describe the observed behavior of the transformer with auxiliary windings. It discusses experimental results, obtained from a high-voltage test transformer associated with a high-voltage pulse generating circuit, and the simulation results obtained from the numerical evaluation of the developed differential equations implemented in Matlab and taking into account the measured transformer parameters.      

Power density of piezoelectric transformers improved using a contact heat transfer structure

Based on contact heat transfer, a novel method to increase power density of piezoelectric transformers is proposed. A heat transfer structure is realized by directly attaching a dissipater to the piezoelectric transformer plate. By maintaining the vibration mode of the transformer and limiting additional energy losses from the contact interface, an appropriate design can improve power density of the transformer on a large scale, resulting from effective suppression of its working temperature rise. A prototype device was fabricated from a rectangular piezoelectric transformer, a copper heat transfer sheet, a thermal grease insulation pad, and an aluminum heat radiator. The experimental results show the transformer maintains a maximum power density of 135 W/cm(3) and an efficiency of 90.8% with a temperature rise of less than 10 °C after more than 36 h, without notable changes in performance.     

圆锥壳的渐进分布传递函数解

本文给出一种求解圆锥薄壳线弹性变形的渐进传递函数方法。壳体的三个位移函数首先沿环向展开为Fourier级数,由此得到解耦的偏微分方程,它包括一个空间变量和一个时间变量。对时间变量进行Laplace变换后进一步将其简化为含复参数s的常微分方程,它的系数是坐标的函数。引入小参数ε＝L／r0sinα,用摄动方法得到一组常微分方程,它可以用渐进分布传递函数方法求解。将各子锥段的解进行综合,构造出了由多段锥壳构成的组合壳体的传递函数解。文中给出了数值算例并与有限元的结果进行了比较。     

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.