燕山大学本科毕业设计(论文)
Abstract
According to traditional design theory of this transducer, the vibration of sandwich transducer is considered as one-dimensional with the Poisson effect and the radial vibration being ignored. Therefore, it is required that the radical dimensions of the transducer must be far less than the longitudinal dimension. Generally speaking, when the radical dimensions are less than a quarter of the longitudinal wavelength, one-dimensional theory can be used and the error between the measured and theoretical resonance frequencies is negligible. However, along with the development of ultrasonic technology, ultrasonic transducers are used in more and more new applications, such as high frequency ultrasonic metal and plastic welding and some practical applications concerning very large ultrasonic power. In these case, radical dimensions are usually large than quarter of a longitudinal wavelength. Therefore, one-dimensional design theory of the sandwich transducer is no longer applicable; Otherwise, large frequency error will be caused. In the above-mentioned cases, the vibration of the transducer is a coupled one of longitudinal and radial vibrations. Therefore, new design theory must be developed in order to study the coupled vibration of the sandwich transducer with a large cross-section or high resonance frequency.
For the coupled vibration of sandwich piezoelectric ultrasonic transducers, numerical methods have been widely used to study the frequency characteristics and vibration modes. Among the numerical methods, the finite element method seems to be the most promising. Nowadays, some commercial software is available in the analysis of vibrational systems, such as ANSYS software.
This article has mainly carried out the following two aspects of research content：
Based on the apparent elasticity method, the couple vibration characteristic of component element of the large dimension piezoelectric will be analyzed respectively. Then, we can get the frequency equation by introducing the concept
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abstract
of the coupling coefficient. Compared with the traditional one dimensional design theory of transducer, the coupling theory accorded with finite element simulation results well.
(2)A set of the large dimension piezoelectric sandwich transducers was designed for modal analysis and harmonic response analysis by finite element software ANSYS. We also extracted the frequency response curve of the transducer, such as Y-F curve and G/B-curve. And we evaluated the updated function of the theory in the paper for precise calculation of large size of sandwich transducer resonant frequency.
Keywords： large dimension piezoelectric transducer, apparent elasticity method,
coupling vibration, finite element analysis
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目 录
摘要 ........................................................................................................................ I ABSTRACT .......................................................................................................... II 第1章 绪论 .......................................................................................................... 1
1.1 夹心式压电超声换能器概述 ................................................................ 1 1.2 本文的选题背景及研究意义 ................................................................ 3 1.3 国内外研究现状 .................................................................................... 3 1.4 本文研究内容 ........................................................................................ 4 第2章 大尺寸弹性超声振动体的振动特性 ...................................................... 5
2.1 短圆柱体的耦合振动 ............................................................................ 5 2.1.1 基于表观弹性法的理论研究 ......................................................... 5 2.1.2 短圆柱体耦合振动状态下有限元分析 ......................................... 7 2.1.3 小结 ................................................................................................. 9 2.2 大尺寸指数超声变幅杆的精确设计 .................................................. 10 2.2.1 基于附加能量法修正变幅杆共振频率的理论 ........................... 10 2.2.2 指数形变幅杆共振频率的修正 ................................................... 12 2.2.3 结果验证及变幅杆的有限元仿真 ............................................... 13 2.2.4 小结 ............................................................................................... 14 2.3 有限尺寸压电体耦合振动特性 .......................................................... 14 2.3.1 有限尺寸压电圆片振子的耦合振动理论 ................................... 14 2.3.2 有限元仿真验证 ........................................................................... 16 2.3.3 小结 ............................................................................................... 19 第3章 大尺寸夹心压电超声换能器振动特性 ................................................ 20
3.1 大尺寸夹心超声换能器的频率方程 .................................................. 20 3.1.1 耦合作用下夹心换能器盖板的径向频率方程 ........................... 21 3.1.2 耦合作用下夹心换能器压电陶瓷圆片的径向频率方程 ........... 22 3.1.3 耦合作用下四分之一波长振子的纵向频率方程 ....................... 23 3.2 有限元仿真 .......................................................................................... 24
3.3 大尺寸夹心超声换能器的振动特性 .................................................. 26 3.4 小结 ...................................................................................................... 27 第4章 大尺寸夹心压电超声换能器的有限元设计 ....................................... 29
4.1 ANSYS有限元软件简介 .................................................................... 29 4.2 ANSYS用于换能器设计的分析方法 ................................................ 29 4.2.1 模态分析原理 ............................................................................... 30 4.2.2 谐响应分析原理 ........................................................................... 30 4.2.3 优化设计原理 ............................................................................... 31 4.3 ANSYS软件分析压电换能器的一般步骤 ........................................ 32 4.4 ANSYS分析压电超声换能器中应注意的几个问题 ........................ 33 结论 ..................................................................................................................... 34 参考文献 ............................................................................................................. 35 致谢 ..................................................................................................................... 37 附录1 .................................................................................................................. 38 附录2 .................................................................................................................. 43 附录 3 ................................................................................................................. 47 附录 4 ................................................................................................................. 58 附录 5 ................................................................................................................. 65 附录 6 ................................................................................................................. 73