Kireeva M.N.
MAIN METHOD OF ULTRASONIC TRANSDUCERS MODELLING *
Аннотация:
This article provides an overview of papers and researches on the topic of current methods of modeling ultrasonic sensors. The most frequently used modelling methods are considered to be: modeling by creating equivalent and electrical circuits of varying complexity, which allow calculating the frequency band of the transducer and the dimensions of its components; modeling of ultrasonic transducers using software based on the finite element method (FEM). The main parts of each method are described on the basis of research from articles, which allows the reader to quickly determine and understand the work of each modeling ultrasound devices method
Ключевые слова:
modeling using software, methods of ultrasonic transducer modelling, ultrasonic transducer, FEM, MSD, creation of electrical and equivalent circuits
DOI 10.24412/2712-8849-2023-562-728-737
УДК 004.4
Kireeva M.N.
PhD student of Department of Mechanical Engineering and Automation,
Harbin Institute of Technology (Shenzhen)
(Shenzhen, China)
MAIN METHOD OF ULTRASONIC TRANSDUCERS MODELLING
Abstract: This article provides an overview of papers and researches on the topic of current methods of modeling ultrasonic sensors. The most frequently used modelling methods are considered to be: modeling by creating equivalent and electrical circuits of varying complexity, which allow calculating the frequency band of the transducer and the dimensions of its components; modeling of ultrasonic transducers using software based on the finite element method (FEM). The main parts of each method are described on the basis of research from articles, which allows the reader to quickly determine and understand the work of each modeling ultrasound devices method.
Keywords: modeling using software, methods of ultrasonic transducer modelling, ultrasonic transducer, FEM, MSD, creation of electrical and equivalent circuits.
INTRODUCTION
Process of modelling allows to save financial resources at the development stage. After all, creating a layout is usually expensive, and each subsequent layout usually differs significantly from the previous version. Modelling contributes to a better understanding of the problem. In addition, we can examine and study the insides of the device. It necessary, change the parameters and characteristics to obtain the best desired result.
The following methods are often used in the development and mоdelling of ultrasonic transducers:
1)creation of equivalent and electrical circuits of varying complexity;
2)mоdelling of ultrasonic transducers using software.
Nowadays, ultrasonic transducer modelling methods involve finite element analysis (FEM), mass-spring-shock absorber (MSD) system, transmission matrices and equivalent circuits [1, 2]. The FEM makes it possible to animatedly determine the vibration modality of the resonant frequency of a mechanical structure. It is typically used for the design and analysis of ultrasonic transducers and is constantly used to analyze the dynamic characteristics and resonant frequency of an ultrasonic transducer. The FEM can anаlyzе the influence of various structures on the dynamic characteristics of the ultrasonic transducer by adjusting the FEM nodes. Therefore, using this method, only the mechanical behаviоr of the ultrasonic transducer design can be accurately evaluated, and it cannot anаlyzе the loss of electrical and external mechanical load [1-12]. The ultrasonic transducer can also be mоdeled as a chain of a mass-spring-damper absorber system [1, 2].
Many researchers have concluded that the critical factor of ultrasound treatment is the stability of ultrasonic vibrations [1-8]. Therefore, it is necessary to create electrical and equivalent circuits to simulate an ultrasonic transducer and obtain optimise ultrasonic vibrations.
For example, to describe a piezoelectric converter, an equivalent MSD system of two orders was considered, in which the contact interface is equivalent to a nonlinear load. These equivalent electrical and mechanical systems explain the dynamics of the machining process [3, 4].
Also, can described the Langevin converter, which is modelled in a rotating reference frame based on a model of an equivalent electrical circuit near resonance. This method enables an independent and dynamic control of the vibration amplitude and its relative phase is not only in steady-state mode, but also in transient mode. Figure 1 shows the block diagram control of the Langevin transducer in a rotating frame.
Fig. 1. Block diagram control of the Langevin transducer in rotating frame, where the voltage Vq is used to control the vibration amplitude Wd, Vd is used to control the vibration amplitude Wq, Re is the real part of the voltage and PI (proportional integral) [7].
It is also possible to study all electro mechanical characteristics of an ultrasonic transducer. Using an equivalent scheme to describe the focused characteristic of static resistance or transmission of an ultrasonic transducer, an impedance model of an ultrasonic transducer was created during the ultrasonic processing. This model effectively predicts the frequency, susceptibility and conductivity of the ultrasonic transducer. Figure 2 shows the created model of the equivalent circuit in the ultrasonic transducer.
Fig. 2. The equivalent circuit model of the ultrasonic transducer, where ZC, ZH, ZF(1), ZF(2) is the input equivalent impedance; Zright is the equivalent impedance of right side of location (a); Zleft is the equivalent impedance of left side of location (a); ZSM+ZPM is the total mechanical impedance of the horn; the electromechanical equivalent impedance of the ultrasonic transducer is U/I [8].
In addition, based on modelling based on the creation of electrical and equivalent circuits, it is also possible to develop a model for a piezoelectric ultrasonic transducer. It is based on an analytical equivalent Mason scheme. The model can be used to predict the effect of the piezoelectric layer on the coupling coefficient and the efficiency of piezoelectric ultrasonic transducers with micro-processing [9].
Using the equivalent circuit method, depending on the exact model of the interaction between the mechanical and electrical parameters of the ultrasonic transducer, it is possible to accurately determine the relationship between the electrical input and the output of mechanical vibration. Many researchers have studied various methods of designing equivalent circuits in order to obtain an accurate model of an ultrasonic transducer.
Software tools for modelling ultrasonic transducers are based on the finite element method. This method has gained great popularity for modelling piezoelectric medium. It includes the following types of analyses: static, modal, harmonic, transient analysis, spectral [1, 2].
The design of an ultrasonic transducer begins with the calculation of the initial geometric dimensions of the transducers by using the theory of electromechanical equivalent. The converters are then dynamically optimized and analyzed based on three-dimensional (3D) FEM by using ANSYS software. The initial geometric dimensions of the transducer are determined.
The ANSYS software helped to identify that a circular notched hinge-based flanks provides a higher deformation potential, compared to the other two types of flanks, and also has least influence on the frequency of longitudinal vibrations. Therefore, circular notched hinge-based flanges demonstrate the best decoupling effect among the three types of flanges. Also, the results of experimental tests are in an agreement with the results of modelling in the ANSYS software. Figure 3 shows the vibration modes and relative vibration amplitudes of the concentrators with flanges that carried out in the ANSYS software.
Fig. 3. Vibration mode and relative vibration amplitude of the concentrators with flanges. (a) Ring. (b) Prismatic beam. (c) Circular notched hinge-based flanges [10].
With the help of SolidWorks software, a model of a new drilling method which is associated with additional vibrations by means of piezoelectric sandwich bending vibration transducer was constructed. The trajectory of particle vibration on the edge of the drill is calculated by using the finite element method. The electric brush is used to prevent the winding of wires, as to conduct electrical voltage. In order to obtain a relatively stationary state and maintain contact with each other, brush and slip ring are clamped by bench drill. The general view of the electric brush and the clamping connection are shown in Figure 4.
Fig. 4. The electric brush: (a) electric brush and its fixture; and (b) slid rings [11].
This ultrasonic drill was also implemented and designed by using the ANSYS software. Since the drill structure is centrosymmetric, it can be argued that the resonant frequencies of the two bending modes in the X and Y directions are almost the same, as shown in Figure 5. This makes it easier to set up the drilling mode. The proposed drill has a greater efficiency. Also, with using the vibration drilling, the surface of the hole is smoother than that with conventional drilling.
Fig. 5. The modes of the bending vibrations in two directions: (a) the vibration mode in Y direction; and (b) the vibration mode in X direction [11].
Only using SolidWorks Simulation, new 3D-UEVT device (ultrasonic elliptical vibration transducers) was proposed and evaluated. The 3D-UEVT device operates in a resonant connection mode of the first mode of longitudinal vibration and two directions of the third mode of bending vibration. In this case, the model modeled in SolidWorks Simulation software by using finite element analysis is shown in Figure 6. These allowed us to determine the conjugate resonant frequency and the final dimensions of the proposed 3D-UEVT device [12].
Fig. 6. Three vibrational mode shapes of the 3D-UEVT, a 1st longitudinal (Z), b 3rd bending (X), and c 3rd Bending (Y) [12].
In the conclusion, presents a simulation of an ultrasonic transducer with using the VHDL-AMS standard [13]. It is a language for describing a super high-speed integrated circuit (analog and mixed signal), designed to determine the characteristics of ultrasound [14].
An approach to modelling an ultrasonic transducer, which is integrated into a nonlinear measuring system, is proposed by modelling a nonlinear acoustic load and electronic excitation. By extracting micro-electromechanical system models from VHDL-AMS, correction and optimization of the ultrasonic transducer can be performed. And with the help of the multiphysics aspect built into the VHDL-AMS standard, it is possible to simulate an ultrasonic transducer in the PSPICE software [13,15].
Fig. 7. Redwood electric model [13].
For modelling, a piezoelectric transducer model, developed by Redwood M, was used. [13], in which a special attention is paid to the characteristics of the piezoelectric converter. The analysis begins with the fundamental piezoelectric equations and the search for a solution. That in turn represent step-by-step reflections (with a time delay) of the mechanical transition process between the end surfaces [16]. Implemented a transducer with a piezoceramic disk vibrating in a central frequency and a piezoceramic ring vibrating in a doubled frequency. The figure 7 shows the Redwood electric model [13].
Modeling of the ultrasonic transducer using the VHDL-AMS language is based on writing various equations of the Redwood scheme elements. The model consists of two acoustic ports and an electrical port consisting of capacitors C0 and –C0, which is the capacitive effect of motion. The ceramic layer is represented by an electric current propagation line. Electroacoustic transformer is integrated with a coefficient corresponding to the characteristic parameter of the transducer. Each branch of the scheme is rearranged in the VHDL-AMS code, an example is shown in the Figure 8. Codes for the nonlinear acoustics layer model and sinusoidal excitement, and the diagram of the measuring cell and appropriate test bench in the VHDL-AMS language were created according to the same principle.
Fig. 8. Redwood model VHDL-AMS code [13].
The Figure 9 shows a simulated reaction of the ring element, in which the study is carried out on the time characteristic and its spectral-frequency analysis.
Fig. 9. Comparison between the measure, the time response of VHDL-AMS model, and their Fourier transform [13].
CONCLUSION
The use of each software showed a good correspondence of the results in practice. For the best result of modelling ultrasonic transducers, researchers need to understand the properties of the device and know the modelling software well. It is always possible to combine certain modelling methods.
Modeling by creating electrical and equivalent circuits copes particularly well with its task of finding the final results for describing the piezoelectric converter of the MSD system. It predicts the frequency, susceptibility and conductivity of the ultrasonic transducer and allows dynamic and independent control of the vibration amplitude.
Modeling of ultrasonic devices based on the use of software is the holistic method that fully allows analyzing, developing and optimizing piezoelectric devices. This article considers the intellectual works by using the following softwares for modeling ultrasonic devices: SolidWorks, ANSYS, PSPICE for the VHDL-AMS standard.
Each method is effective and shows simulation results. To predict the performance, create and modernization ultrasonic systems, it is necessary to use modeling adapted to the concept of the sensor methodology and its characteristics. This paper further discusses frequently used modern principles and methods for modeling ultrasonic devices. And the choice of the method of modelling ultrasonic transducers depends only on the researchers’ ability of using computer softwares.
REFERENCES:
Номер журнала Вестник науки №5 (62) том 4
Ссылка для цитирования:
Kireeva M.N. MAIN METHOD OF ULTRASONIC TRANSDUCERS MODELLING // Вестник науки №5 (62) том 4. С. 728 - 737. 2023 г. ISSN 2712-8849 // Электронный ресурс: https://www.вестник-науки.рф/article/8473 (дата обращения: 29.04.2024 г.)
Вестник науки СМИ ЭЛ № ФС 77 - 84401 © 2023. 16+