Magnetic-mechanical-electric coupling amplitude-change pole simulation method based on finite element analysis

Abstract

The invention discloses a magnetic-mechanical-electric coupling amplitude-change pole simulation method based on finite element analysis, and relates to the technical field of magnetoelectric antenna simulation. The magnetic-mechanical-electric coupling amplitude-change pole simulation method based on finite element analysis comprises the steps that parametric modeling is carried out, and a multi-physical field environment is imported; defining material attributes; solid mechanics, an electrostatic field and a magnetic field are coupled, and piezoelectric and piezomagnetic effects are started; dividing grids and configuring a solver; executing simulation calculation; and evaluating displacement and stress results and performing iterative optimization. According to the magnetic-mechanical-electric coupling amplitude-change pole simulation method based on finite element analysis, through multi-physics field coupling simulation, electric-mechanical-magnetic energy conversion is accurately simulated, the problem of traditional simulation distortion is solved, a high-performance amplitude-change pole capable of amplifying the amplitude of a permanent magnet sheet to 9 micrometers is guided to be designed, and the radiation capacity and reliability are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of magnetoelectric antenna simulation technology, specifically to an analysis and optimization method for amplitude-changing rods to enhance the vibration amplitude of permanent magnets, based on a multi-physics coupled simulation platform. This method, through finite element analysis, simultaneously considers the coupling effects of electric, magnetic, and mechanical vibration fields, achieving accurate simulation of the performance of the amplitude-changing rod structure. It is particularly suitable for magnetoelectric antenna design scenarios requiring high amplitude output. Background Technology

[0002] Magnetoelectric antennas, as an emerging communication device, transmit electromagnetic waves through the coupling effect of piezoelectric and magnetostrictive materials, showing great application potential in low-frequency communication. In these antennas, a piezoelectric drive source, such as a PZT piezoelectric sheet, typically excites a permanent magnet to generate mechanical vibration, which in turn radiates electromagnetic signals outward through displacement. However, the vibration displacement generated by the piezoelectric material itself is usually very small, on the order of micrometers or even nanometers. This directly leads to inherent defects in traditional magnetoelectric antennas, such as weak radiation intensity and low energy conversion efficiency.

[0003] To amplify vibration amplitude, the industry commonly employs a solution of adding an amplitude transformer between the piezoelectric drive source and the permanent magnet. Through its specific structural design, the amplitude transformer amplifies minute displacements at the drive end at the output end, thereby enhancing the radiation capability of the permanent magnet. Currently, the design of amplitude transformers heavily relies on computer simulations. However, existing simulation methods have significant shortcomings: they are mostly limited to single-field analysis (e.g., only structural mechanical modal analysis), completely ignoring the piezoelectric effect of the "electromechanical" conversion in piezoelectric materials, and the piezomagnetic effect of the "mechanical-magnetic" interaction of the permanent magnet during vibration. This simplistic treatment, neglecting key coupling effects, leads to a severe mismatch between the simulation model and actual physical conditions.

[0004] Due to the inability to accurately simulate the complex coupling relationship between electric, magnetic, and mechanical fields, existing simulation methods suffer from the following three interrelated core technical problems: 1. Low simulation accuracy: The simulation results deviate significantly from the actual test data, making it impossible to provide reliable guidance for the precise design and manufacturing of the amplitude transformer.

[0005] 2. Design goals are difficult to achieve: The amplitude amplification capability of the variable amplitude rod designed based on the simulation model of a single physical field is insufficient, making it difficult to effectively amplify the vibration of the permanent magnet sheet to the level of ten micrometers required for practical applications.

[0006] 3. Poor system stability: Due to the failure to accurately calculate the stress distribution under multi-physics coupling, the amplitude transformer is prone to fatigue damage due to local stress concentration during long-term operation, and its magnetic properties are unstable, affecting the antenna's lifespan and reliability.

[0007] Therefore, there is an urgent need in this field for a simulation method that can accurately simulate the multi-physics coupling behavior of the amplitude transformer in a real working environment, so as to solve the technical bottlenecks of simulation distortion, insufficient amplitude and poor stability, and provide key technical support for the development of high-performance magnetoelectric antennas. Summary of the Invention

[0008] To address the three core problems of existing amplitude transformers in permanent magnet amplitude enhancement—insufficient simulation accuracy, high magnetic loss, and low energy transfer efficiency—this invention provides a simulation method for magneto-mechanical-electrical coupled amplitude transformers based on finite element analysis. This method achieves its goals through the following approaches: First, it employs multi-physics coupled finite element analysis to accurately simulate the electro-mechanical-magnetic energy conversion process, fundamentally improving simulation accuracy. Second, based on the simulation results, it guides the design of a dedicated magnetically adapted amplitude transformer structure to achieve efficient transfer and amplification of vibration energy. This method can amplify the peak amplitude of a piezoelectric-driven permanent magnet sheet to 9 micrometers, significantly enhancing its radiation capability while ensuring stable magnetic properties and long-term operational reliability.

[0009] The technical solution adopted in this invention is as follows: A simulation method for a magneto-electro-electric coupled amplitude transformer based on finite element analysis includes the following steps: Parametric modeling and import: Define the geometric parameters of the amplitude transformer, construct a three-dimensional model including the piezoelectric drive section, transition section, amplitude amplification section and permanent magnet sheet, and import it into the multiphysics simulation environment; Material property assignment: Assign corresponding material physical properties to the piezoelectric drive segment, structural segment, and permanent magnet sheet in the 3D model; Multiphysics coupling settings: Add solid mechanical fields, electrostatic fields, and magnetic fields, and set their boundary conditions; establish coupling relationships between physical fields, including piezoelectric effect coupling for simulating electro-mechanical energy conversion, and piezomagnetic effect coupling for simulating mechanical-magnetic energy conversion; Meshing and Solver Configuration: Mesh the 3D model and configure the solver parameters; Perform simulation calculations: Run the simulation to calculate the system response of the amplitude transformer under the magnetic-mechanical-electrical coupling effect; Results Acquisition and Evaluation: Acquire and evaluate the simulation results of displacement and stress distribution of the amplitude transformer; Optimization iteration: Based on the simulation evaluation results of displacement and stress distribution of the amplitude transformer, determine whether the design specifications are met; if not, return to the parametric modeling and import steps, modify the geometric parameters and repeat the simulation until the optimal design is obtained.

[0010] Furthermore, the parametric modeling and import includes: Define geometric parameters: clarify the structural dimensions of the piezoelectric drive section, energy conduction transition section and amplitude amplification section in the amplitude transformer, and determine the bonding position of the permanent magnet sheet; Constructing an integrated model: Based on geometric parameters, an integrated three-dimensional model is established, including the piezoelectric drive section, the energy conduction transition section, the amplitude amplification section, and the permanent magnet sheet; Import and set the boundary domain: Import the integrated 3D model into the multiphysics simulation software and add an infinite element domain to the model to simulate the open boundary of the magnetic field.

[0011] Furthermore, the assignment of material properties includes assigning the following physical properties to each component: Define the density, elastic modulus, Poisson's ratio, relative permittivity matrix, and piezoelectric constant matrix for the piezoelectric drive segment; Define the density, elastic modulus, and Poisson's ratio for the energy conduction transition section and the amplitude amplification section; Define the density, elastic modulus, Poisson's ratio, relative permeability, and coercivity vector for the permanent magnet sheet.

[0012] Furthermore, the multiphysics coupling setup includes: Add physics interfaces: Add interfaces for solid mechanics, electrostatics, and magnetic fields to the simulation environment; Set boundary conditions: Set fixed constraints in the solid mechanics interface; apply AC voltage excitation to the piezoelectric drive section in the electrostatic field interface; set the magnetization direction of the permanent magnet sheet in the magnetic field interface and set the boundary of the infinite element domain to magnetic insulation. Enable multiphysics coupling: Establish the coupling relationship between the solid mechanical field, electrostatic field and magnetic field. The coupling relationship includes piezoelectric effect coupling for simulating the conversion of electrical energy to mechanical energy, and piezomagnetic effect coupling for simulating the conversion of mechanical energy to magnetic energy, to ensure that the simulation logic of the synergistic effect of multiphysics is consistent with the real physical process.

[0013] Furthermore, in the mesh generation and solution configuration, a differentiated meshing strategy is adopted when meshing the 3D model, including: A first-precision grid is used for the piezoelectric drive section and the permanent magnet sheet; a second-precision grid is used for the main structure of the amplitude transformer and the surrounding air domain; wherein, the first precision is higher than the second precision. The solver is configured as follows: select a frequency domain solver and set the operating frequency range and parallel computing.

[0014] Furthermore, the calculation process of the solver configuration is as follows: Configure parameters to solve for the frequency domain response of the following coupled system: The governing equations are: Equilibrium equations for solid mechanical fields: ; Gauss's law for electrostatics: ; The equation for the magnetic vector potential of a magnetic field is: ; In the formula, It is a divergence operator; This represents the net force per unit volume; For Cauchy stress tensor; It is a volume force vector; Angular frequency; The density of the material; It is a displacement vector; This is the inertial force term; It is the electric displacement vector; Free charge density; For curl operator; Permeability; It is the magnetic vector potential; The applied current density vector; The equivalent induced current density originating from vibration; The above equations are coupled through constitutive relations: Piezoelectric effect: and ; Piezomagnetic effect: and ; In the formula, Here is the elastic stiffness matrix; For tensor double dot product, it represents the comprehensive contraction multiplication of matrices; For strain tensor; The piezoelectric stress constant matrix; The electric field intensity vector; Here is the dielectric constant matrix; Here is the elastic stiffness matrix; The matrix represents the piezomagnetic stress constant. It is the magnetic field strength vector; It is the magnetic induction intensity vector; For magnetic permeability tensor; Finally, the above equations are discretized into a system of linear equations, which can be represented in matrix form as follows: ; Configure the solver to solve the coupled system matrix; In the formula, This is the quality matrix; Here is the damping matrix; Here is the structural stiffness matrix; Here is the dielectric stiffness matrix; Here is the magnetic stiffness matrix; and This is the piezoelectric coupling matrix; and This is the piezomagnetic coupling matrix; Let be the vector of displacement degrees of freedom for all nodes; Let be the electric potential degree of freedom vector for all nodes; Let be the magnetic potential degree of freedom vector for all nodes; This is the mechanical load vector; This is the electric load vector; This is the magnetic load vector; It is the imaginary unit.

[0015] Furthermore, the process of performing simulation calculations to solve for the system response after the coupling of magneto-mechanical-electrical multiphysics fields includes: Step 1, Unit Matrix Assembly and System Coupling Matrix Formation: The software first assembles the entire model at each frequency point. The upper part is assembled into a coupled system matrix; the calculation program traverses each element in the 3D model and calculates the element matrix of that element based on material properties and geometry; the element matrix contains the contributions of all physical fields and their coupling terms; Coupling implementation: During the assembly of the element matrix, the constitutive equations for piezoelectric coupling and piezomagnetic coupling are directly embedded into the element stiffness matrix. In the calculation, a global coupling stiffness matrix is ​​thus formed. off-diagonal blocks and ; Piezoelectric constitutive equation: ; Piezomagnetic constitutive equation: ; Step 2, Solve the coupled linear equations: For each frequency point Both require solving a form of A large system of complex linear equations; among which, ; The solution process is as follows: Initialization, given an initial guess of a solution. Iteration, in each iteration In the process of calculating residuals Convergence criterion: If the norm of the residuals... If the value is less than the set tolerance, then the solution is considered... If convergence has been achieved, the computation stops; otherwise, update the solution vector according to the algorithm rules and proceed to the next iteration. ; Step 3, Frequency Domain Scan: The frequency domain scan is repeated within the set frequency range. The solver will scan within the set step size within the frequency range. Within, for each discrete frequency point in sequence Perform the assembly and solution process described in steps 1 and 2 above; The output is: for each frequency point The solver will output a complete solution vector. This includes physical quantities such as displacement, electric potential, and magnetic vector potential of all nodes in the entire model at that frequency; The element matrix includes the element mass matrix. and element stiffness matrix ; This is the system matrix, also known as the effective stiffness matrix; This is the global stiffness matrix; Let be the vector to be solved, containing the degrees of freedom of all nodes, i.e. ; A counter for the iteration steps; For the first The approximate solution obtained by step iteration; The initial guess value for the solution; For the first The residual vector of each iteration; Let be the norm of the residual vector; These are the start and end frequencies for the frequency scan; In the first The discrete frequency value corresponding to each step of the scan; In frequency The system response solution vector is obtained by means of the following.

[0016] Furthermore, the post-processing and performance evaluation of the results include: Data extraction: Extract the peak amplitude data of the permanent magnet sheet and the stress distribution data of the amplitude transformer from the simulation results; data extraction includes drawing displacement distribution cloud maps and stress distribution cloud maps of the amplitude transformer. Performance evaluation: The extracted peak amplitude and stress distribution data are compared with the preset design targets to evaluate whether the performance indicators of the amplitude transformer design meet the standards.

[0017] Furthermore, the adjustment of the amplitude transformer's geometric parameters in the optimization iteration process involves modifying the contraction curve and / or length of the amplitude amplification section.

[0018] The beneficial effects of this invention are: Compared with existing technologies, the magnetic-mechanical-electrical coupling amplitude transformer simulation method based on finite element analysis provided by this invention brings significant technological progress by introducing a multi-physics coupling mechanism and structured design optimization. Its beneficial effects are specifically reflected in the following aspects: 1. A qualitative leap in simulation accuracy and fidelity: Traditional methods, by neglecting the piezoelectric and piezomagnetic coupling effects, result in a severe mismatch between the simulation model and actual working conditions. This invention, by simultaneously loading and coupling solid mechanics, electrostatics, and magnetic fields in a multiphysics simulation platform, and precisely embedding the constitutive equations of the piezoelectric and piezomagnetic effects, for the first time completely reproduces the real physical process of "electromechanical-magnetic" energy conversion and feedback during the operation of the amplitude transformer at the simulation level. This significantly reduces the deviation between simulation results and physical test data, providing a highly reliable theoretical basis and guidance for the precise design and manufacturing of amplitude transformers.

[0019] 2. Breakthrough Improvement in Amplification Performance: The magnetically adapted amplitude transformer structure designed under the guidance of the aforementioned magneto-mechanical-electric multi-physics coupling simulation, particularly the exponentially contracting amplitude transformer section, can efficiently transmit and amplify the minute initial vibrations of the piezoelectric drive section. This invention successfully amplifies the peak vibration amplitude of the permanent magnet sheet to 9 micrometers, reaching the ten-micrometer range required for practical applications. Compared with amplitude transformers designed using traditional methods, the amplitude is increased by approximately 40%, significantly enhancing the radiation capability of the magnetoelectric antenna.

[0020] 3. Significantly Enhanced System Reliability and Stability: The method of this invention can accurately simulate the stress distribution of the amplitude transformer under complex coupled loads, thereby effectively identifying and optimizing potential stress concentration areas during the design phase. This avoids the risk of fatigue damage caused by excessive local stress, ensuring the structural integrity and reliability of the amplitude transformer during long-term vibration operation. By coupling analysis of the magnetic response of the permanent magnet under vibration environment, the stability of its magnetic properties during dynamic operation is ensured, further improving the long-term service life of the entire magnetoelectric antenna system.

[0021] 4. Significantly Improved Design Efficiency and Optimization Capabilities: This invention integrates parametric modeling, multiphysics simulation, and performance evaluation into a single workflow. When simulation results fail to meet design specifications, the system can quickly return to modify geometric parameters and perform iterative optimization. This closed-loop workflow greatly shortens the design cycle, reduces reliance on expensive and time-consuming trial-and-error physical prototypes, and enables rapid, accurate, and automated design of high-performance amplitude transformers.

[0022] In summary, this invention, through its high-precision coupling simulation capabilities, excellent amplitude amplification effect, deep insight into reliability, and efficient design optimization process, systematically solves the three core bottlenecks of simulation distortion, insufficient amplitude, and poor stability in existing technologies, providing key technical support and powerful design tools for the research and development of high-performance magnetoelectric antennas. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0024] Figure 1 This is a flowchart of the simulation method for the magneto-electro-electric coupled amplitude transformer based on finite element analysis according to the present invention; Figure 2 This is a schematic diagram of the structure of the amplitude transformer of the present invention; Figure 3 This is a finite element model diagram of the amplitude transformer of the present invention in multiphysics simulation software; Figure 4 This is a simulation diagram of the magnetic-mechanical-electrical coupling displacement distribution of the amplitude transformer of the present invention; Figure 5 This is a simulation diagram of the magnetic-mechanical-electric coupling stress distribution of the amplitude transformer of the present invention; In the figure, 1-piezoelectric drive section, 2-energy conduction transition section, 3-amplification section, 4-permanent magnet sheet. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] To address the three core problems of existing amplitude transformers in permanent magnet amplitude enhancement—insufficient simulation accuracy, high magnetic loss, and low energy transfer efficiency—this embodiment provides a simulation method for magneto-mechanical-electrical coupled amplitude transformers based on finite element analysis; such as Figure 1 As shown, the simulation method for the magneto-electro-electric coupled amplitude transformer based on finite element analysis includes the following steps: Step 1, Parametric Modeling and Import: This step forms the physical foundation and digital starting point of the simulation method. Its core function is to transform the physical structure of the magneto-electro-electric coupled amplitude transformer to be analyzed into a parameterized three-dimensional geometric model that can be recognized and calculated by subsequent finite element analysis software, and to set a reasonable computational domain for accurate magnetic field analysis. The specific implementation process is as follows: Step 1.1 Parameter Definition: Establish geometric datum; First, the key geometric parameters of each component of the amplitude transformer need to be clearly defined. These parameters serve as the baseline input for subsequent modeling, simulation, and optimization iterations, such as... Figure 2 As shown, it specifically includes: Piezoelectric drive section 1: As the vibration source of the system, its geometry directly determines the magnitude and distribution of the initial excitation force. This section is composed of 10 layers of PZT-5H piezoelectric sheets stacked together, with each layer defined as 18mm in length, 7mm in width, and 0.5mm in thickness.

[0027] Energy conduction transition section 2: As a key link in impedance matching and energy transfer, its dimensions must ensure efficient conduction of vibration energy from the piezoelectric drive section to the amplitude amplification section. This section is designed as a rectangular column with a length of 2mm. Its input end cross-sectional dimensions are adapted to the output end of the piezoelectric drive section, which is 7mm long × 5mm wide.

[0028] Amplification Section 3: This is the core component for amplitude amplification, and its gradually changing structure is key to achieving displacement amplification. This section is 15mm long, and its cross-section is designed as an exponentially tapering profile that smoothly narrows from left to right. The width at the left end is the same as the transition section, at 7mm, while the width at the right end, i.e., the output end, narrows to 1.5mm, and the length of the output end face is 5mm. This narrowing transition is achieved using a 50mm radius arc surface to avoid stress concentration caused by right-angle transitions.

[0029] Permanent magnet sheet 4: Its attachment position is clearly defined on the upper and lower surfaces of the output end of the amplitude amplification section, and its thickness is 27μm.

[0030] Step 1.2 Model Building: Creating Digital Entities Based on the geometric parameters defined above, a three-dimensional geometric model of an integrated amplitude transformer, including a piezoelectric drive section, an energy conduction transition section, an amplitude amplification section, and a permanent magnet sheet, was precisely constructed using three-dimensional computer-aided design software such as SolidWorks and CATIA in a parametric-driven manner. This integrated modeling method ensures the geometric continuity and assembly accuracy between the components, laying a solid geometric foundation for the subsequent accurate simulation of vibration energy transmission.

[0031] Step 1.3 Model Import and Boundary Domain Settings: Preparing the Simulation Environment Import the completed integrated 3D model into multiphysics coupling simulation software, such as COMSOL Multiphysics. To achieve accurate simulation of the magnetic field in open space, an infinite element domain must be added to the solid model of the amplitude rod to enclose it.

[0032] This infinite element domain, as a special boundary condition, functions to simulate the natural attenuation behavior of electromagnetic fields in infinite space. It effectively absorbs outwardly radiated electromagnetic waves, preventing non-physical reflections at the boundaries of the computational domain, thereby ensuring the accuracy of magnetic field simulation results and avoiding simulation distortion caused by improper boundary settings.

[0033] Through the above three sub-steps, the transformation from physical concept to digital model is completed, which prepares the way for subsequent assignment of material properties and application of multiphysics coupling calculations.

[0034] The second step is to assign material properties: This step is crucial for ensuring the physical realism of the simulation model. Its function is to assign the physical property parameters of the corresponding solid material to the constructed geometric model, thereby transforming a simple geometric shape into a digital twin with defined physical behavior. This provides an accurate material property basis for subsequent multiphysics coupling calculations. The specific implementation process is as follows: Step 2.1 Definition of material properties for the piezoelectric drive segment: Material Specification: The material for this part is specified as PZT-5H piezoelectric ceramic. This is a soft piezoelectric material widely used in transducers, possessing a high piezoelectric constant and electromechanical coupling coefficient.

[0035] Attribute parameters and functions: density, elastic modulus, Poisson's ratio are the basic parameters for solid mechanics analysis, used to calculate the inertia, deformation and vibration modes of a structure under stress.

[0036] Relative permittivity matrix: This is a key parameter in electrostatic field analysis, describing the polarization ability of a material under the action of an electric field and determining the internal electric field distribution.

[0037] piezoelectric constant matrix, such as This is the core bridge for realizing electromechanical coupling, i.e., the piezoelectric effect. This matrix precisely quantifies the linear transformation relationship between the electric field (input voltage) and strain (output displacement). For example, This parameter represents the magnitude of the strain produced along the length when an electric field is applied in the thickness direction. Without this parameter, simulations cannot model the fundamental physical process of piezoelectric actuation.

[0038] Step 2.2 Definition of material properties for structural segments: Material Specification: The energy conduction transition section and the amplitude amplification section are both made of titanium alloy TC4. This material has high strength, low density, and excellent fatigue properties, making it suitable for transmitting and amplifying high-frequency mechanical vibrations.

[0039] Attribute parameters and functions: density, elastic modulus, Poisson's ratio, these give the amplitude transformer structure part a real mechanical property, enabling it to accurately simulate the stress wave propagation, resonant frequency and deformation mode generated under piezoelectric drive.

[0040] Step 2.3 Definition of material properties of permanent magnet thin film: Material Specification: This part is specifically made of neodymium iron boron (N52) permanent magnet. This is one of the permanent magnet materials with the highest magnetic energy product currently used in commercial applications, and it can provide a strong bias magnetic field.

[0041] Attribute parameters and functions: density, elastic modulus, Poisson's ratio. These parameters make the permanent magnet sheet not only a magnetic source in the simulation, but also a solid structure with mass and stiffness, which can vibrate together with the amplitude transformer.

[0042] Relative permeability and coercivity vector: These are the core parameters for magnetic field analysis. Relative permeability describes the ease with which a material can be magnetized; for permanent magnets, its value is typically close to 1, i.e., the permeability of free space. The coercivity vector defines the magnitude and direction of the magnetization of the permanent magnet. Correctly setting its direction and value is crucial for simulating the static bias magnetic field generated by the permanent magnet. This bias magnetic field is a prerequisite for subsequent piezomagnetic coupling with mechanical vibrations.

[0043] In summary, this step, by precisely assigning the aforementioned material properties, endows each component in the simulation model with realistic physical behavior, rather than merely a geometric entity: PZT-5H can convert electrical energy into mechanical energy, the titanium alloy structure can conduct and amplify vibrations, and the N52 permanent magnet can act as both a vibrating mass and provide a background magnetic field that interacts with the vibrations. All of this forms the material basis for subsequent simulations of multiphysics coupling of magneto-mechanical-electrical fields.

[0044] Step 3, Multiphysics Coupling Setup: This step is the soul and core innovation of the simulation method. Its function is to break through the limitations of traditional single-physics field simulation, actively establishing and solving the interaction relationships between electric, mechanical, and magnetic fields, thereby accurately simulating the complex energy conversion and transfer process of the amplitude transformer under real working conditions. The specific implementation process is as follows: Step 3.1 Add a physics interface: Build the simulation framework; In a multiphysics simulation environment, the first step is to add the three core physics interfaces involved in this system: Solid Mechanics Interface: Used to calculate the displacement, strain, and stress distribution of the amplitude transformer and permanent magnet sheet under stress.

[0045] Electrostatic field interface: used to calculate the potential and electric field distribution inside a piezoelectric material after a voltage is applied.

[0046] Magnetic field interface: used to calculate the magnetic field distribution generated by permanent magnets and modulated by vibration.

[0047] The function of this step is to build a complete simulation framework that includes mechanical, electrical, and magnetic behaviors for subsequent analysis.

[0048] Step 3.2. Set boundary conditions: Define external excitations and constraints; To realistically simulate the working conditions of the amplitude transformer, appropriate boundary conditions need to be set for the physical field: Solid mechanics boundary conditions: Fixed constraints are applied at appropriate locations on the amplitude transformer, such as a certain end face of the piezoelectric drive section. This condition simulates the clamping state of the amplitude transformer in the actual device and is the basis for mechanical vibration analysis.

[0049] Electrostatic field boundary conditions: An AC voltage excitation is applied to the upper and lower surface electrodes of the piezoelectric drive section PZT-5H, such as: ;in, Instantaneous voltage, representing voltage at any specific moment. The voltage value applied between the upper and lower surface electrodes of the piezoelectric element; The voltage amplitude or peak voltage determines the maximum amplitude of AC voltage oscillation, that is, the maximum value that the voltage can reach in both the positive and negative directions; Frequency is the number of cycles a voltage signal completes per second. Time is the independent variable describing the signal change process. This condition provides the initial power input to the system, simulating the signal applied by the actual drive circuit.

[0050] Magnetic field boundary conditions: Define the magnetization direction of the permanent magnet sheet, for example, along the sheet thickness, to accurately simulate its role as a source of static bias magnetic fields. Set the boundary of the outer infinite element domain to be magnetically insulated. This condition, in conjunction with the infinite element domain in the modeling step, is used to simulate open magnetic field space, ensuring that magnetic field lines can correctly "dissipate" to infinity, avoiding non-physical reflections, and guaranteeing the accuracy of magnetic field calculations.

[0051] Step 3.3 Enable multiphysics coupling: realize energy path simulation; This sub-step is crucial for achieving high-precision simulation and requires actively enabling the following two physical field couplings in the software: Enable piezoelectric coupling: This coupling connects the electrostatic field and the solid mechanical field bidirectionally.

[0052] The piezoelectric effect was used to couple and simulate the conversion path from electrical energy to mechanical energy. Specifically, it used the piezoelectric constant matrix to simulate the electric field strength calculated in the electrostatic field. This is converted into a stress source in the solid mechanical field, i.e., the inverse piezoelectric effect, which drives the amplitude transformer to produce initial vibration. Without this coupling, the driving function of the piezoelectric element cannot be realized.

[0053] Enable piezomagnetic coupling: This coupling connects the solid mechanical field and the magnetic field bidirectionally.

[0054] The piezomagnetic effect coupling was used to simulate the path of mechanical energy conversion to magnetic energy and its reaction. Specifically, it simulates the strain calculated in the solid mechanical field. Converted into an equivalent current source in a magnetic field This allows for the simulation of the magnetization state change of a permanent magnet due to vibration, i.e., the magnetostrictive effect. This change reacts on the mechanical field, affecting the overall vibration response of the system. Introducing this coupling is the core of accurately simulating the dynamic electromagnetic behavior of permanent magnets under vibration conditions and improving simulation accuracy.

[0055] In summary, this step systematically adds physical fields, sets operating boundary conditions, and ultimately utilizes the two core couplings of piezoelectricity and piezomagnetism to fully construct a complete energy flow and physical interaction chain of "electrical signal input → mechanical vibration → magnetic field modulation." It is this setup that enables this simulation method to far surpass traditional single-physical-field analysis, accurately capturing and utilizing multi-field coupling effects, thereby guiding the design of an optimized amplitude transformer structure capable of achieving a 9-micron high-amplitude output.

[0056] Step 4, Mesh Generation and Solver Configuration: This section aims to transform the geometric model into a computable numerical model and, through an efficient and accurate solution strategy, obtain the system response of the amplitude transformer under magneto-mechanical-electrical coupling. Its function is to balance computational accuracy and efficiency, and ultimately solve for the key performance parameters. The specific implementation process is as follows: Step 4.1 Mesh Generation: Implement a differentiated accuracy strategy; To ensure a balance between computational accuracy and efficiency, different meshing strategies are employed for different regions of the 3D model: The core functional area employs a first-precision mesh: this region comprises the piezoelectric drive section and the permanent magnet sheet. The implementation method involves using a regular swept mesh or a refined free tetrahedral mesh for these regions. These regions are the core of energy conversion (piezoelectric effect) and electromagnetic radiation (piezomagnetic effect), where the electric, stress, and magnetic field gradients change dramatically. Using a fine mesh allows for accurate analysis of these critical physical field distributions, ensuring the accuracy of coupled calculations and avoiding energy loss or frequency calculation errors caused by an overly coarse mesh.

[0057] The non-core region employs a second-precision mesh: this region comprises the main structure of the amplitude transformer, namely the energy conduction transition section and the amplitude amplification section, as well as the surrounding air domain, i.e., the infinite element domain. The implementation method uses a relatively coarse free tetrahedral mesh. The physical field changes in these regions are relatively gradual; using a coarser mesh can significantly reduce the total number of elements and nodes, lower the computational degrees of freedom, thereby saving computational resources and time, while maintaining sufficient accuracy in describing the dynamic behavior of the entire system.

[0058] Step 4.2 Solver Configuration: Set the solution strategy and parameters; This step guides the software on how to solve the problem, with the specific configuration as follows. The mathematical basis of this configuration is solving for the frequency domain response of the following coupled system, whose governing equations and coupling relationships constitute the mathematical object of the solution: a. Governing equations and coupling relationships: The behavior of a magneto-mechanical-electric coupled system is described by the following governing equations, which are coupled through constitutive relations: Equilibrium equations for solid mechanical fields: ; Gauss's law for electrostatics: ; The equation for the magnetic vector potential of a magnetic field is: ; In the formula, It is a divergence operator; This represents the net force per unit volume; For Cauchy stress tensor; It is a volume force vector; Angular frequency; The density of the material; It is a displacement vector; This is the inertial force term; It is the electric displacement vector; Free charge density; For curl operator; Permeability; It is the magnetic vector potential; The applied current density vector; This is the equivalent induced current density originating from vibration.

[0059] Constitutive coupling: Piezoelectric effect: and ; Piezomagnetic effect: and ; In the formula, Here is the elastic stiffness matrix; For tensor double dot product, it represents the comprehensive contraction multiplication of matrices; For strain tensor; The piezoelectric stress constant matrix; The electric field intensity vector; Here is the dielectric constant matrix; Here is the elastic stiffness matrix; The matrix represents the piezomagnetic stress constant. It is the magnetic field strength vector; It is the magnetic induction intensity vector; Let be the permeability tensor.

[0060] Ultimately, these equations are discretized into a large system of complex coefficient linear equations, the system matrix of which is as follows: ; ; Configure the solver to solve the coupled system matrix; where, For including piezoelectric coupling blocks With piezomagnetic coupling block The coupling stiffness matrix, Let be the vector of degrees of freedom to be solved.

[0061] In the formula, This is the quality matrix; Here is the damping matrix; Here is the structural stiffness matrix; Here is the dielectric stiffness matrix; Here is the magnetic stiffness matrix; and This is the piezoelectric coupling matrix; and This is the piezomagnetic coupling matrix; Let be the vector of displacement degrees of freedom for all nodes; Let be the electric potential degree of freedom vector for all nodes; Let be the magnetic potential degree of freedom vector for all nodes; This is the mechanical load vector; This is the electric load vector; This is the magnetic load vector; It is the imaginary unit.

[0062] b. Select the frequency domain solver: Type selection: Select frequency domain perturbation solver.

[0063] By directly solving the above system matrix equations, the steady-state harmonic response of the system at a given frequency can be obtained, avoiding time-consuming time-step integration. This method is highly efficient and suitable for finding system resonance peaks.

[0064] c. Set the operating frequency range: Based on theoretical estimations, such as the one-dimensional longitudinal wave formula. ,in, For the material's sound velocity, Set a scanning range that includes the expected resonant frequency for the effective length of the amplitude transformer. .

[0065] This setting guides the solver to perform scanning calculations within this frequency range, thereby accurately plotting the system's frequency response curve (amplitude-frequency curve) and ultimately determining the optimal operating frequency that allows the permanent magnet sheet amplitude to reach its peak value, such as 9 micrometers.

[0066] d. Configure the solution algorithm and parameters: Solution method: Choose an iterative method as the solver for the linear equation system, such as the Generalized Minimum Residual Method (GMRES).

[0067] Convergence criterion: Set the solution tolerance to a small value, for example... .

[0068] Acceleration measures: Configure appropriate preconditioners for the iterative solver, such as incomplete LU decomposition.

[0069] This series of settings informs the solver to employ an efficient and stable numerical algorithm suitable for large-scale sparse matrices. Preconditioners modify the original equations, making the eigenvalue distribution of the coefficient matrix more concentrated, thus greatly accelerating the iterative convergence speed; strict tolerances ensure computational accuracy.

[0070] e. Enable parallel computing: Enable the parallel computing option and specify the number of computing cores. By leveraging the independence of frequency scanning tasks, computing tasks at different frequency points are distributed to multiple CPU cores for parallel execution, significantly reducing the overall computing time.

[0071] Step 5: Perform simulation calculations: This step is the core numerical calculation process automatically executed by the software based on the aforementioned configuration. Its function is to ultimately solve for the system response of the amplitude transformer under the magnetic-mechanical-electrical coupling effect. This process mainly includes: Step 5.1 Assembly of unit matrices and formation of system coupling matrices: The calculation program iterates through each element of the model, considering its material properties and geometry, including the elastic matrix and piezoelectric stress constant matrix. Piezomagnetic stress constant matrix Wait, calculate the element mass matrix. and element stiffness matrix When assembling the element stiffness matrix, the constitutive equations for piezoelectric and piezomagnetic coupling are directly embedded, thus influencing the assembled global stiffness matrix. Naturally formed coupling terms and After all the unit matrices are assembled, the final system matrix is ​​formed. .

[0072] This step transforms a continuous physical problem into a discrete system of algebraic equations that includes all coupling effects.

[0073] Step 5.2, Solve the coupled linear equation system: For each frequency point and the corresponding angular frequency The solver solves the system of equations based on the configured Generalized Minimum Residual Method (GMRES). .

[0074] The process is as follows: Initialize the solution In each iteration In the process of calculating residuals When the norm of the residual When the value is less than the tolerance, the iteration converges and the solution is output. .

[0075] The function of this step is to numerically solve the system of equations to obtain the detailed physical state of the system at that frequency.

[0076] Step 5.3, Frequency Domain Scan and Output: The solver operates within the set frequency range. Within, for each discrete frequency point Repeat steps one and two, and output the complete solution vector at each frequency point. .

[0077] This step systematically acquires the response of the amplitude transformer across the entire frequency band, thereby determining its optimal operating state, such as an amplitude of 9 micrometers.

[0078] Through the process of mesh generation, solution configuration, and simulation calculation, the performance data of the amplitude transformer that accurately reflects the magneto-mechanical-electric coupling effect was finally obtained, providing a reliable basis for subsequent performance evaluation and structural optimization.

[0079] Step 6, Results Acquisition and Evaluation: This step is the output and decision-making stage of the simulation process. Its core function is to quantitatively extract and evaluate the simulation results to determine whether the currently designed amplitude transformer meets the predetermined performance indicators, providing a direct decision-making basis for the final design finalization or iterative optimization. The specific implementation process is as follows: Step 6.1 Data Extraction and Visualization: Quantifying Key Performance Parameters: Perform the following operations using the post-processing module of the multiphysics simulation software: Displacement Distribution Analysis: The overall displacement distribution cloud map of the amplitude transformer at the resonant frequency is read and plotted. On this cloud map, the peak value of the vibration amplitude at the center point or average of the permanent magnet sheet attached to the end of the amplitude amplification section is accurately read. This directly obtains the final amplitude of the permanent magnet sheet—the core performance indicator of this invention. This data is the primary basis for evaluating whether the energy amplification capability of the amplitude transformer meets the standards. This displacement cloud map visually displays the positions of vibration nodes and antinodes, verifying the correctness of the design.

[0080] Stress distribution analysis: Read and plot the stress distribution contour map of the amplitude transformer under operating conditions, typically a von Mises equivalent stress contour map. Focus on analyzing the amplitude transformer structure, especially the stress level in the stress concentration area of ​​the amplitude amplification section. Stress distribution analysis can assess the structural reliability and service life of the amplitude transformer; by identifying the maximum stress value and its location, it can be determined whether it exceeds the fatigue strength or yield strength of the material, thereby avoiding the risk of structural damage due to excessive stress and ensuring the robustness of the design.

[0081] Step 6.2 Performance Evaluation: Compare with design objectives and make a decision; The extracted quantitative data is systematically compared with the preset design goals: Evaluation criteria: For amplitude indicators, determine whether the peak amplitude of the permanent magnet sheet reaches or exceeds the design target of 9 micrometers. For stress indicators, determine whether the maximum stress value of the amplitude transformer is within the safe range of the material's allowable stress.

[0082] If both amplitude and stress meet the above criteria, it indicates that the current amplitude transformer design provides high radiation capability while ensuring structural safety, the performance evaluation is passed, and the design can be finalized.

[0083] If any metric is not met, such as an amplitude of less than 9 micrometers or stress exceeding the safety range, the performance evaluation will fail. This conclusion will trigger subsequent optimization iterations, clearly indicating the need to modify the amplitude transformer structure and re-simulate.

[0084] In summary, this step completes the closed loop from simulation analysis to design verification by transforming abstract simulation data into key performance parameters and making judgments based on clear quantitative standards.

[0085] Step 7, Optimization and Iteration: This step is the closed-loop and optimization phase of the simulation method. Its core function is to establish an automated feedback loop of "design-simulation-evaluation-redesign." By systematically adjusting key design variables, it drives the amplitude transformer structure to evolve in a direction that meets or even exceeds all preset performance indicators, thereby automatically finding the optimal design. The specific implementation process is as follows: Step 7.1 Performance Judgment: Design Verification and Decision-Making; Based on the simulation results of displacement and stress distribution of the amplitude transformer obtained from the results of step six, the following judgments are made: Judgment criteria: Whether the amplitude meets the standard; whether the peak amplitude at the permanent magnet sheet reaches or exceeds 9 micrometers. Whether the stress is safe; whether the maximum working stress of the amplitude transformer is lower than the allowable stress of the material, ensuring long-term reliability.

[0086] Decision-making and Functional Role: If both of the above conditions are met simultaneously, the current amplitude transformer design is considered successful. It can achieve the goal of amplifying the amplitude to 9 micrometers while ensuring structural safety. The design process is complete, and the final design scheme can be output to guide manufacturing. If either condition is not met, the current design is considered unqualified, and the iterative optimization process is immediately initiated. This judgment is the decision switch that triggers design optimization.

[0087] Step 7.2 Iterative optimization: parameter adjustment and iterative resimulation; When the design fails to meet the metrics, perform the following optimization actions: Parameter Adjustment: Core Adjustment Target: Return to step one, parametric modeling and import, and modify the geometric parameters of the amplitude amplification section. This is the most effective means of achieving performance optimization.

[0088] To address insufficient amplitude: prioritize modifying the contraction curve of the amplitude amplification section, for example, by adjusting the curvature or profile of the exponential contraction to optimize the propagation and amplification efficiency of the stress wave within the rod. Simultaneously, consider increasing the length of the amplitude amplification section to provide a longer energy accumulation path.

[0089] To address excessive stress: modify the contraction curve of the amplitude amplification section, especially optimizing the transition fillets in the stress concentration region to make the cross-sectional change smoother and reduce the stress concentration factor. Fine-tuning its length can also be considered to alter the resonance mode and stress distribution.

[0090] Based on the modified geometric parameters, steps two through six are repeated: updating the model, assigning material values, setting the coupling field, meshing, performing the simulation, and re-evaluating the performance. Each iteration represents a targeted design improvement. Through multiple iterations, the simulation model will continuously approach and ultimately lock onto the optimal solution that simultaneously achieves "high amplitude ≥ 9 micrometers" and "low stress".

[0091] In summary, this optimization iterative process connects all the aforementioned steps into an intelligent and automated design system. It is no longer a simple, linear simulation analysis, but a complete methodology with self-correcting and optimization capabilities. In this way, the contradiction between "amplitude" and "strength" in the design of high-performance amplitude transformers is systematically resolved, ensuring the theoretical optimality of the final design and greatly improving the design success rate and efficiency.

[0092] Furthermore, to verify the effectiveness and performance of the finite element analysis-based simulation method for the magneto-electro-electric coupled amplitude transformer, a complete simulation test was conducted in this implementation case. The specific process and results are as follows: 1. Test Model Construction: Based on the method of this invention, a specific simulation model of the amplitude transformer was constructed, and its key parameters are strictly defined as follows: Piezoelectric drive section: Composed of 10 layers of PZT-5H piezoelectric sheets stacked together, each layer measuring 18mm long × 7mm wide × 0.5mm thick. This design provides a sufficiently strong initial driving force. Energy conduction transition section: 2mm long with a rectangular cross-section of 7mm × 5mm, ensuring efficient transfer of vibrational energy from the piezoelectric section to the amplitude amplification section. Amplification amplification section: 15mm long, its cross-section adopts an exponentially contracting design, smoothly transitioning from a width of 7mm at the left end to a width of 1.5mm at the right end, with a transition arc radius of 50mm. This geometry is the core of achieving amplitude amplification. Permanent magnet sheet: Made of N52 neodymium iron boron material, 27μm thick, attached to the upper and lower surfaces of the output end of the amplitude amplification section.

[0093] 2. Simulation Execution and Multiphysics Coupling: Import the above parameterized model into the physics simulation environment. Strictly follow the procedures outlined in this invention: Material property assignment: The piezoelectric ceramic PZT-5H, titanium alloy structure TC4, and permanent magnet N52 are accurately assigned various physical parameters, including elastic modulus, piezoelectric constant, and relative permeability.

[0094] Multiphysics coupling setup: Crucially, solid mechanics, electrostatics, and magnetic fields were simultaneously added and coupled, enabling piezoelectric and piezomagnetic effects. This ensures that the simulation accurately reflects the energy conversion and feedback paths from "electricity to machinery" and "machinery to magnetism to machinery."

[0095] Mesh generation: After setting the mesh precision and completing the mesh generation, a mesh like this is generated. Figure 3 The figure shows the finite element model of the amplitude transformer. This figure visually illustrates the differentiated meshing strategy employed in this invention: it can be clearly seen that in the core functional areas such as the piezoelectric drive section and the permanent magnet sheet, the mesh is significantly refined, ensuring the calculation accuracy of the electric field, stress field, and magnetic field in these critical areas; while in non-core areas such as the main structure of the amplitude transformer and the surrounding air domain, a relatively sparse mesh is used, effectively controlling the computational scale of the model and improving solution efficiency while ensuring overall calculation accuracy.

[0096] Solution calculation: After dividing the grid using a differentiated grid strategy, a frequency domain solver is used to perform scanning calculations within a set frequency range.

[0097] 3. Test Results and Effect Verification: After the simulation calculation was completed, the key results obtained through post-processing are as follows: Displacement distribution results: such as Figure 4 As shown, the displacement distribution cloud map of the amplitude transformer clearly shows the amplification process of vibration along the transformer. Quantitative readings indicate that the peak amplitude of the permanent magnet sheet attached to the end of the amplitude transformer reaches approximately 9.41 micrometers.

[0098] Stress distribution results: such as Figure 5As shown in the stress distribution cloud diagram of the amplitude transformer, although high amplitude output is achieved, its maximum stress value is still within the allowable safety range of the titanium alloy TC4 material, and the structural reliability is guaranteed.

[0099] This simulation test strongly verifies the significant technical effect of this method: High precision and realism: By introducing a fully coupled magnetic-mechanical-electrical analysis, the method of this invention successfully simulates the piezomagnetic feedback effect that is ignored in traditional single-physics field simulation, so that the simulation results are highly consistent with the real physical process, such as 9.41µm, and the simulation accuracy is fundamentally improved.

[0100] Exceptional amplitude amplification capability: The exponential amplitude-changing rod structure designed based on this method successfully amplified the vibration of the permanent magnet sheet to 9.41 micrometers, exceeding the design target of 9 micrometers. This demonstrates the effectiveness of this method in guiding the design of high-radiation-capability magnetoelectric antennas.

[0101] Reliable design guidance: This method can not only predict amplitude, but also accurately predict stress distribution at the same time, thus ensuring the long-term vibration reliability of the product during the design phase.

[0102] In summary, this simulation test fully demonstrates that the simulation method provided by this invention can accurately and reliably guide the design of high-performance amplitude transformers, effectively solving the technical problems of simulation distortion, insufficient amplitude, and poor stability that exist in traditional methods.

[0103] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A magnetic-mechanical-electrical coupled horn simulation method based on finite element analysis, characterized in that, The method comprises the following steps: Parameterized modeling and importing: defining the geometric parameters of the amplitude transformer, constructing a three-dimensional model comprising a piezoelectric driving section, a transition section, an amplitude amplification section, and a permanent magnetic sheet, and importing the model into a multi-physics simulation environment; Material property assignment: assigning corresponding material physical properties to the piezoelectric driving section, the structural section, and the permanent magnetic sheet in the three-dimensional model; Multi-physics coupling setting: adding solid mechanics field, electrostatic field, and magnetic field, and setting their boundary conditions; establishing the coupling relationship between the physical fields, including piezoelectric effect coupling for simulating electric-mechanical energy conversion, and piezomagnetic effect coupling for simulating mechanical-magnetic energy conversion; Meshing and solver configuration: meshing the three-dimensional model, and configuring the parameters of the solver; Performing simulation calculation: running the simulation to calculate the system response of the amplitude transformer under the magnetic-mechanical-electric coupling effect; Result acquisition and evaluation: acquiring and evaluating the displacement and stress distribution simulation results of the amplitude transformer; Optimization iteration: based on the displacement and stress distribution simulation evaluation results of the amplitude transformer, determining whether the design indicators are met; if not, returning to the parameterized modeling and importing step, modifying the geometric parameters and repeating the simulation until the optimal design is obtained.

2. The finite element analysis based simulation method of a magneto-mechanical-electrical coupled amplitude transformer according to claim 1, wherein, The parameterized modeling and importing comprises: Defining geometric parameters: clearly defining the structural dimensions of the piezoelectric driving section, the energy transmission transition section, and the amplitude amplification section in the amplitude transformer, and determining the sticking position of the permanent magnetic sheet; Constructing an integrated model: based on the geometric parameters, establishing an integrated three-dimensional model comprising a piezoelectric driving section, an energy transmission transition section, an amplitude amplification section, and a permanent magnetic sheet; Importing and setting boundary domain: importing the integrated three-dimensional model into the multi-physics simulation software, and adding an infinite element domain to the model for simulating the open boundary of the magnetic field.

3. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method according to claim 1, wherein, The material property assignment comprises assigning the following physical properties to each component: Defining the density, elastic modulus, Poisson's ratio, relative dielectric constant matrix, and piezoelectric constant matrix for the piezoelectric driving section; Defining the density, elastic modulus, and Poisson's ratio for the energy transmission transition section and the amplitude amplification section; Defining the density, elastic modulus, Poisson's ratio, relative magnetic permeability, and coercive force vector for the permanent magnetic sheet.

4. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method of claim 1, wherein, The multi-physics coupling setting comprises: Adding physical field interfaces: adding solid mechanics, electrostatic field, and magnetic field interfaces in the simulation environment; Setting boundary conditions: setting fixed constraints in the solid mechanics interface; applying alternating current voltage excitation to the piezoelectric driving section in the electrostatic field interface; setting the magnetization direction of the permanent magnetic sheet in the magnetic field interface, and setting the infinite element domain boundary as magnetic insulation; Enabling multi-physics coupling: establishing the coupling relationship between the solid mechanics field, the electrostatic field, and the magnetic field, including piezoelectric effect coupling for simulating electric-mechanical energy conversion, and piezomagnetic effect coupling for simulating mechanical-magnetic energy conversion, to ensure that the simulation logic of multi-physics cooperation is consistent with the real physical process.

5. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method according to claim 1, wherein, In the meshing and solver configuration, when meshing the three-dimensional model, a differentiated meshing strategy is adopted, including: Using a first precision mesh for the piezoelectric driving section and the permanent magnetic sheet; using a second precision mesh for the main structure of the amplitude transformer and the peripheral air domain; wherein the first precision is higher than the second precision; The solver is configured to select a frequency domain solver and set a working frequency range and parallel computing.

6. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method according to claim 5, wherein, The solver is configured to perform the following calculation process: Configure parameters to solve the response of the following coupled system in the frequency domain: The control equation is: Equilibrium equations of the solid mechanics field: ; Gauss' law for electrostatic fields: ; Equation of magnetic vector potential of magnetic field: ; where is the divergence operator; represents the net force per unit volume; is the Cauchy stress tensor; is the body force vector; is the angular frequency; is the density of the material; is the displacement vector; is the inertial force term; is the electric displacement vector; is the free charge density; is the curl operator; is the magnetic permeability; is the magnetic vector potential; is the impressed current density vector; is the equivalent induced current density due to vibration; The above equations are coupled through the constitutive relation: piezoelectric effect: and ; magnetostrictive effect: and ; where is the elastic stiffness matrix; is the tensor double product, representing the full contraction of matrices; is the strain tensor; is the piezoelectric stress constant matrix; is the electric field intensity vector; is the dielectric constant matrix; is the elastic stiffness matrix; is the magnetostrictive stress constant matrix; is the magnetic field intensity vector; is the magnetic flux intensity vector; is the permeability tensor; Finally, the above equations are discretized into a linear equation group, which is represented in matrix form as: ； Configure the solver to solve the coupled system matrix; wherein is the mass matrix; is the damping matrix; is the structural stiffness matrix; is the dielectric stiffness matrix; is the magnetic stiffness matrix; and are the piezoelectric coupling matrices; and are the piezomagnetic coupling matrices; is the displacement freedom vector of all nodes; is the electric potential freedom vector of all nodes; is the magnetic vector potential freedom vector of all nodes; is the mechanical load vector; is the electric load vector; is the magnetic load vector; is the imaginary unit.

7. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method according to claim 6, characterized in that, The process of solving the system response after the simulation calculation of the magnetic-mechanical-electric multi-physical field coupling includes: Step 1, Element Matrix Assembly and System Coupling Matrix Formation: The software first assembles the entire model into a coupling system matrix at each frequency point The calculation program traverses each element in the three-dimensional model, and according to the material properties and geometry, calculates the element matrix of the element; the element matrix contains the contributions of all physical fields and their coupling terms; Coupling implementation: During the assembly of the element matrix, the constitutive equations for piezoelectric coupling and piezomagnetic coupling are directly embedded into the element stiffness matrix. In the calculation, a global coupling stiffness matrix is ​​thus formed. off-diagonal blocks and ; Piezoelectric constitutive equations: ; Magnetoelastic constitutive equation: ; Step 2, solve the coupled linear equations: for each frequency point a large complex linear system of equations of the form needs to be solved; where, ; The solution process is as follows: Initialization, given an initial guess of a solution. Iteration, in each iteration In the process of calculating residuals Convergence criterion: If the norm of the residuals... If the value is less than the set tolerance, then the solution is considered... If convergence has been achieved, the computation stops; otherwise, update the solution vector according to the algorithm rules and proceed to the next iteration. ; Step 3, frequency domain scanning: The frequency domain scanning is repeated in the frequency range set, and the solver will perform the assembly and solving process of steps 1 and 2 above on each discrete frequency point in the frequency range set according to the set step size. Step 3, frequency domain scanning: The frequency domain scanning is repeated in the frequency range set, and the solver will perform the assembly and solving process of steps 1 and 2 above on each discrete frequency point in the frequency range set according to the set step size.​ The output is: for each frequency point The solver outputs a complete solution vector , which contains the displacement, electric potential, magnetic vector potential, and other physical quantities of all nodes in the model at that frequency. where the element matrix includes element mass matrix and element stiffness matrix ; is the system matrix, also known as the effective stiffness matrix; is the global stiffness matrix; is the vector to be solved, containing all the degrees of freedom of all nodes, i.e. ; is the counter of iteration steps; is the approximate solution obtained in the th iteration step; is the initial guess value of the solution; is the residual vector of the th iteration step; is the norm of the residual vector; is the start and end frequency of the frequency sweep; is the corresponding discrete frequency value at the th step of the sweep; is the system response solution vector obtained at the frequency .

8. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method of claim 1, wherein, The result post-processing and performance evaluation includes: Data extraction: extract the amplitude peak value data at the permanent magnet thin slice and the stress distribution data of the amplitude transformer from the simulation results; data extraction includes drawing the displacement distribution cloud chart and the stress distribution cloud chart of the amplitude transformer; Performance evaluation: compare the extracted amplitude peak value and stress distribution data with the preset design target to evaluate whether the performance indicators of the amplitude transformer design meet the standards.

9. The finite element analysis based magneto-mechanical-electrical coupled horn simulation method according to claim 1, wherein, The adjustment of the optimization iteration process to modify the geometric parameters of the amplitude transformer is to modify the contraction curve and / or length of the amplitude transformer.

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