Multiphysics-Circuit Co-simulation System and Method for High-Temperature Electromagnetic Ultrasonic Transducers

Abstract

This invention relates to a multiphysics field-circuit co-simulation system and method for high-temperature electromagnetic ultrasonic transducers, belonging to the field of ultrasonic transducer technology. It addresses the problem that existing simulation methods neglect the influence of temperature changes on the power distribution of the EMAT external circuit, leading to significant deviations in the designed EMAT under high-temperature conditions. In this simulation system, the EMAT thermal field calculation module calculates the conductivity, permeability, density, Young's modulus, and Poisson's ratio as a function of temperature. The EMAT electromagnetic field calculation module calculates the magnetic and electric field distributions generated by the EMAT coil based on the conductivity, permeability, and the excitation current output by the EMAT external circuit, thereby obtaining the Lorentz force density on the surface of the specimen. It also calculates the EMAT open-circuit induced voltage based on the conductivity, permeability, and the processing results of the EMAT acoustic field calculation module. Finally, the EMAT acoustic field calculation module calculates the ultrasonic particle vibration velocity in the specimen based on density, Young's modulus, and Poisson's ratio when the Lorentz force causes elastic deformation of the particles.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic transducer technology and relates to a multi-physics field-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer. Background Technology

[0002] The core of high-temperature metallic material testing based on electromagnetic ultrasonic technology is the design of a high-temperature electromagnetic ultrasonic transducer (EMAT). During high-temperature testing, the physical parameters of both the EMAT and the test piece change, primarily causing the following problems: ① The conductivity, permeability, Young's modulus, Poisson's ratio, and density of the test piece change at different temperatures, leading to variations in the EMAT's transduction efficiency during multiphysics calculations; ② The conductivity and permeability of the EMAT differ at different temperatures, altering the output power distribution characteristics of the EMAT's external circuitry. These problems arise because the EMAT, during the testing of high-temperature metallic materials, involves interactions between multiple physical fields (electromagnetic, mechanical, acoustic, and thermal) and with the external circuitry. These issues directly reduce the optimization level of the high-temperature EMAT design.

[0003] Simulation calculations are helpful for better analyzing the interaction between the multiphysics field and the circuit in high-temperature EMAT (Electrical Modulation Amplifier), and are an important means of optimizing the design of high-temperature EMAT. Currently, numerical simulation studies of high-temperature EMAT both domestically and internationally mainly refer to the multiphysics field model of room-temperature EMAT, while repeatedly conducting experimental optimization designs based on experience. In previous simulation methods, the output power and receiving efficiency of the external circuit were set to constant values, without considering the influence of the multiphysics field accompanying temperature changes on the power distribution of the external circuit, thus introducing certain deviations in the simulation results. In short, as the load of the external circuit, the EMAT changes with the temperature of the tested high-temperature metal specimen, and the power distribution characteristics of the external circuit also change accordingly; at this time, the excitation current and receiving voltage of the EMAT will also change to a certain extent, ultimately affecting physical quantities such as the transduction efficiency of the high-temperature EMAT. Summary of the Invention

[0004] This invention aims to address the problem that existing simulation methods neglect the impact of temperature changes on the power distribution of the external circuit of the EMAT, resulting in significant deviations in the designed EMAT under high-temperature conditions.

[0005] A multi-physics field-circuit co-simulation system for high-temperature electromagnetic ultrasonic transducers, including an EMAT external circuit calculation module, an EMAT electromagnetic field calculation module, an EMAT acoustic field calculation module, and an EMAT thermal field calculation module.

[0006] EMAT external circuit calculation module: Calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters;

[0007] EMAT Thermal Field Calculation Module: Calculates conductivity, permeability, density, Young's modulus, and Poisson's ratio as they change with temperature, and updates the calculation at each operating temperature point. The calculated conductivity and permeability are input into the EMAT Electromagnetic Field Calculation Module, and the calculated density, Young's modulus, and Poisson's ratio are input into the EMAT Acoustic Field Calculation Module.

[0008] The EMAT electromagnetic field calculation module calculates the magnetic and electric field distributions generated by the EMAT coil based on conductivity, permeability, and the excitation current output from the EMAT external circuit, thereby obtaining the Lorentz force density on the surface of the specimen; it also calculates the EMAT coil impedance based on the excitation current output from the EMAT external circuit, and calculates the EMAT open-circuit induced voltage based on the processing results of conductivity, permeability, and the EMAT acoustic field calculation module.

[0009] EMAT acoustic field calculation module: Under the condition that the Lorentz force causes elastic deformation of the particles in the specimen, the vibration velocity of the ultrasonic particles in the specimen is calculated based on the density, Young's modulus, and Poisson's ratio.

[0010] Furthermore, the process by which the EMAT electromagnetic field calculation module calculates the magnetic and electric field distributions generated by the EMAT coil based on the conductivity, permeability, and excitation current output from the EMAT external circuit, and thus obtains the Lorentz force density on the surface of the specimen, includes the following steps:

[0011] The external circuit of the EMAT outputs an excitation current to the EMAT coil, generating a magnetic field H.

[0012]

[0013] In the formula, J is the current density through the EMAT coil, and D is the displacement current. For Hamiltonian operators;

[0014] According to Faraday's law of electromagnetic induction, we get:

[0015]

[0016] In the formula, E is the electric field strength and B is the magnetic induction intensity;

[0017] Introducing magnetic vector potential A:

[0018]

[0019] Substituting equation (3) into equation (2) and integrating both sides of the equation, we obtain the electric field E:

[0020]

[0021] In the formula, The potential difference across the EMAT coil;

[0022] Substituting equations (3) and (4) into equation (1), we get:

[0023]

[0024] In the formula, μ is the magnetic permeability and γ is the electrical conductivity;

[0025] According to the Lorentz norm conditions Ignoring the influence of displacement current, the equation for the magnetic field generated by the EMAT coil is obtained based on equation (5):

[0026]

[0027] At the interface between different media, the magnetic vector potential function satisfies the following interface connection condition:

[0028] A i =A i+1 (7)

[0029]

[0030] In the formula, subscript i represents the adjacent medium; subscript t represents the tangent direction at the interface between adjacent media; J i,i+1 The surface current density at the adjacent interface;

[0031] After obtaining the magnetic vector potential, the eddy current density J in the specimen e The distribution is as follows:

[0032]

[0033] The Lorentz force density is obtained as follows:

[0034] f L =J e ×B m (10)

[0035] In the formula, f L B is the Lorentz force density generated in the surface layer of the specimen. m The magnetic flux density provided to the permanent magnet.

[0036] Furthermore, the EMAT acoustic field calculation module calculates the vibration velocity of ultrasonic particles in the specimen based on density, Young's modulus, and Poisson's ratio under the condition that the Lorentz force causes elastic deformation of the particles in the specimen. The process includes the following steps:

[0037] The particles in the specimen undergo elastic deformation under the action of the Lorentz force, and their equation of motion is expressed as:

[0038]

[0039] In the formula, δ is the stress tensor, ρ is the specimen density, and u is the displacement of a particle in the specimen;

[0040] Determine the formula for calculating acoustic impedance Z:

[0041]

[0042] In the formula, ρ is the density of the medium; c is the speed of sound; δ is the stress; v(t,x) is the particle vibration velocity at position x when the sound wave propagates at time t.

[0043] The formulas for calculating the sound velocities of transverse and longitudinal waves are as follows:

[0044]

[0045] In the formula, c s c is the transverse wave velocity; l η is the longitudinal wave velocity; G is the shear modulus; E is Young's modulus; η is Poisson's ratio;

[0046] Substituting equation (13) into equation (12) yields the transverse wave particle vibration velocity ν. s and longitudinal wave particle vibration velocity ν l .

[0047] Furthermore, the vibration velocity ν of the transverse wave particles s and longitudinal wave particle vibration velocity ν l as follows:

[0048]

[0049] In the formula, ν s ν is the vibrational velocity of the transverse wave particles. l The velocity of the longitudinal wave particles is denoted as .

[0050] Furthermore, the EMAT thermal field calculation module calculates the electrical conductivity and magnetic permeability as a function of temperature by including the following steps:

[0051] Within a temperature range, determine the conductivity as a function of temperature:

[0052]

[0053] In the formula, T0 is room temperature, T is actual temperature, γ is actual conductivity, γ0 is room temperature conductivity, and α is temperature compensation coefficient.

[0054] Based on Langevin's paramagnetic theory, neglecting the material's hysteresis effect, the magnetization MLangevin function is obtained, thereby determining the initial magnetic susceptibility χ0 and the saturation magnetization Ms. S As parameters for fitting the magnetization curve using the Langevin function; for the saturation magnetization M S Using saturation magnetic flux density B Sexpress:

[0055] B S =μ0(H S +M S (20)

[0056] The saturation magnetization M of the specimen S Relationship with temperature T K Using mean-field theory, it can be expressed as:

[0057] M S =Nνtanh(νλM S / K B T K ) (twenty one)

[0058] In the formula, N is the number of atoms per unit volume, ν is the atomic magnetic moment, λ is the mean field constant, and K B Boltzmann's constant;

[0059] Solve equation (21) using a numerical method, and let m = M. S / Nν,n=K B T K / Nν 2 λ, Equation (21) simplifies to:

[0060] m=tanh(m / n) (22)

[0061] Plot both sides of equation (22) as functions of m, and the intersection of the two curves is the value of m at different temperatures;

[0062] Let Curie temperature T c Corresponding to n=1 in equation (22), T c =Nν 2 λ / K B Then, the relationship curve between the magnetization intensity and temperature of the material can be calculated;

[0063] Based on the magnetization curves calculated using the Langevin function and the magnetization intensity versus temperature curves calculated using the mean field theory, magnetization curves at different temperatures are obtained.

[0064] Based on the constitutive relations of M and H, the magnetic permeability of the material under high temperature conditions is determined:

[0065]

[0066] In the formula, μ(T) is the permeability at temperature T, M(T) is the magnetization at temperature T, and H(T) is the magnetic field strength at temperature T.

[0067] Furthermore, the Langevin function expression for the material magnetization M is:

[0068]

[0069]

[0070] In the formula, M S χ0 represents the saturation magnetization; L(|H|) is the Langevin function; χ0 is the initial magnetic susceptibility.

[0071] Saturation magnetization M S The initial magnetic susceptibility χ0 is as follows:

[0072] M S =χ0H S (18)

[0073] χ0=μ r0 -1 (19)

[0074] In the formula, μ r0 denoted as the initial permeability.

[0075] Furthermore, the process by which the EMAT electromagnetic field calculation module calculates the EMAT coil impedance includes the following steps:

[0076] The EMAT coil impedance includes: the EMAT coil equivalent resistance and the EMAT coil equivalent inductance;

[0077] The equivalent resistance R of the EMAT coil eq as follows:

[0078]

[0079] In the formula, J is the current density through the EMAT coil, * indicates conjugate, and γ is the conductivity;

[0080] Based on the equivalent inductance of the EMAT coil, the equivalent inductance L of the EMAT coil is obtained. eq :

[0081]

[0082] In the formula, * represents conjugate, and I represents the current intensity flowing through the EMAT coil.

[0083] Furthermore, the process by which the EMAT electromagnetic field calculation module calculates the EMAT open-circuit induced voltage based on the conductivity, permeability, and processing results of the EMAT acoustic field calculation module includes the following steps:

[0084] According to Maxwell's equations, the differential equations for the magnetic vector potential in air and in the specimen are as follows:

[0085]

[0086]

[0087] In the formula, μ0 is the air permeability, ε0 ​​is the air permittivity, μ is the specimen permeability, γ is the specimen conductivity, ω is the angular frequency, and A air Let A be the magnetic vector potential in the air. mat The magnetic vector potential in the specimen;

[0088] Considering the boundary conditions, determine the magnetic vector potential generated in the air by the induced eddy current at depth z0 of the specimen:

[0089]

[0090] In the formula, η is the skin depth, k0 is the wavenumber at ultrasonic frequency ω, z0 is the induced eddy current depth in the specimen, and z1 is the distance between the EMAT coil and the specimen; J e (z0) represents the induced eddy current at a depth z0 on the surface of the specimen caused by particle vibration;

[0091] Integrating over the thickness of the specimen, we obtain the total magnetic vector potential generated by the induced eddy currents in the air above the specimen:

[0092]

[0093] The final total magnetic vector potential is:

[0094]

[0095] In the formula, v0 is the vibration velocity of the particles on the surface of the specimen, and B0 is the magnetic field vector on the surface of the specimen.

[0096] Taking a linear EMAT coil with N turns and a length of l0 as an example, the formula for calculating the open-circuit induced voltage of EMAT is:

[0097]

[0098] Substituting equation (31) into equation (32), we obtain the open-circuit induced voltage of EMAT as follows:

[0099]

[0100] Furthermore, the vibration of the mass particles induces eddy currents at a depth z0 on the surface of the specimen:

[0101] J e (z0)=γv(z0)×B0(z0) (26)

[0102] In the formula, γ is the electrical conductivity of the specimen, v(z0) is the particle velocity at a depth z0 on the surface of the specimen, and B0(z0) is the magnetic field vector of the particle at a depth z0 on the surface of the specimen.

[0103] A multiphysics-circuit co-simulation method for high-temperature electromagnetic ultrasonic transducers (EMATs) is proposed, based on a multiphysics-circuit co-simulation system for the EAT. The method includes the simulation process from the external circuit of the high-temperature EAT to the multiphysics field of the EAT, and / or the simulation process from the multiphysics field of the high-temperature EAT to the external circuit of the EAT.

[0104] The simulation process from the high-temperature EMAT external circuit to the EMAT multiphysics field includes the following steps:

[0105] The EMAT external circuit calculation module calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters, inputs it to the EMAT electromagnetic field calculation module to calculate the force distribution on the surface of the specimen, i.e. the Lorentz force density on the surface of the specimen, and then inputs it to the EMAT acoustic field calculation module to calculate the vibration velocity of the ultrasonic particles in the specimen.

[0106] The simulation process from the high-temperature EMAT multiphysics field to the EMAT external circuit includes two parts, as follows:

[0107] (1) The EMAT thermal field calculation module calculates the density, Young's modulus and Poisson's ratio parameters, which are then input into the EMAT acoustic field calculation module to calculate the vibration velocity of the ultrasonic particles in the specimen. At the same time, the EMAT thermal field calculation module calculates the conductivity and magnetic permeability, which are then input into the EMAT electromagnetic field calculation module to finally calculate the EMAT receiver open circuit induced voltage.

[0108] (2) The conductivity and permeability are calculated by the EMAT thermal field calculation module, which are then used to calculate the impedance parameters of the EMAT coil by the EMAT electromagnetic field calculation module. Finally, the excitation current waveform of the EMAT coil is calculated by the EMAT external circuit calculation module.

[0109] Beneficial effects:

[0110] This invention considers the impact of temperature changes on the power distribution of the external circuit of the EMAT. The maximum error of the high-temperature EMAT designed using this invention does not exceed 6%, thus providing better guidance for EMAT optimization design. Compared with the prior art, the advantages of this invention are: 1) The impedance parameters of the high-temperature EMAT change with temperature and are updated at each operating temperature point; 2) The excitation current waveform calculated by the high-temperature EMAT external circuit calculation module is used in conjunction with the high-temperature EMAT multi-physics field to determine the excitation current value and the open-circuit voltage value of the high-temperature EMAT in real time; 3) The multi-physics-circuit collaborative calculation method of the high-temperature EMAT can be used more accurately for high-temperature EMAT optimization design. Attached Figure Description

[0111] Figure 1This is a schematic diagram of the basic structure of a high-temperature electromagnetic ultrasonic transducer.

[0112] Figure 2 This is a block diagram of a multi-physics field-circuit co-simulation system for a high-temperature electromagnetic ultrasonic transducer.

[0113] Figure 3 The image shows the waveforms of the received signals obtained from experiments using a high-temperature electromagnetic ultrasonic transducer at different temperatures.

[0114] Figure 4 The graph shows the comparison between experimental results and simulation calculation results at different temperatures. Detailed Implementation

[0115] In high-temperature detection, the electromagnetic field (EMAT) is affected by the thermal field, which alters the calculated results of the EMAT electromagnetic field, acoustic field, and external circuitry. The high-temperature EMAT multi-physics field-circuit co-simulation system based on this invention can effectively achieve co-simulation of multi-physics field-circuit in high-temperature EMAT.

[0116] Specific implementation method one, combined with Figure 1 and Figure 2 This implementation method is described below. Figure 1 This is a schematic diagram of the basic structure of a high-temperature electromagnetic ultrasonic transducer (EMAT), which mainly consists of three parts: a high-temperature permanent magnet, a coil, and a test piece. The multi-physics field-circuit co-simulation system for the high-temperature electromagnetic ultrasonic transducer described in this embodiment is as follows: Figure 2 As shown, it mainly consists of four parts: EMAT external circuit calculation module, EMAT electromagnetic field calculation module, EMAT sound field calculation module and EMAT thermal field calculation module.

[0117] EMAT external circuit calculation module: Calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters;

[0118] EMAT Thermal Field Calculation Module: Calculates conductivity, permeability, density, Young's modulus, and Poisson's ratio as they change with temperature, and updates the calculation at each operating temperature point. The calculated conductivity and permeability are input into the EMAT Electromagnetic Field Calculation Module, and the calculated density, Young's modulus, and Poisson's ratio are input into the EMAT Acoustic Field Calculation Module.

[0119] The EMAT electromagnetic field calculation module calculates the magnetic and electric field distributions generated by the EMAT coil based on conductivity, permeability, and the excitation current output from the EMAT external circuit, thereby obtaining the Lorentz force density on the surface of the specimen; it also calculates the EMAT coil impedance based on the excitation current output from the EMAT external circuit, and calculates the EMAT open-circuit induced voltage based on the processing results of conductivity, permeability, and the EMAT acoustic field calculation module.

[0120] EMAT acoustic field calculation module: Based on the density, Young's modulus, Poisson's ratio and the Lorentz force density calculated by the EMAT electromagnetic field module, the vibration velocity of ultrasonic particles in the specimen is calculated.

[0121] There is parameter exchange between the EMAT electromagnetic field calculation module and the EMAT external circuit calculation module.

[0122] The high-temperature EMAT multiphysics-circuit co-simulation system mainly includes two processes: at a working temperature point, EMAT needs to simultaneously complete the calculation from the external circuit to the EMAT multiphysics and the calculation from the multiphysics to the external circuit.

[0123] (I) The simulation process from the high-temperature EMAT external circuit to the EMAT multiphysics field includes the following steps:

[0124] Reference Figure 2 The middle arrow indicates the specific process of the EMAT external circuit to EMAT multiphysics simulation: The EMAT external circuit calculation module calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters (equivalent resistance and equivalent inductance), inputs it to the EMAT electromagnetic field calculation module to calculate the force distribution on the surface of the specimen, and then inputs it to the EMAT acoustic field calculation module to calculate the vibration velocity of the ultrasonic particles in the specimen.

[0125] The processing steps of the EMAT electromagnetic field calculation module include the following:

[0126] The EMAT external circuit calculation module calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters.

[0127] The external circuit of the EMAT outputs an excitation current to the EMAT coil, generating a magnetic field H.

[0128]

[0129] In the formula, J is the current density through the EMAT coil, and D is the displacement current. For Hamiltonian operators.

[0130] According to Faraday's law of electromagnetic induction, we can obtain:

[0131]

[0132] In the formula, E is the electric field strength and B is the magnetic induction intensity.

[0133] To simplify the calculations in the EMAT electromagnetic field calculation module, a magnetic vector potential A is introduced:

[0134] (3)

[0135] Substituting equation (3) into equation (2) and integrating both sides of the equation, we can obtain the electric field E:

[0136]

[0137] In the formula, This represents the potential difference across the EMAT coil.

[0138] Substituting equations (3) and (4) into equation (1), we get:

[0139]

[0140] In the formula, μ is the magnetic permeability and γ is the electrical conductivity.

[0141] According to the Lorentz norm conditions (ε is the dielectric constant), and ignoring the influence of displacement current, simplifying equation (5) yields the equation for the magnetic field generated by the EMAT coil:

[0142]

[0143] At the interface between different media, the magnetic vector potential function satisfies the following interface connection condition:

[0144] A i =A i+1 (7)

[0145]

[0146] In the formula, subscript i represents the adjacent medium; subscript t represents the tangent direction at the interface between adjacent media; J i,i+1 This represents the surface current density at adjacent interfaces.

[0147] After obtaining the magnetic vector potential, the eddy current density J in the specimen e The distribution is as follows:

[0148]

[0149] According to the definition of Lorentz force density:

[0150] f L =J e ×B m (10)

[0151] In the formula, f L B is the Lorentz force density generated in the surface layer of the specimen. m The magnetic flux density provided to the permanent magnet.

[0152] The magnetic field and electric field distribution generated by the EMAT coil are obtained by solving equations (1) and (4). The eddy current density distribution in the specimen is obtained by solving equation (9). Then, the Lorentz force density generated on the surface of the specimen is obtained by solving according to the definition of Lorentz force, i.e., equation (10).

[0153] The Lorentz force density calculated by the EMAT electromagnetic field module is then used to calculate the vibration velocity of ultrasonic particles in the specimen by the EMAT acoustic field calculation module. This process corresponds to the EMAT excitation ultrasonic process.

[0154] The processing steps of the EMAT sound field calculation module include the following:

[0155] Under known surface stress conditions, EMAT sound field calculations were performed. The particles in the specimen undergo elastic deformation under the action of the Lorentz force, and their equation of motion is expressed as:

[0156]

[0157] In the formula, δ is the stress tensor, ρ is the specimen density, and u is the displacement of a particle in the specimen.

[0158] The formula for calculating acoustic impedance Z is:

[0159]

[0160] In the formula, ρ is the density of the medium; c is the speed of sound; δ is the stress; and v(t,x) is the vibration velocity of the particle at position x when the sound wave propagates at time t.

[0161] The formulas for calculating the sound velocities of transverse and longitudinal waves are:

[0162]

[0163] In the formula, c s c is the transverse wave velocity; l η is the longitudinal wave velocity; G is the shear modulus; E is Young's modulus; η is Poisson's ratio.

[0164] Substituting equation (13) into equation (12) yields the following:

[0165]

[0166] In the formula, ν s ν is the vibrational velocity of the transverse wave particles. l The velocity of the longitudinal wave particles is denoted as .

[0167] (II) The simulation process from the high-temperature EMAT multiphysics field to the EMAT external circuit includes the following steps:

[0168] Reference Figure 2As indicated by the middle arrow, the specific processing flow from the EMAT multiphysics field to the EMAT external circuit includes two parts: (1) The EMAT thermal field calculation module calculates the density, Young's modulus and Poisson's ratio parameters, which are then input into the EMAT acoustic field calculation module to calculate the vibration velocity of the ultrasonic particles in the specimen. At the same time, the EMAT thermal field calculation module calculates the conductivity and permeability, which are then input into the EMAT electromagnetic field calculation module to finally calculate the EMAT receiver open-circuit induced voltage; (2) The EMAT thermal field calculation module calculates the conductivity and permeability, which are then input into the EMAT electromagnetic field calculation module to calculate the EMAT coil impedance parameters, which are then input into the EMAT external circuit calculation module to calculate the excitation current waveform of the EMAT coil.

[0169] The EMAT thermal field calculation module is used to calculate the electrical conductivity, magnetic permeability, density, Young's modulus, and Poisson's ratio as a function of temperature. The density, Young's modulus, and Poisson's ratio at different operating temperatures of the material are obtained by consulting material design handbooks. The process of calculating the electrical conductivity and magnetic permeability as a function of temperature using the EMAT thermal field calculation module includes the following steps:

[0170] Within a certain temperature range, conductivity can be approximated as inversely proportional to temperature, and the calculation formula is:

[0171]

[0172] In the formula, T0 is room temperature, T is actual temperature, γ is actual conductivity, γ0 is room temperature conductivity, and α is temperature compensation coefficient.

[0173] According to Langevin's paramagnetic theory, neglecting the material's hysteresis effect, the Langevin function expression for the material's magnetization (M) is obtained as follows:

[0174]

[0175]

[0176] In the formula, M S Let L be the saturation magnetization; L(|H|) be the Langevin function; and χ0 be the initial magnetic susceptibility, satisfying:

[0177] M S =χ0H S (18)

[0178] χ0=μ r0 -1 (19)

[0179] In the formula, μ r0 denoted as the initial permeability.

[0180] As can be seen from equations (16) and (17), fitting the magnetization curve using the Langevin function only requires two parameters: the initial magnetic susceptibility χ0 and the saturation magnetization M. S Considering the saturation magnetization M S Since it is not a directly measurable physical quantity, the saturation magnetic flux density B is used. S express:

[0181] B S =μ0(H S +M S (20)

[0182] Saturation magnetization M of the specimen S Relationship with temperature T K The mean-field theory is used for approximate calculation:

[0183] M S =Nνtanh(νλM S / K B T K ) (twenty one)

[0184] In the formula, N is the number of atoms per unit volume, ν is the atomic magnetic moment, λ is the mean field constant, and K B is the Boltzmann constant.

[0185] Equation (21) cannot be solved analytically, but it can be solved numerically. Let m = M S / Nν,n=K B T K / Nν 2 λ, Equation (21) simplifies to:

[0186] m=tanh(m / n) (22)

[0187] Plot the two sides of equation (22) as functions of m respectively, and the intersection of the two curves is the value of m at different temperatures.

[0188] Let Curie temperature (T) c ) corresponds to n=1 in equation (22), at which time T c =Nν 2 λ / K B Then, the relationship curve between the magnetization intensity and temperature of the material can be calculated.

[0189] Based on the magnetization curves calculated using the Langevin function and the magnetization intensity versus temperature curves calculated using the mean field theory, magnetization curves at different temperatures can be obtained.

[0190] Based on the constitutive relations of M and H, the magnetic permeability of the material under high temperature conditions is determined:

[0191]

[0192] In the formula, μ(T) is the permeability at temperature T, M(T) is the magnetization at temperature T, and H(T) is the magnetic field strength at temperature T.

[0193] The process of calculating the EMAT coil impedance using the EMAT electromagnetic field calculation module includes the following steps:

[0194] The EMAT coil impedance includes: the EMAT coil equivalent resistance and the EMAT coil equivalent inductance.

[0195] The equivalent resistance R of the EMAT coil eq Calculation formula:

[0196]

[0197] In the formula, * denotes conjugation, and γ is the conductivity.

[0198] The equivalent inductance of the EMAT coil is calculated based on the field quantities obtained from equations (1) and (3) above. The equivalent inductance L of the EMAT coil is then obtained. eq Calculation formula:

[0199]

[0200] In the formula, * represents conjugate, and I represents the current intensity flowing through the EMAT coil.

[0201] Based on the processing results of the EMAT sound field calculation module, the processing procedure of the EMAT electromagnetic field calculation module during the EMAT reception of ultrasonic waves includes the following steps:

[0202] Under the influence of an external magnetic field, the vibration of particles on the surface of the specimen generates eddy currents, which in turn induce a voltage across the coil. The induced eddy current at depth z0 on the surface of the specimen caused by particle vibration is given by the following equation:

[0203] J e (z0)=γv(z0)×B0(z0) (26)

[0204] In the formula, γ is the electrical conductivity of the specimen, v(z0) is the particle velocity at a depth z0 on the surface of the specimen, and B0(z0) is the magnetic field vector of the particle at a depth z0 on the surface of the specimen.

[0205] According to Maxwell's equations, the differential equations for the magnetic vector potential in air and in the specimen are as follows:

[0206]

[0207]

[0208] In the formula, μ0 is the air permeability, ε0 ​​is the air permittivity, μ is the specimen permeability, γ is the specimen conductivity, ω is the angular frequency, and A air Let A be the magnetic vector potential in the air. mat The magnetic vector potential in the specimen;

[0209] Considering the boundary conditions, the magnetic vector potential generated by the induced eddy current in the air at depth z0 of the specimen is:

[0210]

[0211] In the formula, η is the skin depth, k0 is the wavenumber at ultrasonic frequency ω, z0 is the induced eddy current depth in the specimen, and z1 is the distance between the EMAT coil and the specimen.

[0212] Integrating over the specimen thickness, the total magnetic vector potential generated by the induced eddy current in the air above the specimen can be obtained:

[0213]

[0214] The final total magnetic vector potential is:

[0215]

[0216] In the formula, v0 is the vibration velocity of the particles on the surface of the specimen, and B0 is the magnetic field vector on the surface of the specimen.

[0217] Taking a linear EMAT coil with N turns and a length of l0 as an example, the formula for calculating the open-circuit induced voltage of EMAT is:

[0218]

[0219] Substituting equation (31) into equation (32), we can obtain the open-circuit induced voltage of EMAT as follows:

[0220]

[0221] The present invention has the following advantages:

[0222] 1) The impedance parameters of the high-temperature EMAT change with temperature and are updated at each operating temperature point; 2) The excitation current waveform calculated by the external circuit calculation module of the high-temperature EMAT is used in conjunction with the multi-physics field of the high-temperature EMAT to determine the excitation current value and the open-circuit voltage value of the high-temperature EMAT in real time; 3) The multi-physics-circuit collaborative calculation method of the high-temperature EMAT can be used more accurately for the optimization design of the high-temperature EMAT.

[0223] Example

[0224] Based on the scheme of Specific Implementation Method 1, the overall calculation process using the high-temperature EMAT multiphysics-circuit co-simulation system is as follows:

[0225] 1. The high-temperature EMAT operates in a thermal environment. The electrical conductivity and magnetic permeability of the EMAT at the operating temperature point are determined by equations (15) and (23). The density, Young's modulus and Poisson's ratio of the material at the operating temperature point are obtained by consulting the material design manual.

[0226] 2. Based on the obtained conductivity and permeability, the impedance parameters of the EMAT coil are solved by the field quantities calculated by equations (1) and (3). The equivalent inductance and equivalent resistance of the EMAT coil are solved by equations (24) and (25), respectively.

[0227] 3. Given the equivalent resistance and equivalent inductance of the EMAT coil, the excitation current waveform of the EMAT coil is obtained by solving the EMAT external circuit calculation module.

[0228] IV. Based on the obtained EMAT coil excitation current waveform, the magnetic field and electromagnetic distribution generated by the EMAT coil are obtained by solving equations (1) and (4), and the eddy current density distribution in the specimen is obtained by solving equation (9). Then, the Lorentz force density generated on the surface of the specimen is obtained by solving according to the definition of Lorentz force, i.e., equation (10).

[0229] V. Under the conditions of known Lorentz force density on the surface of the specimen and density, Young's modulus and Poisson's ratio at the working temperature of the material, the vibration velocity of the ultrasonic particles in the specimen is obtained by solving according to Equation (14).

[0230] 6. Based on the obtained ultrasonic particle vibration velocity in the specimen, the open-circuit induced voltage of the EMAT coil is obtained by solving according to equation (33).

[0231] See Figure 3 The waveforms of high-temperature EMAT received signals at different temperatures were measured in the experiment.

[0232] See Figure 4 The received signal measured by high-temperature EMAT was normalized, and the experimental results and simulation calculation results were compared at different temperatures.

[0233] The simulation results show the same trend and good consistency with the experimental results, with a maximum error of 5.77%, which verifies the effectiveness and accuracy of the high-temperature EMAT multiphysics-circuit co-calculation method.

[0234] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer, characterized in that, Includes the EMAT external circuit calculation module, the EMAT electromagnetic field calculation module, the EMAT acoustic field calculation module, and the EMAT thermal field calculation module; EMAT external circuit calculation module: Calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters; EMAT Thermal Field Calculation Module: Calculates conductivity, permeability, density, Young's modulus, and Poisson's ratio as they change with temperature, and updates the calculation at each operating temperature point. The calculated conductivity and permeability are input into the EMAT Electromagnetic Field Calculation Module, and the calculated density, Young's modulus, and Poisson's ratio are input into the EMAT Acoustic Field Calculation Module. EMAT Electromagnetic Field Calculation Module: Calculates the magnetic and electric field distribution generated by the EMAT coil based on conductivity, permeability and excitation current output from the EMAT external circuit, and then obtains the Lorentz force density on the surface of the specimen. The EMAT coil impedance is calculated based on the EMAT external circuit output excitation current, and the EMAT open-circuit induced voltage is calculated based on the conductivity, permeability and processing results of the EMAT sound field calculation module. EMAT acoustic field calculation module: Under the condition that the Lorentz force causes elastic deformation of the particles in the specimen, the vibration velocity of the ultrasonic particles in the specimen is calculated based on the density, Young's modulus, and Poisson's ratio.

2. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 1, characterized in that, The EMAT electromagnetic field calculation module calculates the magnetic and electric field distributions generated by the EMAT coil based on conductivity, permeability, and the excitation current output from the EMAT external circuit, and then obtains the Lorentz force density on the surface of the specimen. The process includes the following steps: The external circuit of the EMAT outputs an excitation current to the EMAT coil, generating a magnetic field H. (1) In the formula, J is the current density through the EMAT coil, and D is the displacement current. For Hamiltonian operators; According to Faraday's law of electromagnetic induction, we get: (2) In the formula, For electric field strength, It represents the magnetic flux density; Introducing magnetic vector potential A: (3) Substituting equation (3) into equation (2) and integrating both sides of the equation, we obtain the electric field E: (4) In the formula, The potential difference across the EMAT coil; Substituting equations (3) and (4) into equation (1), we get: (5) In the formula, Permeability, Electrical conductivity; According to the Lorentz norm conditions Ignoring the influence of displacement current, the magnetic field equation generated by the EMAT coil is obtained based on equation (5): (6) At the interface between different media, the magnetic vector potential function satisfies the following interface connection condition: (7) (8) In the formula, the subscript i represents the adjacent medium; the subscript t represents the tangent direction at the interface between adjacent media. The surface current density at the adjacent interface; After the magnetic vector potential is obtained, the eddy current density J in the test piece e is distributed as: (9) The Lorentz force density is obtained as follows: (10) In the formula, f L is the Lorentz force density generated in the surface layer of the test piece, B m is the magnetic induction provided by the permanent magnet.

3. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 2, characterized in that, The EMAT acoustic field calculation module calculates the ultrasonic vibration velocity of particles in a specimen based on density, Young's modulus, and Poisson's ratio when Lorentz force causes elastic deformation of particles in the specimen. The process includes the following steps: The particles in the specimen undergo elastic deformation under the action of the Lorentz force, and their equation of motion is expressed as: (11) In the formula, δ is the stress tensor, ρ is the specimen density, and u is the displacement of a particle in the specimen; Determine the formula for calculating acoustic impedance Z: (12) In the formula, ρ is the density of the medium; c is the speed of sound; δ is the stress; Let be the particle vibration velocity at position x when the sound wave propagates to position x at time t. The formulas for calculating the sound velocities of transverse and longitudinal waves are as follows: (13) In the formula, c s c is the transverse wave velocity; l η is the longitudinal wave velocity; G is the shear modulus; E is Young's modulus; η is Poisson's ratio; Substituting equation (13) into equation (12) yields the transverse wave particle vibration velocity ν. s and longitudinal wave particle vibration velocity ν l .

4. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 3, characterized in that, transverse wave particle vibration velocity ν s and longitudinal wave particle vibration velocity ν l as follows: (14) In the formula, ν s ν is the vibrational velocity of the transverse wave particles. l The velocity of the longitudinal wave particles is denoted as .

5. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to any one of claims 1 to 4, characterized in that, The EMAT thermal field calculation module calculates the electrical conductivity and magnetic permeability as a function of temperature, including the following steps: Within a temperature range, determine the conductivity as a function of temperature: (15) In the formula, T0 is room temperature, T is actual temperature, γ is actual conductivity, γ0 is room temperature conductivity, and α is temperature compensation coefficient. Based on Langevin's paramagnetic theory, neglecting the material's hysteresis effect, the magnetization M of the material is obtained as a Langevin function, thus determining the initial magnetic susceptibility. and saturation magnetization M S As parameters for fitting the magnetization curve using the Langevin function; for the saturation magnetization M S Using saturation magnetic flux density B S express: (20) The saturation magnetization M of the specimen S Relationship with temperature T K Using mean-field theory, it can be expressed as: (21) In the formula, N is the number of atoms per unit volume, ν is the atomic magnetic moment, λ is the mean field constant, and K B Boltzmann's constant; Solve equation (21) using a numerical method, and let m = M S / Nν,n = K B T K / Nν 2 λ, Equation (21) simplifies to: (22) Plot both sides of equation (22) as functions of m, and the intersection of the two curves is the value of m at different temperatures; Let Curie temperature T c Corresponding to n = 1 in equation (22), T c = Nν 2 λ / K B Then, the relationship curve between the magnetization intensity and temperature of the material can be calculated; Based on the magnetization curves calculated using the Langevin function and the magnetization intensity versus temperature curves calculated using the mean field theory, magnetization curves at different temperatures are obtained. Based on the constitutive relations of M and H, the magnetic permeability of the material under high temperature conditions is determined: (23) In the formula, μ(T) is the permeability at temperature T, M(T) is the magnetization at temperature T, and H(T) is the magnetic field strength at temperature T.

6. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 5, characterized in that, The Langevin function expression for the magnetization M of a material: (16) (17) In the formula, M S L is the saturation magnetization; L(|H|) is the Langevin function; The initial magnetic susceptibility; Saturation magnetization M S and initial magnetic susceptibility as follows: (18) (19) In the formula, μ r0 denoted as the initial permeability.

7. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 6, characterized in that, The process of calculating the EMAT coil impedance using the EMAT electromagnetic field calculation module includes the following steps: The EMAT coil impedance includes: the EMAT coil equivalent resistance and the EMAT coil equivalent inductance; The equivalent resistance R of the EMAT coil eq as follows: (24) In the formula, J is the current density through the EMAT coil, * indicates conjugate, and γ is the conductivity; Based on the equivalent inductance of the EMAT coil, the equivalent inductance L of the EMAT coil is obtained. eq : (25) In the formula, * represents conjugate, and I represents the current intensity flowing through the EMAT coil.

8. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 7, characterized in that, The process by which the EMAT electromagnetic field calculation module calculates the EMAT open-circuit induced voltage based on the conductivity, permeability, and processing results from the EMAT acoustic field calculation module includes the following steps: According to Maxwell's equations, the differential equations for the magnetic vector potential in air and in the specimen are as follows: (27) (28) In the formula, μ0 is the permeability of air, and ε0 is the permittivity of air. Permeability, Let A be the electrical conductivity, ω be the angular frequency, and A be the angular frequency. air Let A be the magnetic vector potential in the air. mat The magnetic vector potential in the specimen; Considering the boundary conditions, determine the magnetic vector potential generated in the air by the induced eddy current at depth z0 of the specimen: (29) In the formula, η is the skin depth, k0 is the wavenumber when the ultrasonic frequency ω is ω, z0 is the induced eddy current depth in the specimen, and z1 is the distance between the EMAT coil and the specimen. This refers to the induced eddy current at a depth z0 on the surface of the specimen caused by particle vibration; Integrating over the thickness of the specimen, we obtain the total magnetic vector potential generated by the induced eddy currents in the air above the specimen: (30) The final total magnetic vector potential is: (31) In the formula, v0 is the vibration velocity of the particles on the surface of the specimen, and B0 is the magnetic field vector on the surface of the specimen. Taking a linear EMAT coil with N turns and a length of l0 as an example, the formula for calculating the open-circuit induced voltage of EMAT is: (32) Substituting equation (31) into equation (32), we obtain the open-circuit induced voltage of EMAT as follows: (33) 。 9. The multiphysics-circuit collaborative simulation system for a high-temperature electromagnetic ultrasonic transducer according to claim 8, characterized in that, Induced eddy currents at depth z0 on the surface of the specimen caused by particle vibration: (26) In the formula, γ is the electrical conductivity of the specimen, v(z0) is the particle velocity at a depth z0 on the surface of the specimen, and B0(z0) is the magnetic field vector of the particle at a depth z0 on the surface of the specimen.

10. A multi-physics field-circuit collaborative simulation method for high-temperature electromagnetic ultrasonic transducers, characterized in that, The system simulation is based on a multiphysics-circuit co-simulation system for high-temperature electromagnetic ultrasonic transducers (EMAT). The method includes the simulation process from the high-temperature EMAT external circuit to the EMAT multiphysics field and the simulation process from the high-temperature EMAT multiphysics field to the EMAT external circuit. The simulation process from the high-temperature EMAT external circuit to the EMAT multiphysics field includes the following steps: The EMAT external circuit calculation module calculates the EMAT coil excitation current waveform based on the EMAT coil impedance parameters, inputs it to the EMAT electromagnetic field calculation module to calculate the force distribution on the surface of the specimen, i.e. the Lorentz force density on the surface of the specimen, and then inputs it to the EMAT acoustic field calculation module to calculate the vibration velocity of the ultrasonic particles in the specimen. The simulation process from the high-temperature EMAT multiphysics field to the EMAT external circuit includes two parts, as follows: (1) The density, Young's modulus and Poisson's ratio parameters are calculated by the EMAT thermal field calculation module and then input into the EMAT acoustic field calculation module to calculate the vibration velocity of the ultrasonic particles in the specimen. At the same time, the conductivity and permeability are calculated by the EMAT thermal field calculation module and then input into the EMAT electromagnetic field calculation module to finally calculate the open-circuit induced voltage of the EMAT receiver. (2) The conductivity and permeability are calculated by the EMAT thermal field calculation module, which are then used to calculate the EMAT coil impedance parameters by the EMAT electromagnetic field calculation module. Finally, the excitation current waveform of the EMAT coil is calculated by the EMAT external circuit calculation module.

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