Method for obtaining transient response of underwater giant magnetostrictive electro-acoustic transducer

Abstract

The application discloses a kind of transient response acquisition methods of underwater giant magnetostrictive electroacoustic transducer, first, the magnetic field model of transducer is established, then the improved J-A model considering bias magnetic and stress is established, the dynamic magnetization intensity and magnetostrictive strain of Terfenol-D rod different positions are calculated, and the output force of these positions is calculated, the mechanical impedance model of giant magnetostrictive electroacoustic transducer is then established, the output force is connected to the input port of mechanical impedance model, the electro-magnetic-mechanical-acoustic transient response model of transducer is obtained, the model can calculate the instantaneous sound pressure at any distance perpendicular to radiation surface.Based on model, the maximum sound pressure of transducer at different frequencies and its corresponding sound source level when input current is 1A are calculated, and the emission current response of transducer is obtained.The model couples non-uniform field and nonlinear strain of material in mechanical impedance model, so that the model can calculate the input-output characteristics of electroacoustic transducer in time domain, which is helpful to guide the design of transducer.

Description

Technical Field

[0001] This invention relates to the field of underwater giant magnetostrictive electroacoustic transducers, and in particular to a method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer. Background Technology

[0002] Giant magnetostrictive electroacoustic transducers are core equipment in marine exploration and underwater communication systems. The giant magnetostrictive rod driving the transducer undergoes magnetostrictive strain under magnetic field excitation, propelling a mass block to vibrate underwater and generate sound. Currently, most research on electroacoustic transducers is based on linear mechanical impedance models in the frequency domain, failing to reflect the transducer's time-domain response characteristics. Influenced by dynamic losses and the material's magnetomechanical properties, the dynamic magnetization process of giant magnetostrictive materials exhibits significant nonlinearity, easily causing distortion of the radiated sound waves. Therefore, it is necessary to study the transient electro-magnetic-mechanical-acoustic coupling characteristics of giant magnetostrictive transducers. Currently, the main models describing the magnetization of giant magnetostrictive materials include constitutive models, the Jiles-Atherton (JA) model, and the Preisach model. Among these, the JA model's formulas have clear physical meaning and can describe hysteresis loops under dynamic conditions, thus it is widely used in modeling magnetic material devices. To describe the magnetomechanical coupling characteristics of giant magnetostrictive materials, some scholars have proposed models relating the material's magnetostrictive strain ε to magnetization intensity, stress, and temperature, which can simulate the material's nonlinear output. To address the mechatronic characteristics of giant magnetostrictive electroacoustic transducers, many scholars have established mechanical impedance models to describe the frequency response of the transducers. To further describe the transient electroacoustic conversion process of the transducer, it is necessary to link the nonlinearity at the material level with the overall mechanical vibration law of the transducer, and establish a comprehensive transient response model of the electroacoustic transducer to describe its input-output characteristics in the time domain. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a method for obtaining the transient response of an underwater super-magnetostrictive electroacoustic transducer.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer includes the following steps:

[0006] S1. Divide the Terfenol-D rod into n equal segments along its axial direction, with the center of each segment considered as its location. Then, establish a three-dimensional magnetic field model of the giant magnetostrictive transducer in COMSOL finite element software and calculate the bias magnetic field strength H at different locations of the Terfenol-D rod segments. bias.i， i = 1, 2, ..., n;

[0007] S2. Derive the formula for calculating the magnetic field inside a multi-turn densely wound coil based on the Biot-Savart law, and calculate the AC magnetic field strength H at different locations on the Terfenol-D rod. ac ;

[0008] S3, Introducing an effective magnetic field strength H e The model relating stress σ and hysteresis-free magnetization M is used. an Decomposed into bias components M bias and the communication component M an.ac Then, the dynamic JA model under normal excitation state is used as the AC magnetization intensity M. ac The calculation module, then M bias With M ac The actual magnetization M is obtained by summing the results, thus establishing an improved JA model that considers stress and bias magnetization, and determining the model parameters [M]. s ,λ s ,σ s [,β,a,q,k,c];where M s λ represents the saturation magnetization. s σ represents the saturation magnetostrictive strain. s β represents the stress corresponding to the rotational saturation of magnetic domains, a is the temperature-dependent thermo-magnetic coupling coefficient, q is the molecular field coupling coefficient considering stress and temperature, k is the pinning coefficient, and c is the reversibility coefficient.

[0009] S4. Increasing the bias magnetic field strength H at different locations of the Terfenol-D rod. dc and alternating magnetic field strength H ac Substituting into the improved JA model of S3, the magnetization M at different locations of the Terfenol-D rod is calculated. i , i = 1, 2, ..., n;

[0010] S5. Based on the magnetization M at different locations of the Terfenol-D rod i Calculate the magnetostrictive strain λ of the Terfenol-D rod at different locations. i And through formula F i =AEλ i Calculate the magnetostrictive force F generated by these strains. i Where A is the cross-sectional area of ​​the Terfenol-D rod, and E is the Young's modulus of the Terfenol-D material;

[0011] S6. Based on the segmentation of the Terfenol-D rod in step S1, establish an n-order Multi-DOF model of the transducer oscillator; derive the mechanical impedance circuit of the transducer oscillator based on the "mechanical-electrical analogy method"; then, respectively, the front mass block and the rear mass block of the transducer are equivalent to a single-degree-of-freedom first-order vibration model, and the mechanical impedance circuits of the front mass block and the rear mass block are derived based on the "mechanical-electrical analogy method"; connect the equivalent mechanical impedance circuits of the front and rear mass blocks to the mechanical impedance circuit of the transducer oscillator, and introduce the acoustic radiation impedance of the radiation surface of the front mass block underwater to construct a multi-order mechanical impedance model of the giant magnetostrictive electroacoustic transducer, and derive the matrix equation of the multi-order mechanical impedance model based on the loop current method;

[0012] S7. The magnetostrictive force F calculated in S5 i Substituting into the matrix equation, the instantaneous vibration velocity u of the radiation surface at the current time point can be solved. r Then use the formula

[0013] Calculate the instantaneous sound pressure P(d) at a distance d meters from the radiating surface; where ρ w A represents the density of the water at the working depth. h The radiating area of ​​the front mass block is represented by d, and the straight-line distance from the sound field to the radiating surface is represented by d; where π represents pi, ω = 2πf represents the angular frequency, f is the input current frequency, and u r The instantaneous vibration velocity of the radiating surface is represented by t, where t is time and kd is the time delay of the sound wave.

[0014] S8. Set the input current of the underwater giant magnetostrictive electroacoustic transducer to I0 = 1A, the input frequency f to the operating frequency, and the sound wave receiving distance d to 1m. Calculate the instantaneous sound pressure at the underwater distance d meters from the transducer's radiating surface using steps S1-S7, and substitute the maximum sound pressure over multiple cycles into the formula TCR = 20log(|P(d)| / I0) + 120 to calculate the transducer's emission current response TCR at the operating frequency.

[0015] S9. Using step S8, calculate the TCR of the transducer at different input frequencies and plot the "frequency-TCR" curve to obtain the emission current response curve of the giant magnetostrictive electroacoustic transducer in the operating frequency band.

[0016] A further improvement is made to the calculation of the bias magnetic field strength in step S1, which is as follows:

[0017] First, a finite element model of the giant magnetostrictive transducer is established in COMSOL software, setting material parameters including Terfenol-D rods, permanent magnets, coils, and front and rear mass blocks. Then, a physical field study of the "Magnetic Field" is added, and "Ampere's Law" is added to define the geometric domain, selecting all permanent magnets. In this "Ampere's Law" setting, the magnetization model of the "Constituent Relation BH" is set to "Remanent Flux Density," and the vacuum permeability μ0 and recovery permeability μ of the permanent magnets are input. rec Residual magnetic flux density B r Meanwhile, the direction vector of the magnetic flux is defined to be parallel to the axial direction of the rod, and the governing equations of the model are:

[0018] B=μ0μ rec H+B r , Where H is the magnetic field strength, B is the magnetic flux density, μ0 is the free permeability, and μ rec To restore the permeability, B r Let ||B| be the remanent magnetic flux density. r || represents the residual flux density modulus;

[0019] A free triangular mesh is added to divide the finite element model, and the maximum element size of the mesh is set to be smaller than the minimum gap size of the finite element model. A "steady-state" study step is then added, and the simulation model is run to calculate the magnetic field distribution inside the transducer. Points at different mesh locations are selected in the simulation results, and the bias magnetic field H at these points is read. bias.i , i = 1, 2, ..., n.

[0020] In a further improvement, the calculation steps for the alternating magnetic field strength in step S2 are as follows:

[0021] When the excitation coil is placed in a cylindrical coordinate system, according to the Biot-Savart law, when the input current is i = Isin(ωt)A, the infinitesimal circular current with radius r on the coil produces the following alternating magnetic field dH at the spatial point (0,0,z). ac :

[0022]

[0023] Where n is the number of coil turns, I represents the amplitude of the input current, and L c r1 represents the axial length of the coil, r2 represents the inner radius of the coil, z represents the axial position, dr represents the width of the infinitesimal circle current, A represents amperes, ω represents the angular frequency, and t represents time.

[0024] dH along the radial and axial directions of the coil respectively ac Integrating, we obtain the AC magnetic field strength H generated by the coil at any point in space along the axial direction. ac, is represented as:

[0025]

[0026] Substituting the positions of different segments on the Terfenol-D rod into the above formula, the AC magnetic field strength H at these positions can be calculated. ac.i , i = 1, 2, ..., n.

[0027] Further improvements, in step S3, include the following specific modeling steps for the improved JA model considering bias magnetism and stress:

[0028] The relationship between magnetostrictive strain λ, magnetization M, temperature T, and stress σ is:

[0029]

[0030] Where λ0(σ) represents the magnetostrictive strain caused by stress, λ s M represents saturation magnetostrictive strain. s T Represents the temperature-dependent saturation magnetization, β is the thermo-magnetic coupling coefficient, and ΔT = TT. r For temperature difference, T r T represents the spin reorientation temperature of Terfenol-D. c Represents the Curie temperature of Terfenol-D; under the set working stress of the Terfenol-D rod, using the formula...

[0031] Calculate the value of λ0(σ), σ s This represents the stress corresponding to the saturation of magnetic domain rotation.

[0032] Using formula Calculate the effective magnetic field strength H inside Terfenol-D e Where α is the molecular field coupling coefficient and μ0 is the vacuum permeability;

[0033] Under the combined excitation of the coil and the permanent magnet, the magnetic field strength contains a bias component H. bias and the communication component H ac The magnetization generated by the excitation also has a bias component M. bias and the communication component M ac :

[0034] H = H bias +H ac M = M bias +M ac

[0035] Based on the formula for calculating the effective magnetic field strength, the hysteresis-free magnetization M under bias and stress is considered. anfor:

[0036]

[0037] Where a is the shape factor and q is the molecular field coupling coefficient considering stress and temperature;

[0038] When no current is applied to the coil, the Terfenol-D magnet is already magnetized by the bias magnetic field of the permanent magnet, and the bias component M of the magnetization intensity... bias Only by bias magnetic field H bias It is generated and calculated using the following formula:

[0039]

[0040] Hysteresis-free magnetization M an The AC component M an.ac It can be seen as M an With bias component M bis The difference is calculated using the following formula:

[0041]

[0042] The AC component M of hysteresis-free magnetization an.ac Using equations

[0043]

[0044] Calculate the AC component M of the actual magnetization M ac Where δ is the sign function characterizing the change in the external magnetic field H, δ=sign(dH / dt); d represents the differentiation; k is the pinning coefficient, c is the reversibility coefficient, and H e The effective magnetic field strength is given by μ0, where μ is the free permeability; ξ is a function used to ensure consistency between theoretical calculations and the characteristics exhibited by Terfenol-D, using the formula...

[0045] Determine the instantaneous value of ξ; D is the eddy current equivalent diameter of the cross section, ρ is the resistivity, β is the geometric factor (for a cylinder, β = 16), and the dimensionless constant G0 = 0.1356. C H0 is the cross-sectional area of ​​the bar, and H0 is a characteristic parameter.

[0046] Based on the bias component M of the magnetization bis and the communication component M ac Using the formula M = M bis +M ac The dynamic magnetization intensity M at the current time point is calculated.

[0047] Further improvements, in step S6, the specific modeling steps for the mechanical impedance model of the giant magnetostrictive electroacoustic transducer are as follows:

[0048] The dynamic behavior of the Terfenol-D rod is described using the Multi-DOF model, and the motion of each segment of the Terfenol-D rod is expressed by the following equations of motion:

[0049]

[0050] Where x i x represents the displacement of the i-th segment. i-1 M represents the displacement of the previous segment. i K represents the equivalent quality of the current segment. i K represents the stiffness of the current segment. i-1 C represents the stiffness of the preceding segment. i C represents the mechanical damping of the current segment. i-1 F represents the mechanical damping of the previous segment. i F represents the force generated in the current segment. i-1 This represents the force generated in the previous stage;

[0051] Under sinusoidal excitation, each segment of the Terfenol-D rod can be considered as undergoing simple harmonic motion, with the displacement of each segment being: x i =|x i |e jωt The vibration velocity is u i =jω|x i |e jωt Then we have the following formula:

[0052]

[0053] The above equation is equivalent to a circuit using the "mechanical-electrical analogy" method. In the circuit, the current represents the vibration velocity and the voltage represents the force, thereby establishing the mechanical impedance circuit of the transducer oscillator.

[0054] In the underwater super-magnetostrictive electroacoustic transducer, the front mass block is the main acoustic radiation component, and the circular end of the front mass block that contacts the water is the radiation surface of the transducer. Based on the "mechanical-electrical analogy" method, the mechanical impedance circuit of the front mass block is described by the following formula:

[0055]

[0056] Where M h u represents the equivalent mass of the pre-mass block. h u represents the vibration velocity of the front mass block. PM2 K represents the vibration velocity of the permanent magnet. h C represents the stiffness of the pre-mass block. h Z represents the mechanical damping of the front mass block. r ω represents the acoustic radiation impedance of the front mass block, and ω represents the angular velocity.

[0057] The mass of the rear mass is much greater than that of the front mass, and the rear mass has a weaker ability to vibrate and produce sound underwater. Therefore, the mechanical impedance circuit of the rear mass can be described by the following formula:

[0058]

[0059] Where M t For the equivalent mass of the subsequent mass block, u t Let K be the vibration velocity of the rear mass block. t For the stiffness of the rear mass block, C t For the mechanical damping of the rear mass block, K PM1 For the stiffness of the permanent magnet, u PM1 C is the vibration velocity of the permanent magnet. PM1 For the mechanical damping of permanent magnets;

[0060] By connecting the mechanical impedance circuits of the front mass block and the rear mass block to the nth-order mechanical impedance circuit of the oscillator, and connecting the acoustic radiation impedance in parallel after the front mass block, a multi-order mechanical impedance model of the giant magnetostrictive electroacoustic transducer is obtained:

[0061] Based on the loop current method, a solution matrix for the mechanical impedance model is constructed, and the instantaneous vibration velocity u of the radiating surface is obtained using the solution matrix. r :

[0062]

[0063] Among them, F i Let u be the output force of the i-th segment. i Let be the vibration velocity of the i-th segment. t e PM1 e i e n e PM2 e h The coefficients of the matrix can be obtained using the following formula;

[0064]

[0065] The beneficial effects of this invention are as follows:

[0066] This invention proposes an improved JA model considering bias magnetic fields and prestress. The classic JA model can effectively simulate the magnetization of ferromagnetic materials under different frequency inputs, and the formulas have clear physical meaning. This invention, by introducing bias components and stress factors into magnetization, derives an improved expression for the dynamic JA model under bias and stress conditions, and calculates the non-uniform magnetization of materials based on the improved JA formula. Compared with existing JA models, the improved JA model can describe the asymmetric magnetization curves of ferromagnetic materials under various bias states without changing the physical mechanism of the original JA theory. This invention also proposes a method for calculating the transient response of electroacoustic transducers based on a mechanical impedance model. By introducing the non-uniform magnetization of Terfenol-D materials into the multi-order mechanical model of the transducer and incorporating the acoustic radiation impedance of a circular radiating surface, the solution matrix equation of the model is derived. This allows the model to calculate the transient response process of the electroacoustic transducer considering material nonlinearity, and uses formulas to calculate the instantaneous sound pressure distribution. Furthermore, the source level of the transducer at that frequency point is calculated based on the maximum sound pressure over multiple cycles. Compared with existing impedance models for electroacoustic transducers, this method incorporates field nonuniformity and material nonlinearity into the impedance model, enabling the model to better describe the output nonlinearity in the time domain. At the same time, the model retains the frequency response characteristics of the mechanical impedance model, i.e., simulating the current response of the transducer in the frequency domain. These features allow the established model to more effectively describe the actual input-output characteristics of the transducer and better guide transducer design. Attached Figure Description

[0067] The invention will be further illustrated with reference to the accompanying drawings, but the contents of the drawings do not constitute any limitation on the invention.

[0068] Figure 1 This is a flowchart of a transient response calculation method for an underwater super-magnetostrictive electroacoustic transducer involved in this invention;

[0069] Figure 2 This is a schematic diagram illustrating the calculation method for the non-uniform bias magnetic field and alternating magnetic field involved in this invention;

[0070] Figure 3 This is a flowchart illustrating the construction of the JA model considering prestress and bias magnetic field involved in this invention.

[0071] Figure 4 This is a mechanical structure diagram of the supermagnetostrictive electroacoustic transducer involved in this invention;

[0072] Figure 5 This is a 1 / 4 equivalent circuit diagram of the mechanical impedance model of the transducer involved in this invention;

[0073] Figure 6-1 A comparison chart of the instantaneous sound pressure levels of the transducer when the input is 800Hz;

[0074] Figure 6-2 A comparison chart of the instantaneous sound pressure levels of the transducer when the input is 1000Hz;

[0075] Figure 7 This is a comparison chart of the fitted curve and the measured curve of the emission current response involved in this invention; Detailed Implementation

[0076] To make the purpose, technical solution, and advantages of the invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and examples.

[0077] Example 1

[0078] This embodiment corresponds to a simplified flowchart of the transient response calculation for an underwater giant magnetostrictive electroacoustic transducer considering bias magnetic field and stress, as shown below. Figure 1 As shown, the implementation of this embodiment may include:

[0079] Step 1: Divide the Terfenol-D rod into several equal segments (denoted as n segments) along its axial direction. The center of each segment is considered as its position. Then, establish a three-dimensional magnetic field model of the giant magnetostrictive transducer in COMSOL finite element software and calculate the bias magnetic field strength H of the Terfenol-D rod at different positions. bias.i (i = 1, 2, ..., n);

[0080] In this embodiment, step 1 may include:

[0081] Step 1.1: First, establish a finite element model of the giant magnetostrictive transducer in COMSOL software, setting material parameters including Terfenol-D rods, permanent magnets, coils, and front and rear mass blocks; then add a physical field study for "Magnetic Field," and add "Ampere's Law" to define the geometric domain, selecting all permanent magnets; then, in the settings of this "Ampere's Law," set the magnetization model of "Constitutive Relation BH" to "Remanent Flux Density," and input the vacuum permeability μ0 and the restoring permeability μ of the permanent magnets. rec Residual magnetic flux density B r Meanwhile, the direction vector of the magnetic flux is defined to be parallel to the axial direction of the rod, and the governing equations of the model are:

[0082] B=μ0μ rec H+B r , Where H is the magnetic field strength, B is the magnetic flux density, μ0 is the free permeability, and μ rec To restore the permeability, B r Let ||B| be the remanent magnetic flux density. r || represents the residual flux density mode.

[0083] Step 1.2: Add a free triangular mesh to divide the finite element model, and set the maximum element size of the mesh to be smaller than the minimum gap size of the finite element model; then add a "steady-state" study step, run the simulation model, and calculate the magnetic field distribution inside the transducer; select points at different division positions in the simulation results and read the bias magnetic field H at these points. bias.i (i = 1, 2, ..., n).

[0084] Step 2: Derive the formula for calculating the magnetic field inside a multi-turn tightly wound coil based on the Biot-Savart law, and calculate the AC magnetic field strength H at different locations on the Terfenol-D rod. ac .

[0085] In this embodiment, step 2 may include:

[0086] Step 2.1: The alternating magnetic field in the transducer is generated by coil excitation. Place the coil in a cylindrical coordinate system, with the x-axis and y-axis along the radial direction of the Terfenol-D rod and passing through the center point of the cross-section, and the z-axis along the axial direction of the Terfenol-D rod. According to the Biot-Savart law, when the input current is i = Isin(ωt)A, an infinitesimal circular current of radius r on the coil can generate the following alternating magnetic field dH at the spatial point (0,0,z). ac :

[0087]

[0088] Where n is the number of coil turns, I represents the amplitude of the input current, and L c r1 represents the axial length of the coil, r2 represents the inner radius of the coil, z represents the axial position, dr represents the width of the infinitesimal circle current, A represents amperes, ω represents the angular frequency, and t represents time.

[0089] Step 2.2: Adjust dH along the radial direction of the coil. ac Integrating, we obtain the AC magnetic field strength H generated by the coil at any point in space along the axial direction. ac , is represented as:

[0090]

[0091] By substituting the positions of different segments on the Terfenol-D rod into the above formula, the AC magnetic field strength H of the Terfenol-D rod at these positions can be calculated. ac.i (i = 1, 2, ..., n).

[0092] Steps 1 and 2 constitute the method for calculating the real-time magnetic field of the transducer. The detailed implementation flowchart of the method is shown below. Figure 2 As shown.

[0093] Step 3: Introduce an effective magnetic field strength H e The model relating stress σ and hysteresis-free magnetization M is used. an Decomposed into bias components M bias and the communication component M an.ac Then, the dynamic JA model under normal excitation state is used as the AC magnetization M. ac The calculation module, then with M bias With M ac The sum of these values ​​is used as the actual magnetization M, thus establishing an improved JA model that considers stress and bias, and determining the model parameters [M]. s ,λ s ,σ s [,β,a,q,k,c];where M s λ represents the saturation magnetization. s , representing saturation magnetostriction strain, σ s β represents the stress corresponding to the rotational saturation of magnetic domains, a is the temperature-dependent thermo-magnetic coupling coefficient, q is the molecular field coupling coefficient considering prestress and temperature changes, k is the pinning coefficient, and c is the reversibility coefficient.

[0094] In this embodiment, step 3 may include:

[0095] Step 3.1: First, give the relationship between the magnetostrictive strain λ, magnetization M, temperature T, and stress σ of the material:

[0096]

[0097] Where λ0(σ) represents the magnetostrictive strain caused by stress, λ s M represents saturation magnetostrictive strain. s T ΔT represents the temperature-dependent saturation magnetization, β represents the thermo-magnetic coupling coefficient, and ΔT = TT. r T represents the temperature difference, where T is the temperature of the Terfenol-D rod. r The spin reorientation temperature of Terfenol-D materials (typically taken as T) r =0), T c This represents the Curie temperature of the Terfenol-D material.

[0098] Step 3.2: Under the set working prestress of the Terfenol-D bar, use the formula

[0099] The value of λ0(σ) is calculated, σ s This represents the stress corresponding to the rotational saturation of magnetic domains.

[0100] Step 3.3: Based on the classical JA model theory proposed by DCJiles et al., differentiate the energy density A of the material system without considering hysteresis, and use the formula...

[0101]

[0102] Calculate the effective magnetic field strength H inside the Terfenol-D material e .

[0103] Here, α is the molecular field coupling coefficient (different from q), and μ0 represents the permeability of vacuum.

[0104] Step 3.4: Under the joint excitation of the coil and the permanent magnet, the magnetic field strength H simultaneously contains a bias component H0. bias and the communication component H ac The magnetization generated by the excitation also has a bias component M. bias and the communication component M ac :

[0105] H = H bias +H ac M = M bias +M ac

[0106] Step 3.5: Based on the formula for calculating the effective magnetic field strength, consider the hysteresis-free magnetization M under bias and stress. an for:

[0107] Where a is the shape factor and q is the molecular field coupling coefficient considering stress and temperature.

[0108] Step 3.6: When no current is applied to the coil, the Terfenol-D magnet is already magnetized by the bias magnetic field of the permanent magnet. The bias component M of the magnetization intensity... bias Only by bias magnetic field H bias It is generated and calculated using the following formula:

[0109]

[0110] Step 3.7: Hysteresis-free magnetization M an The AC component M an.ac It can be seen as M an With bias component M bis The difference is calculated using the following formula:

[0111]

[0112] Step 3.8: The AC component M of the hysteresis-free magnetization an.ac Using equations

[0113]

[0114] Calculate the AC component M of the actual magnetization M ac Where δ is the sign function characterizing the change in the external magnetic field H, δ=sign(dH / dt); d represents the differentiation; k is the pinning coefficient, c is the reversibility coefficient, and H e The effective magnetic field strength is given by μ0, where μ is the free permeability; ξ is a function used to ensure consistency between theoretical calculations and the characteristics exhibited by Terfenol-D, using the formula...

[0115] Determine the instantaneous value of ξ; D is the eddy current equivalent diameter of the cross section, ρ is the resistivity, β is the geometric factor (for a cylinder, β = 16), and the dimensionless constant G0 = 0.1356. C H0 is the cross-sectional area of ​​the bar, and H0 is a characteristic parameter.

[0116] Step 3.9: Based on the bias component M of the magnetization calculated above bis and the communication component M ac Using the formula M = M bias +M ac The dynamic magnetization intensity M at the current time point is calculated.

[0117] Step 4: Increasing the bias magnetic field strength H at different locations on the Terfenol-D rod. dc and alternating magnetic field strength H ac Substituting into the improved JA model of S3, the magnetization M at different locations of the Terfenol-D rod is calculated. i (i = 1, 2, ..., n).

[0118] Step 5: Based on the magnetization M at different locations of the Terfenol-D rod i Calculate the magnetostrictive strain λ of the Terfenol-D rod at different locations. i And through formula F i =AEλ i Calculate the magnetostrictive force F generated by these strains. i Where A is the cross-sectional area of ​​the Terfenol-D rod, and E is the Young's modulus of the Terfenol-D material.

[0119] Step 6: Based on the segmentation of the Terfenol-D rod in Step S1, establish an n-order Multi-DOF model of the transducer oscillator; derive the mechanical impedance circuit of the transducer oscillator based on the "mechanical-electrical analogy method"; then, respectively, the front mass block and the rear mass block of the transducer are equivalent to a single-degree-of-freedom first-order vibration model, and the mechanical impedance circuits of the front mass block and the rear mass block are derived based on the "mechanical-electrical analogy method"; connect the equivalent mechanical impedance circuits of the front and rear mass blocks to the mechanical impedance circuit of the transducer oscillator, and introduce the acoustic radiation impedance of the radiation surface of the front mass block underwater to construct a multi-order mechanical impedance model of the giant magnetostrictive electroacoustic transducer, and derive the matrix equation of the multi-order mechanical impedance model based on the loop current method.

[0120] In this embodiment, step 6 may include:

[0121] Step 6.1: In S1, the Terfenol-D rod has been divided into several segments, and its dynamic behavior can be described using the Multi-DOF model. In this model, the motion of each segment of the Terfenol-D rod is expressed by the following equation:

[0122]

[0123] Where x i x represents the displacement of the i-th segment. i-1 M represents the displacement of the previous segment. i K represents the equivalent quality of the current segment. i K represents the stiffness of the current segment. i-1 C represents the stiffness of the preceding segment. i C represents the mechanical damping of the current segment. i-1 F represents the mechanical damping of the previous segment. i F represents the strain force generated in the current segment. i-1 This represents the strain generated in the previous stage.

[0124] Step 6.2: Under sinusoidal excitation, each segment of the Terfenol-D rod can be considered as simple harmonic motion, and the displacement of each segment is: x i =|x i |e jωt The vibration velocity is u i =jω|x i |e jωt The previous equations of motion can be rewritten as follows:

[0125]

[0126] The above equation can be converted into a circuit form using the "mechanical-electrical analogy" method. In the circuit, the current represents the vibration velocity and the voltage represents the force, thereby establishing the mechanical impedance circuit of the transducer oscillator.

[0127] Step 6.3: In the transducer used in this patent, the front mass block is the main acoustic radiation component, and the part of the circular end of the front mass block that contacts the water is the radiation surface of the transducer. Based on the "mechanical-electrical analogy" method, the mechanical impedance circuit of the front mass block is described by the following formula:

[0128]

[0129] Where M h u represents the equivalent mass of the pre-mass block. h u represents the vibration velocity of the front mass block. PM2 K represents the vibration velocity of the permanent magnet. h C represents the stiffness of the pre-mass block. h Z represents the mechanical damping of the front mass block. r ω represents the acoustic radiation impedance of the front mass block, and ω represents the angular velocity.

[0130] Step 6.4: The mass of the rear mass is much greater than that of the front mass. The rear mass has a weaker ability to vibrate and produce sound underwater. Therefore, the mechanical impedance circuit of the rear mass can be described by the following formula:

[0131]

[0132] Where M t For the equivalent mass of the subsequent mass block, u t Let K be the vibration velocity of the rear mass block. t For the stiffness of the rear mass block, C t For the mechanical damping of the rear mass block, K PM1 For the stiffness of the permanent magnet, u PM1 C is the vibration velocity of the permanent magnet. PM1 For the mechanical damping of permanent magnets.

[0133] Step 6.5: Connect the mechanical impedance circuits of the front and rear mass blocks to the nth-order mechanical impedance circuit of the oscillator, and connect the acoustic radiation impedance in parallel after the front mass block to obtain the multi-order mechanical impedance model of the giant magnetostrictive electroacoustic transducer. Based on the loop current method, construct the solution matrix of the mechanical impedance model. Then, use the solution matrix...

[0134]

[0135] Solve for the instantaneous vibration velocity u of the radiating surface. r .

[0136] Among them, F i Let u be the output force of the i-th segment. i e represents the vibration velocity of the i-th segment. t e PM1 e i en e PM2 e h The coefficients of the matrix can be obtained using the following formula.

[0137]

[0138] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer, characterized in that, Includes the following steps: S1. Divide the Terfenol-D rod into equal intervals along its axial direction. n The center of each segment is considered as its location. Then, a three-dimensional magnetic field model of the giant magnetostrictive transducer is built in COMSOL finite element software, and the bias magnetic field strength at the location of different segments of the Terfenol-D rod is calculated. Hbias.i,i = 1, 2, … , n ; S2. Derive the formula for calculating the magnetic field inside a multi-turn densely wound coil based on the Biot-Savart law, and calculate the AC magnetic field strength at different locations on the Terfenol-D rod. Hac.i ; S3, Introducing effective magnetic field strength He With stress σ The relational model, and the hysteresis-free magnetization Man Decomposed into bias components Mbias and communication weight Man.ac Then, the dynamic JA model under normal excitation conditions is used as the AC magnetization intensity. Mac The calculation module, and then Mbias and Mac The summation yields the actual magnetization. M Thus, an improved JA model considering stress and bias magnetism is established, and the parameters of the model are determined. Ms , λs , σs , β , a , q , k , c ];in Ms Represents saturation magnetization. λs Represents saturated magnetostrictive strain. σs This represents the stress corresponding to the saturation of magnetic domain rotation. β The temperature-dependent thermo-magnetic coupling coefficient. a The shape factor, q To account for the molecular field coupling coefficients of stress and temperature, k Represents the pinning coefficient. c Represents the invertibility coefficient; S4. Increasing the bias magnetic field strength at different locations of the Terfenol-D rod. Hbias.i and alternating magnetic field strength Hac.i Substituting into the improved JA model of S3, the magnetization intensity at different locations of the Terfenol-D rod is calculated. Mi , i = 1, 2, … , n ; S5. Based on the magnetization intensity at different locations of the Terfenol-D rod. Mi Calculate the magnetostrictive strain of the Terfenol-D rod at different locations λi And through the formula Fi = AEλi Calculate the magnetostrictive force generated by these strains Fi ;in A The cross-sectional area of ​​the Terfenol-D rod is... E The Young's modulus of Terfenol-D material; S6. Based on the segmentation of the Terfenol-D rod in step S1, establish an n-order Multi-DOF model of the transducer oscillator; derive the mechanical impedance circuit of the transducer oscillator based on the "mechanical-electrical analogy method"; then, respectively, the front mass block and the rear mass block of the transducer are equivalent to a single-degree-of-freedom first-order vibration model, and the mechanical impedance circuits of the front mass block and the rear mass block are derived based on the "mechanical-electrical analogy method"; connect the equivalent mechanical impedance circuits of the front and rear mass blocks to the mechanical impedance circuit of the transducer oscillator, and introduce the acoustic radiation impedance of the radiation surface of the front mass block underwater to construct a multi-order mechanical impedance model of the giant magnetostrictive electroacoustic transducer, and derive the matrix equation of the multi-order mechanical impedance model based on the loop current method; S7. The magnetostrictive force calculated in S5 Fi Substituting into the matrix equation, the instantaneous vibration velocity of the radiation surface at the current time point can be solved. ur Then use the formula Calculate the distance to the radiating surface d instantaneous sound pressure at meters P ( d );in ρw The density of the water at the working depth. Ah This represents the radiative area of ​​the premass block. d Represents the straight-line distance from the sound field to the radiating surface; Where π represents the value of a circle's pi. =2π f Represents angular frequency. f The frequency of the input current. The instantaneous vibration velocity representing the radiating surface. t For time, kd This is the time delay of the sound wave; S8. Set the input current of the underwater magnetostrictive electroacoustic transducer to be... I0 =1A, input frequency f The operating frequency and the sound wave receiving distance are specified. d The underwater distance to the transducer's radiating surface is 1m. Steps S1-S7 are used to calculate this. d The instantaneous sound pressure at a distance of meters was calculated, and the maximum sound pressure over multiple cycles was substituted into the formula. The transmit current response of the transducer at the operating frequency was calculated. TCR ; S9. Using step S8, calculate the transducer at different input frequencies. TCR And plot the "frequency- TCR The curve is used to obtain the emission current response curve of the supermagnetostrictive electroacoustic transducer within the operating frequency band.

2. The method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer according to claim 1, characterized in that, In step S1, the calculation steps for the bias magnetic field strength are as follows: First, a finite element model of the giant magnetostrictive transducer is established in COMSOL software, setting material parameters including Terfenol-D rods, permanent magnets, coils, and front and rear mass blocks. Then, a physical field study of the "Magnetic Field" is added, and "Ampere's Law" is added to define the geometric domain, selecting all permanent magnets. Finally, in the settings of this "Ampere's Law," the constitutive relation is set... B - H The magnetization model is set to "remanent flux density", and the vacuum permeability of the permanent magnet is input. μ0 , Reverse permeability μrec Residual magnetic flux density Br Meanwhile, the direction vector of the magnetic flux is defined to be parallel to the axial direction of the rod, and the governing equations of the model are: ,in H The magnetic field strength, B , where is the magnetic flux density The permeability of free space, To restore permeability, The residual magnetic flux density is The residual flux density mode; A free triangular mesh is added to divide the finite element model, and the maximum element size of the mesh is set to be smaller than the minimum gap size of the finite element model. Then, a "steady-state" study step is added, and the simulation model is run to calculate the magnetic field distribution inside the transducer. Points at different mesh locations are selected in the simulation results, and the bias magnetic field at these points is read. Hbias.i,i = 1, 2, … , n .

3. The method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer according to claim 1, characterized in that, In step S2, the calculation steps for the alternating magnetic field strength are as follows: Placing the excitation coil in a cylindrical coordinate system, according to the Biot-Savart law, when the input current is... i = Isin ( ω t At time A, the radius of the coil is r An infinitesimal circular current at the point in space (0, 0, ... z The following alternating magnetic field is generated at ( ). dHac : in n The number of coil turns. I Represents the amplitude of the input current. Lc Represents the axial length of the coil. r1 Represents the inner radius of the coil. r2 Represents the outer radius of the coil. z This refers to the axial position. dr Let A be the width of the infinitesimal circular current, and A be the ampere. Angular frequency, t For time; Along the radial direction of the coil dHac Integrating, we obtain the AC magnetic field strength generated by the coil at any point in space along the axial direction. Hac , represented as: By substituting the positions of different segments on the Terfenol-D rod into the above formula, the AC magnetic field strength at these positions can be calculated. Hac.i, i = 1, 2,… , n .

4. The method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer according to claim 1, characterized in that, In step S3, the specific modeling steps for the improved JA model considering bias magnetism and stress are as follows: Magnetostrictive strain λ Magnetization M ,temperature T and stress σ The relation is: in λ0 ( σ () represents magnetostrictive strain caused by stress. λs Represents saturated magnetostrictive strain. MsT Represents temperature-dependent saturation magnetization. β Thermo-magnetic coupling coefficient, ∆T = T - Tr For temperature difference, Tr The spin reorientation temperature of Terfenol-D is represented by... Tc The Curie temperature representing Terfenol-D; Under the set working stress of the Terfenol-D rod, using the formula calculate λ0 ( σ The value of ) σs This represents the stress corresponding to the saturation of magnetic domain rotation. Using formula Calculate the effective magnetic field strength inside Terfenol-D He ;in α The molecular field coupling coefficient is... μ0 Permeability of free space; Under the combined excitation of the coil and the permanent magnet, the magnetic field strength contains a bias component. Hbias and communication weight Hac The magnetization generated by the excitation also has a bias component. Mbias and communication weight Mac : Based on the formula for calculating the effective magnetic field strength, the hysteresis-free magnetization intensity under bias and prestress is considered. Man for: in a The shape factor, q The molecular field coupling coefficient is taken into account for stress and temperature; When no current is applied to the coil, the Terfenol-D magnet is already magnetized by the bias magnetic field of the permanent magnet. The bias component of the magnetization intensity... Mbias Only by bias magnetic field Hbias The result is generated using the following formula: Hysteresis-free magnetization Man Exchange weight Man.ac It can be seen as Man With bias components Mbis The difference is calculated using the following formula: AC component of hysteresis-free magnetization Man.ac Using equations Calculate the actual magnetization M Exchange weight Mac ;in δ To characterize the external magnetic field H The sign function of change, δ= sign(d H / d t ); d represents the differentiation; k The pinning factor is... c The invertibility coefficient is... He For effective magnetic field strength, Permeability of free space; ξ This is a value-selecting function used to ensure consistency between theoretical calculations and the characteristics exhibited by Terfenol-D, using the formula... Sure ξ The instantaneous value; D It is the eddy current equivalent diameter of the cross section. ρ It is resistivity. β It is a geometric factor, which has the following properties for a cylinder: β =16, dimensionless constant G0 =0.1356, SC It is the cross-sectional area of ​​the bar. H0 For feature parameters; Based on the bias component of magnetization Mbis and communication weight Mac Using the formula M = Mbis + Mac Calculate the dynamic magnetization at the current time point. M .

5. The method for obtaining the transient response of an underwater giant magnetostrictive electroacoustic transducer according to claim 1, characterized in that, In step S6, the specific modeling steps for the mechanical impedance model of the giant magnetostrictive electroacoustic transducer are as follows: The dynamic behavior of the Terfenol-D rod is described using the Multi-DOF model, and the motion of each segment of the Terfenol-D rod is expressed by the following equations of motion: in xi Representing the i The displacement of the segment xi-1 Represents the displacement of the previous segment. Mi Represents the equivalent quality of the current segment. Ki Represents the stiffness of the current segment. Ki-1 Represents the stiffness of the preceding segment. Ci Represents the mechanical damping of the current segment. Ci-1 Represents the mechanical damping of the previous section. Fi Represents the strain generated in the current segment. Fi-1 This represents the strain generated in the previous stage; Under sinusoidal excitation, each segment of the Terfenol-D rod can be considered as undergoing simple harmonic motion, and the displacement of each segment is: xi=|xi|ej ωt The vibration velocity is UI = jω|xi|ejωt Then we have the following formula: The above equation is equivalent to a circuit using the "mechanical-electrical analogy" method. In the circuit, the current represents the vibration velocity and the voltage represents the force, thereby establishing the mechanical impedance circuit of the transducer oscillator. In the underwater super-magnetostrictive electroacoustic transducer, the front mass block is the main acoustic radiation component, and the part of the circular end of the front mass block that contacts the water is the radiation surface of the transducer. Based on the "mechanical-electrical analogy" method, the mechanical impedance circuit of the front mass block is described by the following formula: in Mh This represents the equivalent mass of the previous mass block. uh Represents the vibration velocity of the preceding mass block. uPM2 Represents the vibration velocity of the permanent magnet. Kh This represents the stiffness of the pre-mass block. Ch Represents the mechanical damping of the front mass block. Zr This represents the acoustic radiation impedance of the front mass block. Represents angular velocity; The mass of the rear mass is much greater than that of the front mass, and the rear mass has a weaker ability to vibrate and produce sound underwater. Therefore, the mechanical impedance circuit of the rear mass can be described by the following formula: in Mt The equivalent mass of the subsequent mass block. ut The vibration velocity of the rear mass block. Kt Let be the stiffness of the rear mass block. Ct For the mechanical damping of the rear mass block, KPM1 The stiffness of the permanent magnet. uPM1 The vibration velocity of the permanent magnet. CPM1 For the mechanical damping of permanent magnets; In the oscillator n By connecting the mechanical impedance circuits of the front and rear mass blocks into the first-order mechanical impedance circuit, and connecting the acoustic radiation impedance in parallel after the front mass block, a multi-order mechanical impedance model of the giant magnetostrictive electroacoustic transducer is obtained: Based on the loop current method, a solution matrix for the mechanical impedance model is constructed, and the instantaneous vibration velocity of the radiation surface is obtained using the solution matrix. ur : in, Fi For the first i The output force of the segment, UI For the first i The vibration velocity of the segment; et , ePM1 , ei , en , ePM2 , eh The coefficients of the matrix are obtained using the following formula: .

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