Method and system for analyzing nonlinear time-domain characteristics of a giant magnetostrictive transducer

Abstract

The application discloses a nonlinear time domain characteristic analysis method and system of a giant magnetostrictive transducer. The method comprises a segmented magnetic circuit magnetic field model of the giant magnetostrictive transducer under the consideration of a permanent magnet bias magnetic field, a solid mechanics model of the giant magnetostrictive rod under the consideration of a magnetostrictive effect of the giant magnetostrictive rod, and a pressure acoustic model of underwater vibration of the transducer, a coupling strategy of an electromagnetic field and a solid mechanics field is constructed, and a coupling strategy of the solid mechanics field and a pressure acoustic field is constructed, so that a nonlinear time domain model of the whole electric-magnetic-mechanical-acoustic coupling of the giant magnetostrictive transducer is established, time domain output characteristics of the transducer model are analyzed under different bias magnetic fields and prestress conditions, and thus a method is provided for the design of the giant magnetostrictive electroacoustic transducer.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of time domain characteristic analysis of super magnetostrictive transducer, in particular to a nonlinear time domain characteristic analysis method and system of super magnetostrictive transducer considering permanent magnet bias. BACKGROUND

[0002] The super magnetostrictive transducer is a device with super magnetostrictive material as the core excitation unit, which can realize efficient conversion of electric-magnetic-mechanical-acoustic energy. A reliable and accurate modeling method is the premise of studying the characteristics of the transducer. Compared with the traditional mathematical modeling method, the finite element method has more extensive applicability and effectiveness. It can simulate the complex geometry and boundary conditions of the actual prototype and is also suitable for solving various physical fields and their coupling fields. In the field of super magnetostrictive transducer modeling, the existing technology mostly uses the finite element method to establish the steady-state and frequency domain model of the transducer. However, the transducer has many complex nonlinear dynamic energy conversion processes during operation. The steady-state modeling is suitable for the case where the system is stable, and it cannot truly reflect the multi-field coupling relationship of the transducer. The frequency domain modeling also cannot reflect the dynamic characteristics, and it is not suitable for solving nonlinear problems, lacking accuracy. SUMMARY

[0003] The main purpose of the present application is to provide a nonlinear time domain characteristic analysis method and system of super magnetostrictive transducer considering permanent magnet bias, which aims to solve the above problems existing in the prior art.

[0004] To achieve the above purpose, the present application provides a nonlinear time domain characteristic analysis method of super magnetostrictive transducer, which comprises:

[0005] S1, a physical geometric model of the super magnetostrictive longitudinal vibration transducer is established;

[0006] S2, a magnetic field analysis model of the super magnetostrictive transducer is established;

[0007] S3, a Terfenol-D rod effective magnetic field analysis method considering the influence of permanent magnet bias in the magnetization process.

[0008] S4, a transducer solid mechanics field analysis model considering the magnetostrictive effect of the Terfenol-D rod is established;

[0009] S5, an electromagnetic-mechanical field coupling strategy and solution of the super magnetostrictive transducer are established;

[0010] S6, a transient mechanical-acoustic field coupling strategy and solution of the super magnetostrictive transducer are established, and the construction and solution of the electric-magnetic-mechanical-acoustic multi-field coupling time domain model of the super magnetostrictive transducer are completed;

[0011] S7 analyzes the optimal matching relationship of the transducer prestress and the bias magnetic field, tests multiple bias magnetic field points under different prestresses to find the bias magnetic field corresponding to the maximum displacement amplitude under each prestress, and finds the maximum displacement amplitude under all combinations of prestress and bias magnetic field, so that the corresponding prestress and bias magnetic field can be used as the optimal matching relationship.

[0012] Preferably, the physical geometric model comprises an excitation module, a magnetic circuit module and an output module; the magnetic circuit module comprises a magnetic conducting block, a silicon steel sheet, a permanent magnet, a Terfenol-D rod and a magnetic yoke; the excitation module comprises a coil and a permanent magnet, the coil provides an alternating magnetic field for the Terfenol-D rod, and the permanent magnet provides a bias magnetic field for the Terfenol-D rod; the output module comprises a magnetic conducting block, a silicon steel sheet, a permanent magnet, a front mass block, a rear mass block and the Terfenol-D rod, and the macroscopic output result of the physical geometric model is an output displacement at the top end of the front mass block and an acoustic pressure in a water area.

[0013] Preferably, the step S2 comprises:

[0014] The giant magnetostrictive transducer works in an electromagnetic field excited by an applied coil current density, and Maxwell equations are applied to the electromagnetic field description of the Terfenol-D rod by the finite element method as formula (1):

[0015]

[0016] Wherein, H ac represents the alternating magnetic field intensity generated by the coil current in the Terfenol-D rod, J s is the current density of the excitation coil, J E is the current density related to the eddy current term, σ c is the conductivity of the rod, and A is the magnetic vector potential.

[0017] The weak form equation of formula (1) is derived using the weighted residual method, and the variation δA of the magnetic vector potential A is used to weight formula (1), so that the weak form equation of formula (1) is as formula (2):

[0018]

[0019] Wherein, V A is the volume domain of the electromagnetic field in the finite element simulation, is the closed region of the electromagnetic field, H ac × n is the boundary tangential magnetic field;

[0020] The bias magnetic field intensity Hbias , and the magnetic field strength H of the Terfenol-D rod in the giant magnetostrictive transducer is represented by formula (3) as follows:

[0021] H = H ac + H bias (3).

[0022] Preferably, the step S3 comprises:

[0023] The nonlinear magnetization process of the Terfenol-D rod under magnetic field excitation is described by the Jiles-Atherton model, and the specific expression is formula (5) as follows:

[0024]

[0025] where H e is the effective magnetic field strength, a is the average field coupling coefficient, l s is the saturation magnetostriction coefficient, s is the stress tensor inside the rod, M s is the saturation magnetization, M an is the non-magnetic hysteresis magnetization, a is the shape coefficient, M is the magnetization, M rev and M irr are the reversible and irreversible magnetization respectively, c is the reversible coefficient, d1 is the direction coefficient, when dH / dt>0, d1 is 1, when dH / dt<0, d1 is 0, k is the pinning coefficient, At this point, formula (5) can be solved by the fourth-order Runge-kutta method to obtain the magnetization M and the effective magnetic field strength H e .

[0026] Preferably, the step S4 comprises:

[0027] According to Newton's second law and Navier's equation, the stress balance equation inside the Terfenol-D rod is formula (8) as follows:

[0028]

[0029] where p is the density of the rod, z is the mechanical damping of the rod, u is the total output displacement of the rod, F v is the given mechanical body force:

[0030] The weak form equation of formula (8) is formula (9) as follows:

[0031]

[0032] where Vu for the volume domain of the solid mechanics field in the finite element simulation, for the closed boundary of the solid mechanics field, σn is the surface traction of the mechanical field boundary, the weak form equations of formula (2) and formula (9) show the balance of the virtual work inside and outside the transducer system.

[0033] Preferably, the stress tensor σ in formula (9) includes the mechanical stress σ el and the pre-stress σ pre = [σ pre.r σ pre.z σ pre.Φ σ pre.rz ] T , as formula (10):

[0034] σ = σ el + σ pre (10)

[0035] wherein σ pre.r , σ pre.z , σ pre.Φ , σ pre.rz respectively represent the components of the variable σ in the r-axis, z-axis, Φ-axis and rz-axis directions, σ pre is given by the external boundary load condition.

[0036] Preferably, the mechanical stress σ el and the mechanical strain ε el comply with Hooke's law, and then σ el can be calculated by formula (12)

[0037]

[0038] wherein D is the elastic coefficient matrix, E is the Young's modulus of the rod, and v is the Poisson's ratio.

[0039] Preferably, the step S5 includes: the magnetic field and the mechanical field of the Terfenol-D rod are coupled through the magnetostrictive Joule effect and the Villari effect, the magnetization M solved by the Jiles-Atherton model in the step S3 is substituted into the secondary domain switching model to calculate the displacement of the solid mechanics field, which embodies the magnetostrictive Joule effect; the stress tensor σ of the solid mechanics field is substituted into the Jiles-Atherton model to calculate the effective magnetic field strength H e , which embodies the Villari effect.

[0040] Preferably, the step S6 includes: the output displacement u and the output sound pressure p of the transducer in the fluid domain are calculated, and the sound pressure in the fluid domain satisfies the basic equation of acoustic wave motion, as formula (17):

[0041]

[0042] Where ρ w Let be the density of the fluid, which is water in this model; c0 be the speed of sound in the fluid; and p be the sound pressure. Similarly, by weighting equation (17) with the variational δp of p, the weak form of equation (17) can be written as equation (18).

[0043]

[0044] Where V a The volume domain representing the pressure acoustic field, Represents the boundary connecting solid mechanics and the acoustic field;

[0045] The electro-magnetic-mechanical-acoustic multi-field coupled nonlinear time-domain model of the super magnetostrictive transducer is fully constructed by the process of steps S1-S6.

[0046] The present invention also provides a time-domain characteristic analysis system for a giant magnetostrictive transducer, comprising one or more processors and a memory, wherein the memory stores one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors perform the steps of the method described above.

[0047] The beneficial effects of this invention are as follows:

[0048] This paper proposes a nonlinear time-domain characteristic analysis method for giant magnetostrictive transducers considering permanent magnet bias. This method utilizes a model to account for the magnetic field distribution and output displacement characteristics of a permanent magnet-Terfenol-D rod interleaved structure, verifying the feasibility of applying prestress and bias magnetic fields to this structure. Furthermore, it eliminates the need for a DC coil for bias, reducing heat generation in the coil and saving internal space in the transducer. In addition, this invention extends the model to fluid domain pressure acoustic modeling, expanding the transducer's application from the air domain to water, providing strong support for the design of underwater acoustic transducers. The constructed model is a time-domain transient model, effectively simulating the real dynamic working process of the transducer. It provides more accurate results than common steady-state and frequency-domain models for solving the magnetostriction curves of the transducer under different prestresses, facilitating the setting of accurate bias magnetic fields and prestresses to achieve optimal output characteristics. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0050] Figure 1 Flow chart for multi-physical field solving process of finite element time domain model of super magnetostrictive transducer

[0051] Figure 2 Figure for geometric model of super magnetostrictive transducer

[0052] Figure 3 Time-displacement waveform of transducer under no bias magnetization

[0053] Figure 4 Magnetic field-displacement curve of transducer under different bias magnetization

[0054] Figure 5 Figure for magnetic flux density distribution of Terfenol-D rod

[0055] Figure 6 Magnetic field-displacement curve under working condition of different pre-stress and bias magnetic density

[0056] Figure 7 Displacement amplitude of transducer under working condition of different pre-stress and bias magnetization

[0057] Figure 8 Flow chart for steps of nonlinear time domain characteristic analysis method of super magnetostrictive transducer of the application

[0058] The implementation, functional features and advantages of the application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the application.

[0060] It should be noted that the technical solutions in the various embodiments of the application can be combined with each other, but it must be based on that a person of ordinary skill in the art can realize the combination, and when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, and is not within the protection scope of the application.

[0061] Embodiment 1

[0062] The flow chart of a nonlinear time domain characteristic analysis method of super magnetostrictive transducer considering permanent magnet bias corresponding to the embodiment is shown in Figure 1 、 8 The analysis method of the embodiment comprises:

[0063] Step S1, a physical geometric model of the magnetostrictive longitudinal vibration transducer. Specifically, as shown in Figure 2 the transducer geometric model in the embodiment includes an excitation module, a magnetic circuit module, and an output module. The excitation module includes a coil and a permanent magnet, the coil providing an alternating magnetic field for the Terfenol-D rod, and the permanent magnet providing a bias magnetic field for the rod; the magnetic circuit module includes (upper and lower) magnetic conductive blocks, a silicon steel sheet, a permanent magnet, a Terfenol-D rod, and a magnetic yoke, wherein a small air gap exists between the magnetic yoke and the magnetic conductive blocks, which reduces the influence of leakage magnetic while ensuring the free movement of the magnetic conductive blocks, and constitutes a relatively closed magnetic circuit; the output module is composed of the magnetic conductive blocks, the silicon steel sheet, the permanent magnet, front and rear mass blocks, and the Terfenol-D rod, and the macroscopic output of the final model can be embodied in the output displacement of the top of the front mass block and the sound pressure in the water area.

[0064] Step S2, establishing a magnetic field analysis model of the magnetostrictive transducer. The entire magnetostrictive transducer works in an electromagnetic field excited by an applied coil current density, and the finite element method applies the Maxwell equation set to the electromagnetic field description of the Terfenol-D rod as formula (1):

[0065]

[0066] where H ac represents the alternating magnetic field intensity generated by the coil current in the Terfenol-D rod, J s is the current density of the excitation coil, J E is the current density related to the eddy current term, σ c is the conductivity of the rod, and A is the magnetic vector potential.

[0067] The weak form equation of formula (1) can be derived using the weighted residual method, and the variation δA of the magnetic vector potential A is used to weight formula (1), then the weak form equation of formula (1) is as formula (2):

[0068]

[0069] where V A is the volume domain of the electromagnetic field in the finite element simulation, is the closed region of the electromagnetic field, H ac × n is the boundary tangential magnetic field.

[0070] The model provides bias magnetic density by permanent magnet. The magnetization model of the permanent magnet needs to select "residual magnetic flux density model" in the finite element software, and then assign "residual magnetic flux density" at the permanent magnet material attribute, so as to provide bias in this way. However, due to the low relative permeability of the permanent magnet and the Terfenol-D rod, the bias magnetic density provided by the permanent magnet cannot completely enter the Terfenol-D rod due to the influence of magnetic leakage. By setting the relative permeability of the permanent magnet, silicon steel sheet and rod, the bias magnetic field strength H generated by the permanent magnet in the Terfenol-D rod can be calculated by the finite element software under the condition of no other external excitation. bias .

[0071] Therefore, the magnetic field strength H of the Terfenol-D rod in the giant magnetostrictive transducer can be expressed as formula (3):

[0072] H = H ac + H bias (3)

[0073] Solving the electromagnetic field equation of formula (1) needs to give the boundary value and initial value of the magnetic vector potential, such as formula (4):

[0074]

[0075] Where A0 is the initial value of the magnetic vector potential calculation iteration, A * is the boundary value of the magnetic vector potential of the closed boundary of the magnetic field region.

[0076] Step S3, analyze the effective magnetic field of the Terfenol-D rod considering the bias effect of the permanent magnet in the magnetization process. The nonlinear magnetization process of the Terfenol-D rod under the magnetic field excitation can be described by the Jiles-Atherton model (hereinafter referred to as J-A model). The specific expression of J-A model is formula (5):

[0077]

[0078] Where H e is the effective magnetic field strength, α is the average field coupling coefficient, λ s is the saturation magnetostriction coefficient, σ is the stress tensor inside the rod, M s is the saturation magnetization, M an is the non-magnetic hysteresis magnetization, a is the shape coefficient, M is the magnetization, M rev and M irr are the reversible and irreversible magnetization, respectively, c is the reversible coefficient, δ1 is the direction coefficient, δ1 is 1 when dH / dt>0, δ1 is 0 when dH / dt<0, k is the pinning coefficient, The fourth-order Runge-Kutta method can be used to iteratively solve equation (5) to obtain the magnetization M and effective magnetic field H in the Terfenol-D rod e . The magnetic flux density B can be calculated from equation (6)

[0079] B = μ0(H + M) (6)

[0080] The magnetic vector potential A can be solved by Maxwell's equation as shown in equation (7)

[0081] B = ▽ × A (7)

[0082] Step S4, a solid mechanics field analysis model of the transducer considering the magnetostrictive effect of the Terfenol-D rod is established. According to Newton's second law and Navier's equation, the stress equilibrium equation in the Terfenol-D rod is as shown in equation (8)

[0083]

[0084] wherein ρ is the density of the rod, ζ is the mechanical damping of the rod, u is the total output displacement of the rod, F v is the given mechanical body force.

[0085] The weak form equation of equation (8) can be obtained by weighting equation (8) with the variation δu of u and integrating equation (8) over the entire solid mechanics domain as shown in equation (9):

[0086]

[0087] wherein V u is the volume domain of the solid mechanics field in the finite element simulation, is the closed boundary of the solid mechanics field, and σn is the surface traction of the mechanical field boundary. The weak form equations of equations (2) and (9) show the balance of virtual work inside and outside the transducer system.

[0088] Before solving equation (9), the stress tensor σ is derived, which includes the mechanical stress σ el and the pre-stress σ pre = [σ pre.r σ pre.z σ pre.Φ σ pre.rz T The variables with subscripts r, z, Φ and rz represent the components in the r-axis, z-axis, Φ-axis and rz-axis directions respectively as shown in equation (10):

[0089] σ = σ el + σ pre (10)

[0090] wherein σ​pre The value is given by the applied boundary load condition. Before prestress is applied, a fixed constraint needs to be applied to the transducer. The position of the fixed constraint is the lower boundary of the solid mechanics field closed boundary The prestress σ pre is applied to the upper boundary of the solid mechanics field closed boundary And make sure that the axial prestress is applied. The way of applying the fixed constraint and the boundary load is as formula (11):

[0091]

[0092] The mechanical stress σ el and the mechanical strain ε el comply with Hooke's law. Then σ el can be calculated by formula (12)

[0093]

[0094] Where D is the elastic coefficient matrix, E is the Young's modulus of the rod, and v is the Poisson's ratio. The mechanical strain ε el value can be calculated by formula (13):

[0095] ε el = ε - ε me - ε pre (13)

[0096] Where ε represents the total strain, ε me represents the magnetostrictive strain, and ε pre represents the pre-strain generated by the prestress. The magnetostrictive strain ε me value can be calculated by substituting M solved in formula (5) into the second domain switching model, as formula (14):

[0097]

[0098] The total strain ε value can be obtained by calculating the gradient of the total displacement u, as formula (15):

[0099]

[0100] Substitute formula (13)-(15) into formula (12) to solve the mechanical stress σ el , and then the stress σ inside the rod can be solved by formula (10).

[0101] In addition, the initial value and boundary condition of the solid mechanics field need to be given to solve formula (9), as formula (16):

[0102]

[0103] where u0 is the initial value of the mechanical displacement field iteration calculation, is the initial value of the time derivative of the mechanical displacement, * is the mechanical displacement boundary value of the solid mechanics field closed boundary.

[0104] Step S5, establishing the electromagnetic-mechanical field coupling strategy of the giant magnetostrictive transducer and solving. The magnetic field and mechanical field of the Terfenol-D rod are coupled through the magnetostrictive Joule effect and Villari effect. The traditional linear magnetostrictive equation is difficult to describe the magneto-mechanical nonlinear coupling process of the transducer, so the J-A model in step S3 is used to replace the linear magnetostrictive equation, the magnetization M solved by the J-A model is substituted into the second domain switching model as a ring in the calculation of the solid mechanics field displacement, the magnetostrictive Joule effect is embodied, and the solid mechanics field stress tensor σ is substituted into the J-A model to calculate the effective magnetic field strength H e , which embodies the Villari effect.

[0105] In the solving of the weak form equation (2), the initial and boundary conditions formula (4) are needed to drive first, and the process quantity M solved by the J-A model needs to be calculated through formula (6) and (7) to obtain the process quantity A, and then the value of H is solved by formula (2) and substituted back into the J-A model to calculate the next iteration of M value, until M converges, the calculation of the magnetic field part is completed, and then the magnetostrictive strain ε me of the next iteration is obtained from formula (14) as the process quantity of the solid mechanics field calculation, so the solving process of the weak form equation (2) not only completes the solving of the magnetic field part, but also embodies the coupling relationship between the solid mechanics field and the magnetic field.

[0106] In the solving process of the weak form equation (9), the initial and boundary conditions formula (16) are needed to drive the calculation first, and the process quantity σ solved in the calculation process needs to be iterated back to the J-A model to update the effective magnetic field strength H e of the next iteration of the J-A model, and the total stress value in the calculation formula, realizing the coupling calculation from the solid mechanics field to the magnetic field, and the displacement u calculated by σ is also a process quantity, which needs to be substituted back to formula (15) to calculate the total strain ε value and update the ε el value of the next iteration, until the displacement u converges, realizing the calculation of the solid mechanics field.

[0107] Step S6, establishing the transient mechanical-acoustic field coupling strategy of the magnetostrictive transducer and solving, completing the construction and solving of the magnetostrictive transducer electric-magnetic-mechanical-acoustic multi-field coupling time-domain model. On the basis of the magnetic field and solid mechanics field calculation in step 5, the coupling relationship between the transducer solid mechanics field output displacement and the fluid domain pressure acoustic field is further solved, the magnetostrictive transducer acoustic coupling transient model is constructed, the output displacement u of the transducer in the fluid domain and the output acoustic pressure p in the fluid domain are calculated, and the acoustic pressure in the fluid domain satisfies the acoustic wave equation, as formula (17):

[0108]

[0109] Wherein, ρ w is the density of the fluid, the fluid is selected as water in the model, c0is the acoustic velocity in the fluid, and p is the acoustic pressure. Similarly, the weak form equation of formula (17) can be written as formula (18) by weighting formula (17) with the variation δp of p.

[0110]

[0111] Wherein, V a represents the volume domain of the pressure acoustic field, represents the solid mechanics and acoustic field connection boundary. Due to the coupling relationship between the solid mechanics field and the pressure acoustic field, the solid mechanics field and the pressure acoustic field are discretized into a finite number of elements for solving, and the discrete state acoustic wave equation and the solid mechanics internal stress balance equation can be expressed as:

[0112]

[0113] Wherein, M e , and respectively represent the element solid mechanics mass matrix, the acoustic mass matrix and the two-field coupling mass matrix, K e , and represent the element solid mechanics stiffness matrix, the fluid stiffness matrix and the two-field coupling stiffness matrix, and respectively represent the element mechanical force matrix and the acoustic force matrix.

[0114] Solving the coupling machine-acoustic coupling matrix of formula (19) needs to combine the boundary initial value of the displacement field and the boundary initial value of the pressure acoustic field. The displacement final value calculated in step 5 can be used as the initial value of the displacement field of the transducer machine-acoustic coupling model, and the boundary condition and initial value of the pressure acoustic field are shown in formula (20):

[0115]

[0116] The first formula in formula (20) represents a perfect matched layer hard sound field boundary condition, and the second and third formulas represent initial conditions of a pressure acoustic solution, wherein n is a surface normal vector of an acoustic fluid, p0 and represent initial values of sound pressure and a first-order time derivative of sound pressure, respectively.

[0117] In the transducer electro-mechanical-acoustic coupling solution process, the sound pressure initial value in formula (20) is substituted into the first formula of formula (19), and the displacement initial value is substituted into the second formula of formula (19), to respectively solve the second iteration displacement u1 and the sound pressure p1, as the initial value in the next iteration formula (19), until the displacement u and the sound pressure p converge.

[0118] The electro-magnetic-mechanical-acoustic multi-field coupling nonlinear time domain model of the giant magnetostrictive transducer and its solution can be completely built by the flow of steps S1-S6.

[0119] Step S7, analyze the optimal matching relationship of the transducer prestress and bias magnetic field, test multiple bias magnetic field points under different prestresses to find the bias magnetic field corresponding to the maximum displacement amplitude under each prestress, and find the maximum displacement amplitude under the combination of all prestresses and bias magnetic fields, so as to take the corresponding prestress and bias magnetic field as the optimal matching relationship. Applying the prestress and bias magnetic field to the transducer can adjust the working point position of the transducer, and reasonable application of the prestress can improve the shape of the magnetostrictive curve of the transducer, so that the “linear region” of the magnetostrictive curve is longer. Reasonably adjusting the bias magnetic field to make the transducer work in the “linear region” of the magnetostrictive curve is the ideal working condition of the transducer.

[0120] The relationship between the bias magnetic field and the prestress and the transducer output displacement has a nonlinear effect, and each prestress corresponds to an optimal bias magnetic field to make the transducer have the maximum output displacement under the prestress. Therefore, the prestress and bias magnetic field optimization strategy used in this paper is to test multiple bias magnetic field points under different prestresses to find the bias magnetic field corresponding to the maximum displacement amplitude under each prestress, and find the maximum displacement amplitude under the combination of all prestresses and bias magnetic fields, so as to take the corresponding prestress and bias magnetic field as the optimal matching relationship.

[0121] Embodiment 2

[0122] In other embodiments of the present application, the analysis method further comprises the following steps:

[0123] Step S8, numerical examples are used to verify the effectiveness and feasibility of the bias magnetic field applied by the permanent magnet in the model. A sinusoidal alternating current 10*sin(2*pi*300*t) [A] is applied to the coil, the number of turns of the coil is 1000 turns, and the pre-stress of 10 MPa is applied by the boundary load. By the method of step 1, the "residual magnetic flux density" of the permanent magnet is set to 0T, 0.6T, 1T, 1.5T, 2T, 3T and 5T by using the parameterized scanning function of the finite element software, and the displacement characteristics of the transducer under different biases are observed. At the same time, the calculation results of B r =2T are taken to analyze the total magnetic flux density B tot distribution in the axial direction of the Terfenol-D rod.

[0124] From Figure 3 the displacement and current time-domain waveforms of the transducer without bias magnetic field, it can be seen that when no bias magnetic field is applied to the transducer, under the excitation of alternating current, due to the fixed constraint at the bottom end, the Terfenol-D rod only shows elongation to the outside, resulting in that the transducer only has positive output, the frequency of the output displacement time-domain waveform is twice that of the current time-domain waveform, that is, "frequency doubling phenomenon" occurs, and the output displacement amplitude is only 3.526μm; Figure 4 the magnetic field-displacement curve of the transducer under different bias magnetic flux densities, with the increase of the bias magnetic field, the "frequency doubling phenomenon" disappears, which is because the existence of the bias magnetic field makes the Terfenol-D rod elongate in advance, when the bias magnetic field is consistent with the direction of the applied magnetic field, the rod shows elongation, when the bias magnetic field is opposite to the direction of the applied magnetic field, the rod shows shortening; in the process of increasing the bias magnetic field from 0.6T to 5T, the effective value of the output displacement of the transducer first increases and then decreases, from the results of parameterized scanning, when B r increases from 0.6T to 1.5T, the effective value of the output displacement of the transducer continues to increase, when B r =1.5T, the transducer has a maximum output displacement effective value of 8.16μm, and when B r value continues to increase, the output displacement begins to decrease, when B r =3T, the positive output displacement of the transducer begins to appear saturation phenomenon, the H-x curve presents "water drop shape", and when B r rises to 5T, the magnetic field almost completely enters the saturation region, and the output displacement of the transducer further decreases. Connecting the center points of the output displacement hysteresis loops at each bias point can obtain the approximate magnetostrictive curve, as shown by the dark blue curve in Figure 4 .

[0125] Figure 5 The red and blue curves in rUnder the condition of =2T, the model of the application calculates the distribution of the magnetic flux density in the axial direction of the rod, and it can be seen that the magnetic flux density value of the rod element increases with the distance from the permanent magnet, that is, the smaller the magnetic flux density near the middle of the rod, the larger the magnetic flux density near the two ends of the rod, which is due to the low magnetic permeability of the rod, part of the magnetic field leaks into the air, which cannot completely enter the rod, causing uneven distribution of the magnetic flux density, which is consistent with the experimental law, indicating that the model using the permanent magnet to provide the bias magnetic field by the residual magnetic flux density is reasonable.

[0126] In summary, under the condition of no bias magnetic field, the output displacement of the transducer will produce "frequency multiplication phenomenon", and after the "frequency multiplication phenomenon" disappears, the output displacement of the transducer presents the trend of first increasing and then decreasing with the increase of the bias magnetic field, which is consistent with the regularity of the magnetostriction curve under the stress of 10MPa, the model of the application can simulate the output displacement characteristics of the giant magnetostrictive transducer under different bias magnetic field conditions, and at the same time Figure 5 The results also verify the non-uniform distribution of the bias magnetic field, which is more concentrated at the two ends of the rod, and the minimum value of the magnetic flux density in the middle of the rod, which is consistent with the experimental phenomenon, and verifies the effectiveness and feasibility of the model of the application for the permanent magnet to provide the bias magnetic field by the "residual magnetic flux density".

[0127] Step S9, the effectiveness and feasibility of the pre-stress applied by the model of the application are verified by numerical examples. Similarly, the coil is applied with an alternating current of 10*sin(2*pi*300*t)[A], the process of step S8 is used to apply a fixed constraint to the giant magnetostrictive transducer, and a pre-stress of 0MPa and 30MPa is applied at the top end of the upper magnetic block, under the two pre-stresses, different bias magnetic fields are applied by the permanent magnet, the output displacement characteristics of the transducer model are recorded, and the magnetostriction curve of the transducer under different pre-stresses is drawn.

[0128] The calculation results of the output displacement and the magnetostriction curve of the model of the application under the above working conditions are as follows Figure 6, the red loop is the output displacement curve of the transducer with 0 MPa pre-stress, it can be seen that the effective value of the output displacement of the transducer gradually decreases with the increase of the bias magnetic field from 1 T to 6 T; the blue loop is the output displacement curve of the transducer with 30 MPa pre-stress, the output displacement characteristics are similar to the case of 10 MPa pre-stress in step 8, both increase first and then decrease with the increase of the bias magnetic field from 0.6 T to 6 T, which is consistent with the characteristics of magnetostrictive material, under the condition of 30 MPa pre-stress, the magnetostrictive effect of Terfenol-D rod is divided into three stages, the first stage is the stage of small magnetic field, the pre-stress plays a dominant role, which makes the internal magnetic domain direction almost perpendicular to the direction of the applied magnetic field, and the small magnetic field is difficult to make the magnetic domain rotate too much, which macroscopically shows that the output displacement of the transducer is small, corresponding to the "dead zone" of the magnetostrictive curve; the second stage, with the increase of the magnetic field, many magnetic domains break away from the pinning and pre-stress and occur irreversible rotation, the strain of the rod increases suddenly, and the output displacement of the transducer also increases, which occurs the Barkhausen effect, corresponding to the "linear region" of the magnetostrictive curve; the third stage, with the continuous increase of the magnetic field, the magnetic domain rotates to the direction consistent with the external magnetic field, and the strain of the rod gradually reaches saturation, at this time, increasing the applied magnetic field will not make the strain of the rod change too much, corresponding to the "saturation region" of the magnetostrictive curve.

[0129] The output displacement curves of the same bias points on the two curves are compared, in B r =1 T bias point, the effective value of the output displacement of the transducer under the condition of 30 MPa pre-stress is smaller than that without pre-stress; in B r =2 T bias point, the displacement under the conditions of with and without pre-stress is basically the same, compared with the previous bias point, the output displacement under the condition of without pre-stress decreases, while the output displacement under the condition of 30 MPa increases, and B r =2 T is also the bias point with the largest output displacement among the bias points of 1 T-6 T under the condition of 30 MPa pre-stress; in B r =3 T bias point, the output displacement under the condition of 30 MPa is greater than that without pre-stress, compared with the previous bias point, the output displacement under the condition of without pre-stress continues to decrease, and the output displacement under the condition of 30 MPa is not much different from the previous bias point, which shows that the "linear region" is longer under the condition of 30 MPa pre-stress; in the following bias points, the output displacements under the conditions of with and without pre-stress continue to decrease with the increase of the residual magnetic flux density of the permanent magnet, and the output displacement under the condition of 30 MPa is greater than that without pre-stress in the corresponding bias points, which shows that the saturation strain of the magnetostrictive curve under the condition of 30 MPa pre-stress is greater than that without pre-stress, the magnetic field required to reach saturation is also larger, and it has a larger saturation magnetostrictive coefficient.

[0130] In summary, the prestress affects the magnetostrictive effect of the Terfenol-D rod, and in the case of no prestress, the slope of the magnetostrictive curve decreases with the increase of the magnetic field, and the "linear region" is short, in the case of 30MPa prestress, the slope of the magnetostrictive curve first increases and then decreases, and the "linear region" of the magnetostrictive curve is longer than that in the case of no prestress, the saturation strain is larger, and it is more beneficial to set the bias point of the transducer.

[0131] Step S10, in the case of an applied excitation current of 10*sin(2*pi*300) [A] and 1000 turns of coil, the transducer displacement output characteristics under 8-28MPa prestress and 0.6-5T bias magnetic density are solved, and the maximum displacement amplitude of the transducer under each working condition is recorded and processed into a three-dimensional graph, as shown in Figure 7 .

[0132] From Figure 7 It can be seen that under the fixed prestress, the bias magnetic density increases from 0.6T to 5T, the transducer displacement amplitude has the same law as step 7, that is, it first increases and then decreases, which again shows that there is an optimal characteristic of the bias magnetic field, from the maximum displacement amplitude under different prestresses, the maximum displacement amplitude of the transducer first increases and then decreases with the increase of the prestress, which shows that there is an optimal characteristic of the prestress, from Figure 7 It can be seen that the maximum displacement amplitude of the transducer under all the above working conditions is 13.3μm, and the corresponding working condition is 20MPa prestress and 2T bias magnetic density, which can be used as the optimal matching relationship of the transducer prestress and bias magnetic field.

[0133] In addition, the present application also provides a super magnetostrictive transducer time domain characteristic analysis system, comprising one or more processors and memories, the memory stores one or more programs, when the one or more programs are executed by the one or more processors, the one or more processors realize the steps of the method of any one of claims 1-9. The specific steps of the method are referred to the above embodiments, since the analysis system adopts all the technical solutions of the above embodiments, it at least has all the beneficial effects brought by the technical solutions of the above embodiments, which will not be repeated here.

[0134] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, any equivalent structural transformation made under the inventive concept of the present application, or direct / indirect application in other related technical fields is included in the patent protection scope of the present application.

Claims

1. A method for analyzing the nonlinear time-domain characteristics of a giant magnetostrictive transducer, characterized in that, include: S1 establishes the physical geometric model of the supermagnetostrictive longitudinal vibration transducer; S2. Establish the magnetic field analysis model of the super magnetostrictive transducer; S3 Analysis of the effective magnetic field of Terfenol-D rods considering the influence of permanent magnet bias during magnetization; S4. Establish a solid mechanical field analysis model for the transducer that considers the magnetostrictive effect of the Terfenol-D rod. S5 establishes the electromagnetic-mechanical field coupling strategy and solution for the super magnetostrictive transducer; S6 establishes and solves the transient mechanical-acoustic coupling strategy of the giant magnetostrictive transducer, and completes the construction and solution of the electro-magnetic-mechanical-acoustic multi-field coupling nonlinear time-domain model of the giant magnetostrictive transducer; S7 analyzes the optimal matching relationship between transducer prestress and bias magnetic field. Tests are conducted at multiple bias magnetic field points under different prestresses to find the bias magnetic field corresponding to the maximum displacement amplitude under each prestress. The maximum displacement amplitude is found under all combinations of prestress and bias magnetic field, and the corresponding prestress and bias magnetic field can be taken as the optimal matching relationship. The physical geometric model includes an excitation module, a magnetic circuit module, and an output module. The magnetic circuit module includes a magnetically conductive block, a silicon steel sheet, a permanent magnet, a Terfenol-D rod, and a magnetic yoke. The excitation module includes a coil and a permanent magnet. The coil provides an alternating magnetic field to the Terfenol-D rod, and the permanent magnet provides a bias magnetic field to the Terfenol-D rod. The output module consists of a magnetically conductive block, a silicon steel sheet, a permanent magnet, a front mass block, a rear mass block, and the Terfenol-D rod. The macroscopic output of the physical geometric model is the output displacement at the top of the front mass block and the sound pressure in the water. Step S2 includes: The super magnetostrictive transducer operates in an electromagnetic field excited by an external coil current density. The electromagnetic field description of the Terfenol-D rod is given by applying Maxwell's equations to the Terfenol-D rod using the finite element method, as shown in equation (1): (1) Among them, H ac J represents the AC magnetic field strength generated by the coil current in the Terfenol-D rod. s J is the current density of the excitation coil. E For the current density associated with the eddy current term, σ c Let be the electrical conductivity of the rod, and A be the magnetic vector potential; The weak form of equation (1) is derived using the weighted residual method, employing the variation of the magnetic vector potential A. δ A performs a weighted calculation on equation (1), and the weak form of equation (1) is shown in equation (2): (2) in V A For the volume domain of electromagnetic fields in finite element simulation, əV A H is a closed region of electromagnetic field. ac × n is əV A Boundary tangential magnetic field; The bias magnetic field strength H generated by the permanent magnet in the Terfenol-D rod was obtained by calculating the leakage magnetic field using finite element software. bias Therefore, the magnetic field strength H of the Terfenol-D rod in the supermagnetostrictive transducer is expressed by equation (3): (3)； Step S3 includes: The nonlinear magnetization process of the Terfenol-D rod under magnetic field excitation is described by the Jiles-Atherton model, and its specific expression is shown in equation (5): (5) Where H e For effective magnetic field strength, α The mean field coupling coefficient is... λ s Where σ is the saturation magnetostriction coefficient, and σ is the internal stress tensor of the rod. M s M is the saturation magnetization. an The magnetization is hysteresis-free. a M is the shape factor, M is the magnetization, M rev and M irr These represent reversible and irreversible magnetization, respectively. c The invertibility coefficient is... δ 1 is the direction coefficient, when dH / d t When >0, δ 1 is 1, when dH / d t When <0, δ 1 is 0, k The pinning factor is... Therefore, equation (5) can be solved iteratively using the fourth-order Runge-Kutta method to obtain the magnetization M and effective magnetic field strength H in the Terfenol-D rod. e .

2. The method for analyzing the nonlinear time-domain characteristics of a giant magnetostrictive transducer as described in claim 1, characterized in that, Step S4 includes: According to Newton's second law and Navier's equation, the stress balance equation inside the Terfenol-D bar is as shown in equation (8): (8) in ρ The density of the bar. ζ Let F be the mechanical damping of the bar, u be the total output displacement of the bar, and F be the mechanical damping of the bar. v For a given mechanical volume force; Variations using u δ By weighting equation (8) and integrating it over the entire solid mechanics domain, we can obtain the weak form of equation (8) as shown in equation (9): (9) in V u This refers to the volume domain of the solid mechanical field in finite element simulation. əV u Let σn be the closed boundary of the solid mechanical field and σn be the surface traction force of the mechanical field boundary. The weak form equations of equations (2) and (9) show the balance of virtual work inside and outside the transducer system.

3. The method for analyzing the nonlinear time-domain characteristics of a giant magnetostrictive transducer as described in claim 2, characterized in that, The stress tensor σ in equation (9) includes mechanical stress σ el and preload stress σ pre = [ σ pre.r σ pre.z σ pre.Φ σ pre.rz ] T As in equation (10): (10) in σ pre.r , σ pre.z , σ pre.Φ , σ pre.rz They represent the variables σ respectively. r axis, z axis, Φ shaft and rz Axial component, σ pre The value is given by the external boundary load condition.

4. The method for analyzing the nonlinear time-domain characteristics of a giant magnetostrictive transducer as described in claim 3, characterized in that, The mechanical stress σ el With mechanical strain ε el If the relationship conforms to Hooke's Law, then σ el It can be calculated using equation (12): (12) Where D is the elasticity coefficient matrix. E The Young's modulus of the bar stock. v It is Poisson's ratio.

5. The method for analyzing the nonlinear time-domain characteristics of a giant magnetostrictive transducer as described in claim 4, characterized in that, Step S5 includes: the magnetic and mechanical fields of the Terfenol-D rod are coupled through the magnetostrictive Joule and Villari effects; the magnetization M obtained by the Jiles-Atherton model in step S3 is substituted into the second-order domain shift model to calculate the displacement of the solid mechanical field, reflecting the magnetostrictive Joule effect; the stress tensor σ of the solid mechanical field is substituted into the Jiles-Atherton model to calculate the effective magnetic field strength H. e This reflects the Villari effect.

6. The method for analyzing the nonlinear time-domain characteristics of a giant magnetostrictive transducer as described in claim 1, characterized in that, Step S6 includes: calculating the output displacement u and output sound pressure p of the transducer in the fluid domain, wherein the sound pressure in the fluid domain satisfies the basic equation of sound wave, as shown in equation (17): (17) in ρ w Let be the density of the fluid; in this model, the fluid is chosen to be water. c 0 Let be the speed of sound in the fluid, and p be the sound pressure; similarly, a variation of p is used. δ If p is weighted, then the weak form of equation (17) can be written as equation (18): (18) in V a The volume domain representing the pressure acoustic field. əV sa Represents the boundary connecting solid mechanics and acoustic fields; The electro-magnetic-mechanical-acoustic multi-field coupled nonlinear time-domain model of the super magnetostrictive transducer is fully constructed by the process of steps S1-S6.

7. A system for analyzing the time-domain characteristics of a giant magnetostrictive transducer, characterized in that, include: One or more processors; A memory having stored one or more programs that, when executed by one or more processors, cause the one or more processors to perform the steps of the method according to any one of claims 1-6.

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