CN107423506B - Method for calculating maximum external magnetization intensity of magnetostrictive material - Google Patents
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Abstract
The invention provides a method for calculating the maximum external magnetization intensity of a magnetostrictive material, which comprises the following steps: establishing a nonlinear free energy equation by taking a single magnetic domain in a magnetostrictive material as a research object; substituting a preset value of an external magnetic field and a preset value of external stress into a nonlinear free energy equation to solve; analyzing the influence rule of the external magnetic field and the stress on the magnetic domain deflection according to the solving result; obtaining the optimal values of the external magnetic field and the stress; and calculating the maximum magnetization intensity of the magnetostrictive material generated outwards. Compared with the prior art, the method has the advantages that the extreme value is solved by the nonlinear free energy equation of the single-domain particles in the material, the law of magnetic domain angle deflection in the magnetostrictive material is researched, the magnetization and magnetomechanical coupling characteristics of the material are further described, the optimal values of an external magnetic field and stress are obtained, and accordingly the magnetization intensity of the magnetostrictive material externally generated is calculated.
Description
Technical Field
The invention relates to the technical field of magnetostrictive materials, in particular to a method for calculating the maximum external magnetization intensity of a magnetostrictive material.
Background
The establishment and the perfection of the magnetic energy coupling model of the magnetostrictive material machine are always hot points and difficulties researched by experts of scholars at home and abroad, and are also the premise of directly influencing and restricting the application of wide-band and high-performance devices of magnetostrictive materials. When the actuator based on the magnetostrictive material works, the actuator is subjected to the coupling action of double heavy loads of an excitation magnetic field and mechanical stress, the constitutive relation of the material is established into a mathematical model of not less than two coupling fields, and the mutual superposition of the actions of the mechanical magnetic coupling fields greatly increases the difficulty of establishing a material theoretical model. In engineering application, a material model is simplified by generally adopting an approximately linear piezomagnetic relationship, and a coupling relationship of materials is established. The linear constitutive relation of the established material at present is used for analyzing and describing the internal conversion relation between magnetic machines in the material, can only be used for engineering application with low precision, and the established model can only reflect the coupling relation of the material in a certain specific linear region and cannot be used for describing the nonlinear relation of the giant magnetostrictive material.
Because the establishment of the magnetostrictive material model in the prior art is too simple, the important parameters in the magnetostrictive material device are difficult to be accurately valued, and the magnetostrictive material cannot obtain the optimal application performance.
Disclosure of Invention
In view of this, the present invention provides a method for calculating the maximum external magnetization of a magnetostrictive material, which can calculate the maximum external magnetization of the magnetostrictive material more accurately.
The invention provides a method for calculating the maximum external magnetization intensity of a magnetostrictive material, which comprises the following steps:
establishing a nonlinear free energy equation by taking a single magnetic domain in a magnetostrictive material as a research object;
substituting a preset value of the external stress and a preset value of the external magnetic field into the nonlinear free energy equation to solve;
analyzing the influence rule of the external magnetic field and the stress on the magnetic domain deflection according to the solving result;
obtaining the optimal values of the external magnetic field and the stress according to the influence rule of the external magnetic field and the stress on the magnetic domain deflection;
and calculating the maximum magnetization intensity of the magnetostrictive material generated outwards according to the optimal values of the external magnetic field and the stress.
Preferably, the nonlinear free energy equation is:
E＝Ek+Eσ+EHformula 1;
in formula 1, E is free energy;
Ekvarious properties of magnetic crystal;
Eσthe stress is different in performance;
EHis the magnetization energy.
Preferably, the formula 1 is expressed in an X coordinate system as:
in the formula 2, K1And K2Is a constant of magnetocrystalline anisotropy, and,
α1is the direction cosine of the magnetization M to the x-axis, alpha2Is the direction cosine of the magnetization M to the y-axis, α3Is the direction cosine of the magnetization M to the z-axis;
β1for the direction cosine of the applied magnetic field H and stress sigma to the x-axis, beta2For the direction cosine of the applied magnetic field H and stress sigma to the y-axis, beta3Cosine of the direction of the applied magnetic field H and stress sigma to the z-axis;
λ100is a magnetostrictive material in<100>Coefficient of magnetostriction in the direction, λ111Is a magnetostrictive material in<111>The magnetostriction coefficient of the direction;
h is the external magnetic field intensity, and sigma is the external stress;
μ0for vacuum permeability, MsIs the saturation magnetization;
the X coordinate system takes the [100] crystal axis direction as an X axis, the [010] crystal axis direction as a y axis and the [001] crystal axis direction as a z axis.
Preferably, the directions of the external magnetic field and the stress are both the [110] crystal axis direction.
Preferably, equation 2 is transformed in polar coordinates such that the direction of magnetization M in the X coordinate system is
Preferably, the formula 2 is expressed in a Y coordinate system as:
the direction of the x axis in the Y coordinate system is [001]]The y-axis being in the direction
The z-axis is in the direction of
Preferably, the method for solving the nonlinear free energy equation is to use MATLAB software to solve.
Preferably, the preset value of the applied stress is 0 to-12 MPa.
Preferably, the preset value of the external magnetic field is 0-120000A/m.
Preferably, the optimal value of the external magnetic field is 45000-55000A/m.
Preferably, the optimal value of the external stress is-4.5 to-5.5 MPa.
Compared with the prior art, the method takes the single domain particles in the magnetostrictive material as a research object of a magnetic domain deflection model, solves an extreme value through a nonlinear free energy equation of the single domain particles in the material, researches the law of magnetic domain angle deflection in the giant magnetostrictive material, further describes the magnetization and magnetomechanical coupling characteristics of the material, and obtains the optimal value of an external magnetic field and stress, thereby calculating the externally generated magnetization intensity of the magnetostrictive material.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic diagram of an X-coordinate system in an embodiment of the present invention;
FIG. 2 is a calculation result of MATLAB when the applied magnetic field and the stress are 0 in the embodiment of the present invention;
FIG. 3 is a calculation result of MATLAB when the applied stress is 0 and the applied magnetic field is 10000A/m in the embodiment of the present invention;
FIG. 4 is a calculation result of MATLAB when the applied stress is 0 and the applied magnetic field is 50000A/m in the embodiment of the present invention;
FIG. 5 is the calculation result of MATLAB when the applied stress is 0 and the applied magnetic field is 90000A/m in the embodiment of the present invention;
FIG. 6 is a calculation result of MATLAB when the applied magnetic field is 0 and the applied stress is-1 MPa in the embodiment of the present invention;
FIG. 7 is a calculation result of MATLAB when the applied magnetic field is 0 and the applied stress is-1 MPa in the embodiment of the present invention;
FIG. 8 is a calculation result of MATLAB when the applied magnetic field is 0 and the applied stress is-5 MPa in the embodiment of the present invention;
FIG. 9 is a calculation result of MATLAB when the applied magnetic field is 0 and the applied stress is-5 MPa in the embodiment of the present invention;
FIG. 10 is a diagram showing the calculation results of MATLAB when the applied magnetic field is 0 and the applied stress is-10 MPa in the embodiment of the present invention;
FIG. 11 is a calculation result of MATLAB when the applied magnetic field is 0 and the applied stress is-10 MPa in the embodiment of the present invention;
FIG. 12 shows the calculation results of MATLAB at an applied magnetic field of 50000A/m and an applied stress of-5 MPa in the examples of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method for calculating the maximum external magnetization intensity of a magnetostrictive material, which comprises the following steps:
establishing a nonlinear free energy equation by taking a single magnetic domain in a magnetostrictive material as a research object;
substituting the preset value of the external stress and the preset value of the external magnetic field into a nonlinear free energy equation to solve;
analyzing the influence rule of the external magnetic field and the stress on the magnetic domain deflection according to the solving result;
obtaining the optimal values of the external magnetic field and the stress according to the influence rule of the external magnetic field and the stress on the magnetic domain deflection;
and calculating the maximum magnetization intensity of the magnetostrictive material generated outwards according to the optimal values of the external magnetic field and the stress.
In the invention, under the action of an external magnetic field H and stress sigma, the generated magnetocrystalline anisotropy EkVarious properties of stress EσAnd magnetization energy EHCan affect the deflection of a single magnetic domain in the magnetostrictive material, thereby affecting the free energy of the single magnetic domain; the invention preferably establishes a nonlinear free energy equation according to the magnetic crystal anisotropy, the stress anisotropy and the magnetization energy:
E＝Ek+Eσ+EHformula 1;
in formula 1, E is free energy;
Ekvarious properties of magnetic crystal;
Eσthe stress is different in performance;
EHis the magnetization energy.
In the present invention, it is preferable to express formula 1 by using an X coordinate system having a crystal axis direction of [100] as an X axis, a crystal axis direction of [010] as a y axis, and a crystal axis direction of [001] as a z axis. The direction of the applied magnetic field and the stress is not particularly limited, and those skilled in the art can select the applied direction of the applied magnetic field and the applied direction of the stress according to actual conditions. In the invention, the magnetostrictive material with a rod-shaped structure is preferably selected, and the external magnetic field and the stress are loaded in the axial direction of the rod-shaped magnetostrictive material, namely the direction of the crystal axis [110 ].
In the present invention, formula 1 in the X coordinate system can be represented as:
in the formula 2, K1And K2Is a constant of magnetocrystalline anisotropy, and,
α1is the direction cosine of the magnetization M to the x-axis, alpha2Is the direction cosine of the magnetization M to the y-axis, α3Is the direction cosine of the magnetization M to the z-axis;
β1for the direction cosine of the applied magnetic field H and stress sigma to the x-axis, beta2For the direction cosine of the applied magnetic field H and stress sigma to the y-axis, beta3Cosine of the direction of the applied magnetic field H and stress sigma to the z-axis;
λ100is a magnetostrictive material in<100>Coefficient of magnetostriction in the direction, λ111Is a magnetostrictive material in<111>The magnetostriction coefficient of the direction;
h is the external magnetic field intensity, and sigma is the external stress;
μ0for vacuum permeability, MsThe saturation magnetization.
In the present invention, the first term and the second term in formula 2 are magnetocrystalline anisotropy energy EkThe third term and the fourth term are stress anisotropy energy EσThe fifth term is magnetization energy EHIs shown.
In the invention, the solving process of the non-free energy equation shown in the formula 2 is complex, the calculated amount is large, and the polar coordinate transformation method is preferably adopted to transform the formula 2 so as to simplify the solving of the non-linear free energy equation.
In the present invention, the method of polar coordinate transformation is preferably:
let the direction of magnetization M in the X coordinate system be
Then alpha is1、α2And alpha3The transformation is:
let the direction of the externally applied magnetic field in the X coordinate system be
The direction of the external stress is
Because the invention prefers to use axial [110] in X coordinate system]Direction of applied magnetic field and stressAfter polar coordinate transformation, the direction of an external magnetic field and stress is as follows:
in the same way, beta1、β2And beta3The transformation is:
continuously transforming the X coordinate system to obtain a Y coordinate system, wherein the Y coordinate system is represented by [110]]Oriented z-axis to be perpendicular to [110]]Plane of direction [110]]Establishing an x axis and a y axis; the direction of the x axis in the Y coordinate system is [001]]The y-axis being in the direction
The z-axis is in the direction of
In the Y coordinate system, β1、β2And beta3，α1、α2And alpha3The conversion continues to:
bringing equations 5 and 6 into equation 2, to obtain the nonlinear free energy equation after coordinate transformation:
the invention preferably solves the nonlinear free energy equation through MATLAB software, analyzes the influence rule of an external magnetic field and stress on magnetic domain deflection according to the solving result, and can solve the nonlinear free energy equation shown in the formula 7 by adopting the MATLAB software, wherein the specific solving process is as follows:
selecting K in formula 71、K2、MsAnd λ100The value of the parameter;
programming calculation is carried out on the formula 7 to obtain E, theta and theta under the preset values of the applied magnetic field and the stress
The numerical value of (c).
In the present invention, each parameter in the nonlinear free energy equation shown in formula 7 is preferably as follows:
in the present invention, the programmed calculation for equation 7 is preferably as follows:
Clear；clc；close；
k1 ═ -60000; % anisotropy constant k1
k2 ═ 200000; % anisotropy constant k2
A0 ═ 50; % magnetostriction coefficient [100] direction
A1 ═ 1640; % magnetostriction coefficient [111] direction
b1 is 1/2^ 0.5; % stress and magnetic field direction cosine
b2＝1/2^0.5；
b3＝0；
o is 0; % stress load
H is 0; % magnetic field load
x is 0:1: 180; % Angle 1 division
y is 0:1: 360; % angle 2 division
[ p0, p1] ═ meshgrid (x, y); % definition cell grid
z ═ cos (p0/180 × pi); % direction cosine calculation
y＝sin(p1/180*pi).*sin(p0/180*pi)；
x＝sin(p0/180*pi).*cos(p1/180*pi)；
B ═ 001; sqrt (2)/2-sqrt (2)/20; sqrt (2)/2sqrt (2)/20 ]; % coordinate transformation criteria definition
B1＝B(:,1)；
B2＝B(:,2)；
B3＝B(:,3)；
B1＝B1'；
B2＝B2'；
B3＝B3'；
B11＝B1(:,1)；
B12＝B1(:,2)；
B13＝B1(:,3)；
B21＝B2(:,1)；
B22＝B2(:,2)；
B23＝B2(:,3)；
B31＝B3(:,1)；
B32＝B3(:,2)；
B33＝B3(:,3)；
x1＝B11*x+B12*y+B13*z；
y1＝B21*x+B22*y+B23*z；
z1＝B31*x+B32*y+B33*z；
a1 ═ x 1; % complete coordinate transformation
a2＝y1；
a3＝z1；
A, a 2+ a, a 2-1.5, a o (a 2, b, a 2+ a2, b, a2, b2, a2, b 2-3 a, a b a + b a, a, b, a, b, c; % calculated free energy number
% mesh (p0, p1, E)% drawing three-dimensional graph
contours (p0, p1, E, 50)% rendering equipotential curves, i.e. two-dimensional projection
xlabel ('p0'), ylabel ('p 1')% set tag
In the invention, the programmed calculation program is the calculation of formula 7 when the preset value of the applied magnetic field and the stress is 0, when the applied magnetic field and the stress of other preset values need to be calculated, only o and H in the program need to be set as corresponding applied stress values and preset values of the applied magnetic field, and the three-dimensional graph and two output after calculation according to the program can be usedDimension projection graph obtaining E, theta and
the numerical value of (c).
In the present invention, the method for analyzing the influence rule of the applied magnetic field and stress on the magnetic domain deflection is preferably as follows:
calculating a nonlinear free energy equation when the preset value of the external stress is 0 and the preset value of the external magnetic field is within the range of 0-120000A/m, and analyzing the influence rule of the external magnetic field on magnetic domain deflection;
and calculating a nonlinear free energy equation in the range of an external magnetic field with a preset value of 0 and an external stress with a preset value of 0-12 MPa (the external stress is a negative value to represent the applied pressure stress), and analyzing the influence rule of the external stress on the magnetic domain deflection.
In the present invention, the law of influence of an external magnetic field on the magnetic domain deflection is as follows:
when the external magnetic field and the stress are both 0, the free energy has 8 minimum values, and when the external magnetic field is increased to 10000A/m, the minimum value of the free energy rotates to gradually approach the direction of the external magnetic field; when the external magnetic field is increased to 50000A/m, 6 of 8 free energy minimum values disappear, and the rest 2 free energy minimum values gradually approach to the direction of the external magnetic field; when the external magnetic field exceeds 50000A/m and reaches 120000A/m, only 2 free energy minima still exist.
In the present invention, the law of the influence of the applied stress on the magnetic domain deflection is as follows:
when the external stress is increased from-1 MPa to-5 MPa, the magnetic field energy of magnetic domain transition at the minimum value of the two free energies is changed under the action of the stress, and the increase of the stress is favorable for reducing the magnetic field required by the magnetic domain at the minimum value of the two free energies; and continuously increasing the stress to enable the stress to exceed-5 MPa to reach-12 MPa, and increasing the stress to enable the magnetic domain to deflect towards the direction vertical to the magnetization intensity.
In the invention, the method for obtaining the optimal values of the applied magnetic field and the stress is preferably as follows:
when the magnetostrictive material is in an external magnetic field, the volume of a magnetic domain with a small angle formed by the spontaneous magnetization direction and the external magnetic field direction is enlarged along with the increase of the external magnetic field, so that the magnetization direction of the magnetic domain is further turned to the external magnetic field direction; the volumes of other magnetic domains with large angles formed by the spontaneous magnetization direction and the direction of the external magnetic field are gradually reduced, and at the moment, the magnetostrictive material externally presents macroscopic magnetism; the external magnetic field is continuously increased until all magnetic domains are arranged along the external magnetic field to reach saturation, and when unit magnetic moments in each magnetic field are arranged orderly, the magnetostrictive material generates maximum magnetization intensity outwards.
According to the influence of the external magnetic field on the magnetic domain deflection rule, the magnetic domain gradually deflects towards the direction of the external magnetic field along with the increase of the external magnetic field, when the external magnetic field is low (less than 50000A/m), the minimum value of the free energy is too much, and along with the increase of the external magnetic field, the minimum value of the free energy is gradually reduced, but when the external magnetic field is too large (more than 50000A/m), the reduction of the minimum value of the free energy is slowly kept by 2 basically (theoretically, the magnetic field is continuously increased, and finally, one minimum value of the free energy can be obtained, but the required external magnetic field is very large); the influence of an external magnetic field on magnetic domain deflection and the factors of magnetic field energy consumption in the practical application process are comprehensively considered, and the optimal value of the external magnetic field is preferably 45000A/m-55000A/m, more preferably 50000A/m.
According to the influence of the external stress on the magnetic domain deflection rule, the external stress is favorable for reducing the magnetic field energy required by magnetic field transition along with the increase (< -5MPa) of the external stress; however, as the applied stress further increases (> -5MPa), the magnetic domain is deflected in a direction perpendicular to the magnetization, and the stress anisotropy can hinder the deflection and transition of the magnetic domain, thereby increasing the magnetic field required for saturation magnetization and making the magnetization of the material more difficult. It can be seen that the magnetization of the material is facilitated by using a small applied stress, and the optimal value of the applied stress is preferably-4.5 to-5.5 MPa, and more preferably-5 MPa.
In the invention, the calculation method of the maximum magnetization intensity generated by the magnetostrictive material to the outside comprises the following steps:
substituting the optimal values of the external magnetic field and the stress into a nonlinear free energy equation for calculation;
obtaining theta at the minimum value of the free energy according to the calculation resultnAnd
a value;
according to the formula:
M＝MScosθnformula 9
Wherein M issIs the saturation magnetization;
and calculating the maximum magnetization intensity of the magnetostrictive material generated outwards.
Examples
Taking a giant magnetostrictive rod made of Terfenol-D material as an example to calculate the maximum external magnetization intensity of the magnetostrictive material, wherein the length of the giant magnetostrictive rod is 40mm, and the diameter of the giant magnetostrictive rod is 5 mm.
A free energy equation is established by taking a single magnetic domain in a magnetostrictive material as a research object:
E＝Ek+Eσ+EHformula 1
In formula 1, E is free energy;
Ekvarious properties of magnetic crystal;
Eσthe stress is different in performance;
EHis the magnetization energy.
in the formula 2, K1And K2Is a constant of magnetocrystalline anisotropy, and,
α1is the direction cosine of the magnetization M to the x-axis, alpha2Is the direction cosine of the magnetization M to the y-axis, α3Is the direction cosine of the magnetization M to the z-axis;
β1for the direction cosine of the applied magnetic field H and stress sigma to the x-axis, beta2For the direction cosine of the applied magnetic field H and stress sigma to the y-axis, beta3Cosine of the direction of the applied magnetic field H and stress sigma to the z-axis;
λ100is a magnetostrictive material in<100>Coefficient of magnetostriction in the direction, λ111Is a magnetostrictive material in<111>The magnetostriction coefficient of the direction;
h is the external magnetic field intensity, and sigma is the external stress;
μ0for vacuum permeability, MsThe saturation magnetization.
The formula 2 is subjected to polar coordinate transformation, and the direction of the magnetization M in the X coordinate system is
In the formula 2,. alpha.1、α2And alpha3The transformation is:
the direction of the applied magnetic field and stress in the X coordinate system is as follows:
in the formula 2,. beta.1、β2And beta3The transformation is:
continue to transform the X coordinate system to [110]]Oriented z-axis to be perpendicular to [110]]Plane of direction [110]]Establishing an x axis and a Y axis to obtain a Y coordinate system, wherein the direction of the x axis in the Y coordinate system is [001]]The y-axis being in the direction
The z-axis is in the direction of
In the formula 2,. beta.1、β2And beta3，α1、α2And alpha3The conversion continues to:
bringing formulas 5 and 6 into formula 2 yields:
the calculation of equation 7 was performed using MATLAB software:
the values of the parameters in formula 7 are:
MATLAB, the programming program was as follows:
Clear；clc；close；
k1 ═ -60000; % anisotropy constant k1
k2 ═ 200000; % anisotropy constant k2
A0 ═ 50; % magnetostriction coefficient [100] direction
A1 ═ 1640; % magnetostriction coefficient [111] direction
b1 is 1/2^ 0.5; % stress and magnetic field direction cosine
b2＝1/2^0.5；
b3＝0；
o is 0; % stress load
H is 0; % magnetic field load
x is 0:1: 180; % Angle 1 division
y is 0:1: 360; % angle 2 division
[ p0, p1] ═ meshgrid (x, y); % definition cell grid
z ═ cos (p0/180 × pi); % direction cosine calculation
y＝sin(p1/180*pi).*sin(p0/180*pi)；
x＝sin(p0/180*pi).*cos(p1/180*pi)；
B ═ 001; sqrt (2)/2-sqrt (2)/20; sqrt (2)/2sqrt (2)/20 ]; % coordinate transformation criteria definition
B1＝B(:,1)；
B2＝B(:,2)；
B3＝B(:,3)；
B1＝B1'；
B2＝B2'；
B3＝B3'；
B11＝B1(:,1)；
B12＝B1(:,2)；
B13＝B1(:,3)；
B21＝B2(:,1)；
B22＝B2(:,2)；
B23＝B2(:,3)；
B31＝B3(:,1)；
B32＝B3(:,2)；
B33＝B3(:,3)；
x1＝B11*x+B12*y+B13*z；
y1＝B21*x+B22*y+B23*z；
z1＝B31*x+B32*y+B33*z；
a1 ═ x 1; % complete coordinate transformation
a2＝y1；
a3＝z1；
A, a 2+ a, a 2-1.5, a o (a 2, b, a 2+ a2, b, a2, b2, a2, b 2-3 a, a b a + b a, a, b, a, b, c; % calculated free energy number
% mesh (p0, p1, E)% drawing three-dimensional graph
contours (p0, p1, E, 50)% rendering equipotential curves, i.e. two-dimensional projection
xlabel ('p0'), ylabel ('p 1')% set tag
And changing the H value when o is 0 according to the programming procedure, increasing the H value from 0 to 120000A/m, and performing multiple calculations each time the H value is increased by 1000A/m to obtain multiple calculation results.
The value of o was changed according to the above programming procedure when H is 0, and o was increased from 0 to-12 MPa, and a plurality of calculations were performed for each increase of 0.1MPa, to obtain a plurality of calculation results.
And analyzing the influence rule of the external magnetic field and the stress on the magnetic domain deflection according to the calculation result:
fig. 2 is a free energy calculation result (two-dimensional projection) obtained when the applied magnetic field and the stress are 0, and as can be seen from fig. 2, there are 8 free energy minima in the graph, and the corresponding X-system coordinates are:
when the stress is 0, an external magnetic field is applied, and when the magnetic field is increased to H10000A/m, 8 free energy minima rotate along with the increase of the magnetic field and gradually approach the direction of the external magnetic field, as shown in fig. 3, and fig. 3 is a two-dimensional projection graph output by MATLAB calculation.
When the magnetic field reaches 50000A/m,
the magnetic domain of the direction generates a transition effect with a minimum value
Completely disappear, and the minimum value is increased along with the magnetic field
And also fades gradually, as shown in fig. 4, which is a two-dimensional projection of the MATLAB computational output.
When the magnetic field reaches H90000A/m,
direction of rotationThe magnetic domain of (A) produces a transition effect of minimum value
Disappearance, minimum value
[111]The gradually outwardly applied magnetic field direction approaches, as shown in fig. 5, fig. 5 is a two-dimensional projection of the MATLAB calculation output.
When the magnetic field is 0, external stress is applied, when the stress is increased to-1 MPa,
direction minima slightly above
Direction due to stress
The part of the direction is deflected and transits to
And (4) direction. The stress action will change the magnetic field energy required for the magnetic domain transition, and the increase of the stress is beneficial to reduce
Magnetic fields required for magnetic domain transitions in directions, as shown in fig. 6 and 7, fig. 6 is a three-dimensional diagram of MATLAB calculation output, and fig. 7 is a cross-sectional view of the three-dimensional diagram in fig. 6.
When the stress reaches-5 MPa,
direction minima significantly higher than
The direction of the light beam is changed,
the direction of most magnetic domains is deflected and transitedTo
And (4) direction. For the
The directional domain, compressive stress, will become the resistance of the domain transition during its magnetoelastic process, increasing the magnetic field required for the domain transition, as shown in fig. 8 and 9, fig. 8 is a three-dimensional diagram of the mallab output, and fig. 9 is a cross-sectional view of the three-dimensional diagram in fig. 8.
When the stress reaches-10 MPa,
the direction curve is too drooping, the minimum value is too small, and the direction curve is already correct
The directional domain shift produces resistance against the maximum magnetization, as shown in fig. 10 and 11, fig. 10 is a three-dimensional graph of MATLAB calculation output, and fig. 11 is a cross-sectional view of the three-dimensional graph in fig. 10.
The influence law of the external magnetic field and the stress on the magnetic domain deflection is as follows:
the minimum values of the 8 free energies gradually approach to the direction of the external magnetic field along with the increase of the external magnetic field, namely, the magnetic domains gradually deflect towards the direction of the magnetization intensity, the external magnetic field is continuously increased until all the magnetic domains are arranged along the external magnetic field to reach saturation, and when the unit magnetic moments in each magnetic domain are arranged orderly, the magnetostrictive material generates the maximum magnetization intensity outwards; at a minimum with increasing stress
The greater the degree of free energy depression, i.e. increasing the stress causing the domain to deflect perpendicular to the applied field, will increase the area of the magnetostrictive material
Volume fraction of oriented magnetic domains, increase of magnetic field required for saturation of magnetization, mainly due to stress anisotropy energyThe magnetic domain deflection and transition are hindered, the magnetization of the material is more difficult, and the stress anisotropy performance is not favorable for the magnetization of the material from the viewpoint of energy conversion.
Obtaining maximum values of the applied magnetic field and stress:
the magnetic domain is deflected towards the direction of the external magnetic field along with the increase of the external magnetic field, which is beneficial to obtaining the maximum magnetization intensity generated by the magnetostrictive material, but when the external magnetic field exceeds 50000A/m, the magnetic domain deflection basically reaches saturation, and even if the external magnetic field is increased, the minimum value of the free energy is difficult to reduce; when the external stress is between-1 and-5 MPa, the magnetic domain deflects towards the direction of the external magnetic field along with the increase of the external stress, which is beneficial to the magnetostrictive material to generate the maximum magnetization intensity outwards, and when the external stress exceeds-5 MPa, the magnetic domain deflects towards the direction vertical to the external magnetic field to prevent the magnetostrictive material from generating the maximum magnetization intensity outwards.
Therefore, the optimal value of the external magnetic field is 50000A/m, and the maximum value of the external stress is-5 MPa.
Calculating the maximum magnetization of the magnetostrictive material generated outwards:
setting H in the programming program to 50000 and setting o to-5, and calculating;
the calculated two-dimensional projection is shown in fig. 12, and as can be seen from fig. 12, the coordinates at the two minimum values of the free energy are:
calculating the maximum magnetization intensity of the magnetostrictive material generated outwards according to a formula:
M＝MScosθnformula 8;
due to two thetanThe value, then equation 8 is rewritten as:
in formula 9, Ms is 0.765A/m, theta1＝θ2＝18；
The maximum magnetization M was calculated to be 0.73A/M.
Experimental verification calculation results:
and testing the magnetic flux density B of the Terfenol-D bar by using a magnetic flux density measuring instrument, and then according to a formula:
B＝μ0m is formula 10;
calculation of the magnetization M, in equation 10, μ0Is the permeability of the Terfenol-D material.
The test result shows that the magnetization intensity is 0.7473A/m when the external magnetic field is 50000A/m and is-5 MPa (compressive stress); the experimental result is close to the calculation result obtained by the theoretical calculation method provided by the invention, and the calculation method provided by the invention is more accurate.
When the external magnetic field is 60000A/m and is-5 MPa (compressive stress), the test result shows that the magnetization intensity is 0.7478A/m (the magnetic field is increased by 10000A/m, the magnetization intensity is only increased by 0.0004A/m, and the energy consumption is larger); the test result shows that the magnetization intensity is 0.6758A/m when the external magnetic field is 40000A/m and is-5 MPa (compressive stress); the test result is 0.7398A/m when the external magnetic field is 50000A/m and is-4 MPa (compressive stress); the test result is 0.7337A/m when the external magnetic field is 50000A/m and is-6 MPa (compressive stress); the test result is 0.7351A/m when the applied magnetic field is 60000A/m and is-6 MPa (compressive stress); the test result is 0.6930A/m when the external magnetic field is 40000A/m and is-4 MPa (compressive stress); the test result is 0.7038A/m when the applied magnetic field is 60000A/m and should be-4 MPa (compressive stress); the test result is 0.6576A/m when the external magnetic field is 40000A/m and is-6 MPa (compressive stress); it can be seen that the magnetostrictive material in the embodiment of the invention indeed obtains the maximum magnetization at the optimal values of the applied magnetic field and stress, and the method provided by the invention has higher accuracy.
From the above embodiments, the present invention provides a method for calculating the maximum external magnetization of a magnetostrictive material, including: establishing a nonlinear free energy equation by taking a single magnetic domain in a magnetostrictive material as a research object; substituting preset values of an external magnetic field and stress into a nonlinear free energy equation to solve; analyzing the influence rule of the external magnetic field and the stress on the magnetic domain deflection according to the solving result; obtaining the optimal values of the external magnetic field and the stress; and calculating the maximum magnetization intensity of the magnetostrictive material generated outwards. Compared with the prior art, the method has the advantages that the extreme value is solved by the nonlinear free energy equation of the single-domain particles in the material, the law of magnetic domain angle deflection in the magnetostrictive material is researched, the magnetization and magnetomechanical coupling characteristics of the material are further described, the optimal values of an external magnetic field and stress are obtained, and accordingly the magnetization intensity of the magnetostrictive material externally generated is calculated.
Claims (6)
1. A method of calculating the maximum externally generated magnetization of a magnetostrictive material, comprising:
establishing a nonlinear free energy equation by taking a single magnetic domain in a magnetostrictive material as a research object;
substituting a preset value of the external stress and a preset value of the external magnetic field into the nonlinear free energy equation to solve;
analyzing the influence rule of the external magnetic field and the stress on the magnetic domain deflection according to the solving result;
obtaining the optimal values of the external magnetic field and the stress according to the influence rule of the external magnetic field and the stress on the magnetic domain deflection;
calculating the maximum magnetization intensity of the magnetostrictive material generated outwards according to the optimal values of the external magnetic field and the stress;
the nonlinear free energy equation is:
E＝Ek+Eσ+EHformula 1;
in formula 1, E is free energy;
Ekvarious properties of magnetic crystal;
Eσthe stress is different in performance;
EHis magnetization energy;
the formula 1 is expressed in an X coordinate system as:
in the formula 2, K1And K2Is a constant of magnetocrystalline anisotropy, and,
α1is the direction cosine of the magnetization M to the x-axis, alpha2Is the direction cosine of the magnetization M to the y-axis, α3Is the direction cosine of the magnetization M to the z-axis;
β1for the direction cosine of the applied magnetic field H and stress sigma to the x-axis, beta2For the direction cosine of the applied magnetic field H and stress sigma to the y-axis, beta3Cosine of the direction of the applied magnetic field H and stress sigma to the z-axis;
λ100is a magnetostrictive material in<100>Coefficient of magnetostriction in the direction, λ111Is a magnetostrictive material in<111>The magnetostriction coefficient of the direction;
h is the external magnetic field intensity, and sigma is the external stress;
μ0for vacuum permeability, MsIs the saturation magnetization;
the X coordinate system takes the [100] crystal axis direction as an X axis, takes the [010] crystal axis direction as a y axis and takes the [001] crystal axis direction as a z axis;
the formula 2 is subjected to polar coordinate transformation, and the direction of the magnetization M in the X coordinate system is
The formula 2 is expressed in a Y coordinate system as:
the direction of the x axis in the Y coordinate system is [001]]The y-axis being in the direction
The z-axis is in the direction of
The external magnetic field is applied toSubstituting the optimal value of the force into the nonlinear free energy equation for calculation; obtaining theta at the minimum value of the free energy according to the calculation resultnAnd
a value;
the maximum magnetization of the magnetostrictive material to the outside is calculated according to equation 9:
M＝MScosθnformula 9;
wherein M issThe saturation magnetization.
2. The calculation method according to claim 1, wherein the nonlinear free energy equation is solved by using MATLAB software.
3. The calculation method according to claim 1, wherein the preset value of the applied stress is between 0 and-12 MPa.
4. The calculation method according to claim 1, wherein the predetermined value of the applied magnetic field is 0 to 120000A/m.
5. The calculation method according to claim 1, wherein the optimum value of the externally applied magnetic field is 45000-55000A/m.
6. The calculation method according to claim 1, wherein the optimum value of the applied stress is-4.5 to-5.5 MPa.
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