阅读说明：本技术 一种复合材料介电常数计算方法及系统 (Composite material dielectric constant calculation method and system ) 是由 黄猛 宋翰林 吴延宇 吕玉珍 于 2020-12-03 设计创作，主要内容包括：本发明公开了一种复合材料介电常数计算方法及系统。将复合材料划分为独立的立方体单元结构,对立方体结构进行了区域划分,对界面极化不规则区域进行了电路等效,考虑了不同材料间的界面极化,不但能计算高频段的介电谱,也能计算复合材料的中、低频段的介电谱；并且利用第二关系式,能够根据基体和填充物的介电谱线计算复合材料的介电常数频谱,亦可根据复合材料及其中一种材料的介电谱线反推另外一种材料的介电常数频谱,极大降低了工作量,节约了测试时间。(The invention discloses a method and a system for calculating a dielectric constant of a composite material. The composite material is divided into independent cubic unit structures, the cubic structures are subjected to region division, the interface polarization irregular regions are subjected to circuit equivalence, the interface polarization among different materials is considered, and not only can the dielectric spectrum of a high frequency band be calculated, but also the dielectric spectra of medium and low frequency bands of the composite material can be calculated; and by utilizing the second relational expression, the dielectric constant frequency spectrum of the composite material can be calculated according to the dielectric spectral lines of the matrix and the filler, and the dielectric constant frequency spectrum of another material can be reversely deduced according to the dielectric spectral lines of the composite material and one material, so that the workload is greatly reduced, and the test time is saved.)

1. A method for calculating the dielectric constant of a composite material is characterized by comprising the following steps:

dividing the composite material into units to obtain a plurality of same cubic units; each cubic unit comprises a filler positioned at the center of the cubic unit and a matrix arranged on the outer surface of the filler;

dividing the cubic unit into a first area and a second area, and generating an equivalent circuit according to the first area and the second area; wherein the first region comprises a first matrix and the second region comprises an upper matrix, a filler and a lower matrix; the equivalent circuit comprises a first equivalent circuit unit and a second equivalent circuit unit which are connected in parallel; the first equivalent circuit unit is determined according to the first base body, and the second equivalent circuit unit is determined according to the upper base body, the filler and the lower base body;

establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relational expression;

establishing a relational expression among the matrix dielectric constant, the filler dielectric constant and the composite material dielectric constant according to the first relational expression to obtain a second relational expression;

and acquiring the dielectric constant frequency spectrums of any two materials of the three materials of the matrix, the filler and the composite material, and determining the dielectric constant frequency spectrum of the other material by adopting a least square method according to the second relational expression.

2. The method for calculating the dielectric constant of the composite material according to claim 1, wherein the generating an equivalent circuit according to the first region and the second region specifically comprises:

generating a first equivalent circuit unit according to the first area; the first equivalent circuit unit comprises a plurality of first RC parallel circuits which are connected in parallel, and the parameters of the first RC parallel circuits are determined according to the first substrate;

dividing the second region into a plurality of second sub-regions in a direction perpendicular to the electric field;

equating the second sub-region to a second equivalent circuit subunit; the second equivalent circuit subunit is a second RC parallel circuit, a third RC parallel circuit and a fourth RC parallel circuit which are mutually connected in series, the parameters of the second RC parallel circuit are determined according to the upper base body, the parameters of the third RC parallel circuit are determined according to the fillers, and the parameters of the fourth RC parallel circuit are determined according to the lower base body;

connecting a plurality of second equivalent circuit subunits in parallel to generate a second equivalent circuit unit;

and connecting the first equivalent circuit unit and the second equivalent circuit unit in parallel to generate an equivalent circuit.

3. The method for calculating the dielectric constant of the composite material according to claim 2, wherein the establishing a relation between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relation specifically comprises:

according to the parameters of the first RC parallel circuit, determining the equivalent impedance of the first RC parallel circuit in the first area by adopting the following formula:

wherein the content of the first and second substances,

in the formula,. DELTA.Z₁Is a first region of a first regionEquivalent resistance, Δ R, of an RC parallel circuit₁Is the equivalent resistance, Δ C, of the first RC parallel circuit of the first region₁Is the equivalent capacitance of the first RC parallel circuit in the first region, omega is angular frequency, epsilon'_mIs the real part of the complex dielectric constant of the matrix, ε ″)_mThe imaginary part of the complex dielectric constant of the matrix is, a is the side length of the cubic unit, and deltas is the area of the infinitesimal base of the first area which is discretized into a plurality of infinitesimals;

according to the parameters of the second RC parallel circuit, the parameters of the third RC parallel circuit and the parameters of the fourth RC parallel circuit, determining the equivalent impedance of the second sub-area by adopting the following formula:

ΔZ₂＝Z_2a+Z_2m+Z_2b

wherein the content of the first and second substances,

in the formula,. DELTA.Z₂Is a secondEquivalent impedance of the sub-region, Z_2aIs an upper base equivalent impedance, Z_2bIs lower base equivalent impedance, Δ R_2aIs the equivalent resistance of the upper substrate, Δ R_2bIs the equivalent resistance of the lower substrate, Δ C_2aIs the equivalent capacitance of the upper substrate, Δ C_2bIs the equivalent capacitance of the lower substrate, R is the radius of the filler, R is the distance from any point on the cross section of the second region to the center of the cross section, R<R，Z_2mΔ R being equivalent resistance of the filler_2mIs the equivalent resistance, Δ C, of the filler_2mIs the equivalent capacitance of the filler, epsilon'_fIs the real part of the dielectric constant of the filler, ε ″_fIs the imaginary part of the dielectric constant of the filler;

determining the equivalent impedance of the cubic unit by adopting the following formula according to the equivalent impedance of the first RC parallel circuit of the first area and the equivalent impedance of the second subarea to obtain a first relational expression:

in the formula, Z_eqIs the equivalent impedance of a cubic cell.

4. The method for calculating the dielectric constant of the composite material according to claim 3, wherein the establishing a relation among the dielectric constant of the matrix, the dielectric constant of the filler and the dielectric constant of the composite material according to the first relation to obtain a second relation specifically comprises:

decomposing the equivalent impedance of the cubic unit by adopting the following formula to obtain the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit:

wherein the content of the first and second substances,

Z_eq＝Z′_eq-jZ″_eq

in the formula, C_eqEquivalent capacitance being a cubic unit, R_eqIs the equivalent resistance of a cubic cell, Z'_eqIs the real part of the equivalent impedance of the cubic unit, Z ″)_eqIs the equivalent impedance imaginary part of the cubic unit;

calculating the dielectric constant of the composite material by adopting the following formula according to the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit to obtain a second relational expression:

in the formula (II) is epsilon'_effIs the real part of the dielectric constant, epsilon ″, of the composite material_effIs the imaginary part of the dielectric constant of the composite material.

5. A composite dielectric constant calculation system, comprising:

the composite material dividing module is used for dividing the composite material into units to obtain a plurality of same cubic units; each cubic unit comprises a filler positioned at the center of the cubic unit and a matrix arranged on the outer surface of the filler;

the equivalent circuit generating module is used for dividing the cubic unit into a first area and a second area and generating an equivalent circuit according to the first area and the second area; wherein the first region comprises a first matrix and the second region comprises an upper matrix, a filler and a lower matrix; the equivalent circuit comprises a first equivalent circuit unit and a second equivalent circuit unit which are connected in parallel; the first equivalent circuit unit is determined according to the first base body, and the second equivalent circuit unit is determined according to the upper base body, the filler and the lower base body;

the first relational expression determining module is used for establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relational expression;

the second relational expression determining module is used for establishing a relational expression among the matrix dielectric constant, the filler dielectric constant and the composite material dielectric constant according to the first relational expression to obtain a second relational expression;

and the dielectric constant calculation module is used for acquiring the dielectric constant frequency spectrums of any two materials of the three materials of the matrix, the filler and the composite material, and determining the dielectric constant frequency spectrum of the other material by adopting a least square method according to the second relational expression.

6. The composite dielectric constant calculation system according to claim 5, wherein the equivalent circuit generation module specifically comprises:

a first equivalent circuit unit generating unit for generating a first equivalent circuit unit according to the first area; the first equivalent circuit unit comprises a plurality of first RC parallel circuits which are connected in parallel, and the parameters of the first RC parallel circuits are determined according to the first substrate;

a second region dividing unit for dividing the second region into a plurality of second sub-regions in a direction perpendicular to the electric field direction;

the second equivalent unit is used for equivalent the second sub-area into a second equivalent circuit subunit; the second equivalent circuit subunit is a second RC parallel circuit, a third RC parallel circuit and a fourth RC parallel circuit which are mutually connected in series, the parameters of the second RC parallel circuit are determined according to the upper base body, the parameters of the third RC parallel circuit are determined according to the fillers, and the parameters of the fourth RC parallel circuit are determined according to the lower base body;

the second equivalent circuit unit generating unit is used for connecting a plurality of second equivalent circuit sub-units in parallel to generate a second equivalent circuit unit;

and the equivalent circuit generating unit is used for connecting the first equivalent circuit unit and the second equivalent circuit unit in parallel to generate an equivalent circuit.

7. The composite dielectric constant calculation system of claim 6, wherein the first relational expression determination module specifically comprises:

the equivalent impedance determination unit of the first RC parallel circuit of the first area is used for determining the equivalent impedance of the first RC parallel circuit of the first area by adopting the following formula according to the parameters of the first RC parallel circuit:

wherein the content of the first and second substances,

in the formula,. DELTA.Z₁Is the equivalent impedance, Δ R, of the first RC parallel circuit of the first region₁Is the equivalent resistance, Δ C, of the first RC parallel circuit of the first region₁Is the equivalent capacitance of the first RC parallel circuit in the first region, omega is angular frequency, epsilon'_mIs the real part of the complex dielectric constant of the matrix, ε ″)_mThe imaginary part of the complex dielectric constant of the matrix is, a is the side length of the cubic unit, and deltas is the area of the infinitesimal base of the first area which is discretized into a plurality of infinitesimals;

the equivalent impedance determining unit of the second sub-area is configured to determine the equivalent impedance of the second sub-area according to the parameter of the second RC parallel circuit, the parameter of the third RC parallel circuit, and the parameter of the fourth RC parallel circuit by using the following formula:

ΔZ₂＝Z_2a+Z_2m+Z_2b

wherein the content of the first and second substances,

in the formula,. DELTA.Z₂Is the equivalent impedance of the second subregion, Z_2aIs an upper base equivalent impedance, Z_2bIs lower base equivalent impedance, Δ R_2aIs the equivalent resistance of the upper substrate, Δ R_2bIs the equivalent resistance of the lower substrate, Δ C_2aIs the equivalent capacitance of the upper substrate, Δ C_2bIs the equivalent capacitance of the lower substrate, R is the radius of the filler, R is the distance from any point on the cross section of the second region to the center of the cross section, R<R，Z_2mΔ R being equivalent resistance of the filler_2mIs the equivalent resistance, Δ C, of the filler_2mIs the equivalent capacitance of the filler, epsilon'_fIs the real part of the dielectric constant of the filler, ε ″_fIs the imaginary part of the dielectric constant of the filler;

the first relational expression determining unit is configured to determine the equivalent impedance of the cubic unit by using the following formula according to the equivalent impedance of the first RC parallel circuit in the first region and the equivalent impedance of the second subregion, so as to obtain a first relational expression:

in the formula, Z_eqIs the equivalent impedance of a cubic cell.

8. The composite dielectric constant calculation system of claim 7, wherein the second relational expression determination module specifically comprises:

the equivalent impedance decomposition unit is used for decomposing the equivalent impedance of the cubic unit by adopting the following formula to obtain the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit:

wherein the content of the first and second substances,

Z_eq＝Z′_eq-jZ″_eq

in the formula, C_eqEquivalent capacitance being a cubic unit, R_eqIs the equivalent resistance of a cubic cell, Z'_eqIs the real part of the equivalent impedance of the cubic unit, Z ″)_eqIs the equivalent impedance imaginary part of the cubic unit;

the second relational expression determining unit is used for calculating the dielectric constant of the composite material by adopting the following formula according to the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit to obtain a second relational expression:

in the formula (II) is epsilon'_effIs the real part of the dielectric constant, epsilon ″, of the composite material_effIs the imaginary part of the dielectric constant of the composite material.

Technical Field

The invention relates to the technical field of material performance evaluation, in particular to a method and a system for calculating a dielectric constant of a composite material.

Background

With the development of modern science and technology, a plurality of novel composite dielectric materials including nanoparticle filling materials, foaming materials, fiber films and the like appear in a power system, in the process of designing the composite dielectric materials, the dielectric constants of a matrix and a filler which form a two-phase composite medium have important reference values, but the dielectric constants cannot be obtained by respectively carrying out dielectric response tests on the matrix and the filler under the influence of pores of the matrix material, so that the dielectric spectrum of the components needs to be reversely deduced through the whole dielectric spectrum. Meanwhile, the dielectric response test time is long, and in order to quickly and primarily know the performance of the synthesized material, the overall dielectric spectrum needs to be reversely deduced through the dielectric spectrum of the components of the composite material so as to improve the research and development efficiency and save the test time.

In order to ensure the safe, stable and reliable operation of electrical equipment in a power system, the insulation performance of the materials needs to be monitored, wherein the dielectric performance of the materials is a key index. In the insulation state diagnosis of materials, the dielectric parameters under low frequency can reflect the defects of the materials better, but the existing multi-phase composite material dielectric property prediction model mainly represents the high-frequency dielectric property of the materials, does not consider the interface polarization of different materials, can only be matched with an actually measured spectrum in a high-frequency band, has larger difference in a medium-frequency band and a low-frequency band, and cannot analyze the dielectric property of the materials under the medium-frequency band and the low-frequency band. And dielectric materials with different structures need to be subjected to dielectric response test respectively, theoretical analysis cannot be carried out, and the operation is complex and time-consuming.

Disclosure of Invention

The invention aims to provide a method and a system for calculating the dielectric constant of a composite material, which consider the interface polarization among different materials, can efficiently calculate dielectric spectrums of high, middle and low frequency bands, greatly reduce the workload and save the test time.

In order to achieve the purpose, the invention provides the following scheme:

a composite dielectric constant calculation method, comprising:

dividing the composite material into units to obtain a plurality of same cubic units; each cubic unit comprises a filler positioned at the center of the cubic unit and a matrix arranged on the outer surface of the filler;

dividing the cubic unit into a first area and a second area, and generating an equivalent circuit according to the first area and the second area; wherein the first region comprises a first matrix and the second region comprises an upper matrix, a filler and a lower matrix; the equivalent circuit comprises a first equivalent circuit unit and a second equivalent circuit unit which are connected in parallel; the first equivalent circuit unit is determined according to the first base body, and the second equivalent circuit unit is determined according to the upper base body, the filler and the lower base body;

establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relational expression;

establishing a relational expression among the matrix dielectric constant, the filler dielectric constant and the composite material dielectric constant according to the first relational expression to obtain a second relational expression;

and acquiring the dielectric constant frequency spectrums of any two materials of the three materials of the matrix, the filler and the composite material, and determining the dielectric constant frequency spectrum of the other material by adopting a least square method according to the second relational expression.

Optionally, the generating an equivalent circuit according to the first region and the second region specifically includes:

generating a first equivalent circuit unit according to the first area; the first equivalent circuit unit comprises a plurality of first RC parallel circuits which are connected in parallel, and the parameters of the first RC parallel circuits are determined according to the first substrate;

dividing the second region into a plurality of second sub-regions in a direction perpendicular to the electric field;

equating the second sub-region to a second equivalent circuit subunit; the second equivalent circuit subunit is a second RC parallel circuit, a third RC parallel circuit and a fourth RC parallel circuit which are mutually connected in series, the parameters of the second RC parallel circuit are determined according to the upper base body, the parameters of the third RC parallel circuit are determined according to the fillers, and the parameters of the fourth RC parallel circuit are determined according to the lower base body;

connecting a plurality of second equivalent circuit subunits in parallel to generate a second equivalent circuit unit;

and connecting the first equivalent circuit unit and the second equivalent circuit unit in parallel to generate an equivalent circuit.

Optionally, the establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameter of the equivalent circuit to obtain a first relational expression specifically includes:

according to the parameters of the first RC parallel circuit, determining the equivalent impedance of the first RC parallel circuit in the first area by adopting the following formula:

wherein the content of the first and second substances,

in the formula,. DELTA.Z₁Is the equivalent impedance, Δ R, of the first RC parallel circuit of the first region₁Is the equivalent resistance, Δ C, of the first RC parallel circuit of the first region₁Is the equivalent capacitance of the first RC parallel circuit in the first region, omega is angular frequency, epsilon'_mIs the real part of the complex dielectric constant of the matrix, ε "_mIs the imaginary part of the complex dielectric constant of the matrix, a is the side length of the cubic unit, and deltas is the area of the base of the micro-elements formed by discretizing the first area into a plurality of micro-elements;

according to the parameters of the second RC parallel circuit, the parameters of the third RC parallel circuit and the parameters of the fourth RC parallel circuit, determining the equivalent impedance of the second sub-area by adopting the following formula:

ΔZ₂＝Z_2a+Z_2m+Z_2b

wherein the content of the first and second substances,

in the formula,. DELTA.Z₂Is the equivalent impedance of the second subregion, Z_2aIs an upper base equivalent impedance, Z_2bIs lower base equivalent impedance, Δ R_2aIs the equivalent resistance of the upper substrate, Δ R_2bIs the equivalent resistance of the lower substrate, Δ C_2aIs the equivalent capacitance of the upper substrate, Δ C_2bIs the equivalent capacitance of the lower substrate, R is the radius of the filler, R is the distance from any point on the cross section of the second region to the center of the cross section, R<R，Z_2mΔ R being equivalent resistance of the filler_2mIs the equivalent resistance, Δ C, of the filler_2mIs the equivalent capacitance of the filler, epsilon'_fIs the real part of the dielectric constant, epsilon'_fIs the imaginary part of the dielectric constant of the filler;

determining the equivalent impedance of the cubic unit by adopting the following formula according to the equivalent impedance of the first RC parallel circuit of the first area and the equivalent impedance of the second subarea to obtain a first relational expression:

in the formula, Z_eqIs the equivalent impedance of a cubic cell.

Optionally, the establishing a relational expression among the matrix dielectric constant, the filler dielectric constant, and the composite dielectric constant according to the first relational expression to obtain a second relational expression specifically includes:

decomposing the equivalent impedance of the cubic unit by adopting the following formula to obtain the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit:

wherein the content of the first and second substances,

Z_eq＝Z'_eq-jZ”_eq

in the formula, C_eqEquivalent capacitance being a cubic unit, R_eqIs the equivalent resistance of a cubic cell, Z'_eqIs the real part of the equivalent impedance of a cubic unit, Z "_eqIs the equivalent impedance imaginary part of the cubic unit;

calculating the dielectric constant of the composite material by adopting the following formula according to the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit to obtain a second relational expression:

in the formula (II) is epsilon'_effIs the real part of the dielectric constant, epsilon'_effIs the imaginary part of the dielectric constant of the composite material.

The invention also provides a composite material dielectric constant calculation system, comprising:

the composite material dividing module is used for dividing the composite material into units to obtain a plurality of same cubic units; each cubic unit comprises a filler positioned at the center of the cubic unit and a matrix arranged on the outer surface of the filler;

the equivalent circuit generating module is used for dividing the cubic unit into a first area and a second area and generating an equivalent circuit according to the first area and the second area; wherein the first region comprises a first matrix and the second region comprises an upper matrix, a filler and a lower matrix; the equivalent circuit comprises a first equivalent circuit unit and a second equivalent circuit unit which are connected in parallel; the first equivalent circuit unit is determined according to the first base body, and the second equivalent circuit unit is determined according to the upper base body, the filler and the lower base body;

the first relational expression determining module is used for establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relational expression;

the second relational expression determining module is used for establishing a relational expression among the matrix dielectric constant, the filler dielectric constant and the composite material dielectric constant according to the first relational expression to obtain a second relational expression;

and the dielectric constant calculation module is used for acquiring the dielectric constant frequency spectrums of any two materials of the three materials of the matrix, the filler and the composite material, and determining the dielectric constant frequency spectrum of the other material by adopting a least square method according to the second relational expression.

Optionally, the equivalent circuit generating module specifically includes:

a first equivalent circuit unit generating unit for generating a first equivalent circuit unit according to the first area; the first equivalent circuit unit comprises a plurality of first RC parallel circuits which are connected in parallel, and the parameters of the first RC parallel circuits are determined according to the first substrate;

a second region dividing unit for dividing the second region into a plurality of second sub-regions in a direction perpendicular to the electric field direction;

the second equivalent unit is used for equivalent the second sub-area into a second equivalent circuit subunit; the second equivalent circuit subunit is a second RC parallel circuit, a third RC parallel circuit and a fourth RC parallel circuit which are mutually connected in series, the parameters of the second RC parallel circuit are determined according to the upper base body, the parameters of the third RC parallel circuit are determined according to the fillers, and the parameters of the fourth RC parallel circuit are determined according to the lower base body;

the second equivalent circuit unit generating unit is used for connecting a plurality of second equivalent circuit sub-units in parallel to generate a second equivalent circuit unit;

and the equivalent circuit generating unit is used for connecting the first equivalent circuit unit and the second equivalent circuit unit in parallel to generate an equivalent circuit.

Optionally, the first relational expression determining module specifically includes:

the equivalent impedance determination unit of the first RC parallel circuit of the first area is used for determining the equivalent impedance of the first RC parallel circuit of the first area by adopting the following formula according to the parameters of the first RC parallel circuit:

wherein the content of the first and second substances,

in the formula,. DELTA.Z₁Is the equivalent impedance, Δ R, of the first RC parallel circuit of the first region₁Is the equivalent resistance, Δ C, of the first RC parallel circuit of the first region₁Is firstThe equivalent capacitance ω of the first RC parallel circuit in the region is the angular frequency ε'_mIs the real part of the complex dielectric constant of the matrix, ε "_mThe imaginary part of the complex dielectric constant of the matrix is, a is the side length of the cubic unit, and deltas is the area of the infinitesimal base of the first area which is discretized into a plurality of infinitesimals;

the equivalent impedance determining unit of the second sub-area is configured to determine the equivalent impedance of the second sub-area according to the parameter of the second RC parallel circuit, the parameter of the third RC parallel circuit, and the parameter of the fourth RC parallel circuit by using the following formula:

ΔZ₂＝Z_2a+Z_2m+Z_2b

wherein the content of the first and second substances,

in the formula,. DELTA.Z₂Is the equivalent impedance of the second subregion, Z_2aIs an upper base equivalent impedance, Z_2bIs lower base equivalent impedance, Δ R_2aIs the equivalent resistance of the upper substrate, Δ R_2bIs the equivalent resistance of the lower substrate, Δ C_2aIs the equivalent capacitance of the upper substrate, Δ C_2bIs the equivalent capacitance of the lower substrate, R is the radius of the filler, R is the distance from any point on the cross section of the second region to the center of the cross section, R<R，Z_2mΔ R being equivalent resistance of the filler_2mIs the equivalent resistance, Δ C, of the filler_2mIs the equivalent capacitance of the filler, epsilon'_fIs the real part of the dielectric constant, epsilon'_fIs the imaginary part of the dielectric constant of the filler;

the first relational expression determining unit is configured to determine the equivalent impedance of the cubic unit by using the following formula according to the equivalent impedance of the first RC parallel circuit in the first region and the equivalent impedance of the second subregion, so as to obtain a first relational expression:

in the formula, Z_eqIs the equivalent impedance of a cubic cell.

Optionally, the second relational expression determining module specifically includes:

the equivalent impedance decomposition unit is used for decomposing the equivalent impedance of the cubic unit by adopting the following formula to obtain the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit:

wherein the content of the first and second substances,

Z_eq＝Z'_eq-jZ”_eq

in the formula, C_eqEquivalent capacitance being a cubic unit, R_eqIs the equivalent resistance of a cubic cell, Z'_eqIs the real part of the equivalent impedance of a cubic unit，Z”_eqIs the equivalent impedance imaginary part of the cubic unit;

the second relational expression determining unit is used for calculating the dielectric constant of the composite material by adopting the following formula according to the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit to obtain a second relational expression:

in the formula (II) is epsilon'_effIs the real part of the dielectric constant, epsilon'_effIs the imaginary part of the dielectric constant of the composite material.

Compared with the prior art, the invention has the beneficial effects that:

the invention provides a method and a system for calculating the dielectric constant of a composite material, wherein the composite material is divided into a cubic unit structure, the cubic structure is divided into areas, the area with irregular interface polarization is subjected to circuit equivalence, the interface polarization among different materials is considered, and the dielectric spectrum of a high frequency band and the dielectric spectrum of a medium and low frequency band of the composite material can be calculated; and by utilizing the second relational expression, the dielectric constant frequency spectrum of the composite material can be calculated according to the dielectric spectral lines of the matrix and the filler, and the dielectric constant frequency spectrum of another material can be reversely deduced according to the dielectric spectral lines of the composite material and one material, so that the workload is greatly reduced, and the test time is saved.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.

FIG. 1 is a flow chart of a method for calculating the dielectric constant of a composite material according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a cube cell in an embodiment of the invention;

FIG. 3 is a schematic diagram of an equivalent circuit according to an embodiment of the present invention;

FIG. 4 is a block diagram of a system for calculating the dielectric constant of a composite material according to an embodiment 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 aims to provide a method and a system for calculating the dielectric constant of a composite material, which consider the interface polarization among different materials, can efficiently calculate dielectric spectrums of high, middle and low frequency bands, greatly reduce the workload and save the test time.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

Examples

Fig. 1 is a flowchart of a method for calculating a dielectric constant of a composite material according to an embodiment of the present invention, and as shown in fig. 1, the method for calculating a dielectric constant of a composite material includes:

step 101: dividing the composite material into units to obtain a plurality of identical and independent cubic units; each cubic unit includes a filler at a central position of the cubic unit and a matrix disposed on an outer surface of the filler.

As shown in fig. 2, the composite material is divided into m × n × h identical individual cubic units of size a × b × c. Each cube contains an arbitrarily shaped medium in the center. The embodiment of the invention is a cube with side length a, wherein the cube contains a spherical medium with radius R, the spherical medium in the middle of the cube is a filler, the volume ratio of the spherical medium in the cube is equal to the volume ratio of the filler in a composite material, the medium in other parts is a matrix, and the volume ratio can be obtained by adopting a dipping method and other methods. The cylinder tangent to the sphere is identified as region 2(Area2) and the remainder of the cube as region 1(Area 1).

Step 102: dividing the cubic unit into a first area (area1) and a second area (area2), and generating an equivalent circuit according to the first area and the second area; wherein the first region comprises a first substrate, and the second region comprises an upper substrate, a filler and a lower substrate; the equivalent circuit comprises a first equivalent circuit unit and a second equivalent circuit unit which are connected in parallel; the first equivalent circuit unit is determined according to the first base, and the second equivalent circuit unit is determined according to the upper base, the filler and the lower base.

Step 102, specifically comprising:

generating a first equivalent circuit unit according to the first area; the first equivalent circuit unit comprises a plurality of first RC parallel circuits which are connected in parallel, and the parameters of the first RC parallel circuits are determined according to the first base body;

dividing the second area into a plurality of second sub-areas in the direction perpendicular to the electric field;

equating the second sub-region to a second equivalent circuit subunit; the second equivalent circuit subunit is a second RC parallel circuit, a third RC parallel circuit and a fourth RC parallel circuit which are mutually connected in series, the parameters of the second RC parallel circuit are determined according to the upper substrate, the parameters of the third RC parallel circuit are determined according to the filler, and the parameters of the fourth RC parallel circuit are determined according to the lower substrate;

connecting a plurality of second equivalent circuit subunits in parallel to generate a second equivalent circuit unit;

and connecting the first equivalent circuit unit and the second equivalent circuit unit in parallel to generate an equivalent circuit.

The media in the cubic cells are assumed to be linearly isotropic, homogeneous media. An alternating electric field is applied along the z-axis. Each cube cell is discretized into two intervals as shown in fig. 2. CubeThe various dielectrics in the cell may be equated with capacitance and resistance. The upper and lower surfaces of the second region are discretized into squares having a side length Δ a (Δ a → 0). As shown in FIG. 3, the number of the second sub-regions is n, Δ R_1nIs the equivalent resistance of the first region, Δ C_1nIs the equivalent capacitance of the first region, Δ R_anIs the equivalent resistance, Δ C, of the upper matrix of the nth second subregion_anIs the equivalent capacitance, Δ R, of the upper substrate of the nth second subregion_mnIs the equivalent resistance, Δ C, of the filling of the nth second sub-region_mnIs the equivalent capacitance, Δ R, of the filling of the nth second sub-region_bnIs the equivalent resistance, Δ C, of the lower matrix of the nth second subregion_bnIs the equivalent capacitance of the lower matrix of the nth second subregion.

Step 103: establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relational expression; the base body includes a first base body, an upper base body, and a lower base body.

Step 103, specifically comprising:

determining an equivalent impedance of the first RC parallel circuit of the first area according to the parameters of the first RC parallel circuit by adopting the following formula:

wherein the content of the first and second substances,

in the formula,. DELTA.Z₁Is the equivalent impedance, Δ R, of the first RC parallel circuit of the first region₁Is the equivalent resistance, Δ C, of the first RC parallel circuit of the first region₁Of a first RC parallel circuit of the first regionEquivalent capacitance, ω is angular frequency, ε'_mIs the real part of the complex permittivity of the matrix at a frequency corresponding to the angular frequency omega, epsilon'_mIs the imaginary part of the complex dielectric constant of the matrix under the frequency corresponding to the angular frequency omega, a is the side length of the cubic unit, and deltas is the area of the base of the micro element formed by discretizing the first area into a plurality of micro elements, namely the upper surface and the lower surface of the area are discretized into a plurality of squares with the side length delta a (delta a → 0); the sum of Δ s is (a)²-πR²) I.e. by

According to the parameters of the second RC parallel circuit, the parameters of the third RC parallel circuit and the parameters of the fourth RC parallel circuit, determining the equivalent impedance of the second subregion by adopting the following formula:

ΔZ₂＝Z_2a+Z_2m+Z_2b

wherein the content of the first and second substances,

in the formula,. DELTA.Z₂Is the equivalent impedance of the second subregion, Z_2aIs an upper base equivalent impedance, Z_2bIs lower base equivalent impedance, Δ R_2aIs the equivalent resistance of the upper substrate, Δ R_2bIs the equivalent resistance of the lower substrate, Δ C_2aIs the equivalent capacitance of the upper substrate, Δ C_2bIs the equivalent capacitance of the lower substrate, R is the radius of the filler, R is the distance from any point on the cross section of the second region to the center of the cross section, R<R，Z_2mΔ R being equivalent resistance of the filler_2mIs the equivalent resistance, Δ C, of the filler_2mIs the equivalent capacitance of the filler, epsilon'_fIs the real part of the dielectric constant, epsilon'_fIs the imaginary part of the dielectric constant of the filler;

according to the equivalent impedance of the first RC parallel circuit in the first area and the equivalent impedance of the second sub-area, determining the equivalent impedance of the cubic unit by adopting the following formula to obtain a first relational expression:

in the formula, Z_eqIs the equivalent impedance of a cubic cell.

Step 104: and establishing a relational expression among the matrix dielectric constant, the filler dielectric constant and the composite material dielectric constant according to the first relational expression to obtain a second relational expression.

Step 104, specifically comprising:

decomposing the equivalent impedance of the cubic unit by adopting the following formula to obtain the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit:

wherein the content of the first and second substances,

Z_eq＝Z'_eq-jZ”_eq

in the formula, C_eqEquivalent capacitance being a cubic unit, R_eqIs the equivalent resistance of a cubic cell, Z'_eqIs the real part of the equivalent impedance of a cubic unit, Z "_eqIs the equivalent impedance imaginary part of the cubic unit;

calculating the dielectric constant of the composite material by adopting the following formula according to the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit to obtain a second relational expression:

in the formula (II) is epsilon'_effIs the real part of the dielectric constant, epsilon'_effIs the imaginary part of the dielectric constant of the composite material.

Wherein the content of the first and second substances,

the total equivalent capacitance and the total equivalent resistance of a composite material consisting of m × n × h identical cubic units are:

since the dielectric constant of the sample is equal to that of a single cube, the calculation can be performed using a single cube unit:

step 105: and obtaining the dielectric constant frequency spectrums of any two materials of the three materials of the matrix, the filler and the composite material, and determining the dielectric constant frequency spectrum of the other material by adopting a least square method according to a second relational expression.

And (3) inputting the dielectric constants and the conductivities of any two of the dielectric constants and the conductivities by mathematical software capable of performing fitting calculation such as python, matlab and the like according to the established relation among the dielectric constants of the matrix, the filler and the composite material, calculating the dielectric constant of the other material by a least square method and drawing a dielectric spectrum.

FIG. 4 is a block diagram of a system for calculating the dielectric constant of a composite material according to an embodiment of the present invention. As shown in fig. 4, a composite dielectric constant calculation system includes:

the composite material dividing module 201 is used for dividing the composite material into units to obtain a plurality of same cubic units; each cubic unit includes a filler at a central position of the cubic unit and a matrix disposed on an outer surface of the filler.

The equivalent circuit generating module 202 is configured to divide the cubic unit into a first area and a second area, and generate an equivalent circuit according to the first area and the second area; wherein the first region comprises a first substrate, and the second region comprises an upper substrate, a filler and a lower substrate; the equivalent circuit comprises a first equivalent circuit unit and a second equivalent circuit unit which are connected in parallel; the first equivalent circuit unit is determined according to the first base, and the second equivalent circuit unit is determined according to the upper base, the filler and the lower base.

The equivalent circuit generating module 202 specifically includes:

a first equivalent circuit unit generating unit for generating a first equivalent circuit unit according to the first area; the first equivalent circuit unit comprises a plurality of first RC parallel circuits which are connected in parallel, and the parameters of the first RC parallel circuits are determined according to the first base body;

a second region dividing unit for dividing the second region into a plurality of second sub-regions in a direction perpendicular to the electric field direction;

the second equivalent unit is used for equivalent the second sub-area into a second equivalent circuit subunit; the second equivalent circuit subunit is a second RC parallel circuit, a third RC parallel circuit and a fourth RC parallel circuit which are mutually connected in series, the parameters of the second RC parallel circuit are determined according to the upper substrate, the parameters of the third RC parallel circuit are determined according to the filler, and the parameters of the fourth RC parallel circuit are determined according to the lower substrate;

the second equivalent circuit unit generating unit is used for connecting a plurality of second equivalent circuit sub-units in parallel to generate a second equivalent circuit unit;

and the equivalent circuit generating unit is used for connecting the first equivalent circuit unit and the second equivalent circuit unit in parallel to generate an equivalent circuit.

The first relational expression determining module 203 is used for establishing a relational expression between the dielectric constant of the matrix and the dielectric constant of the filler and the equivalent impedance of the cubic unit according to the parameters of the equivalent circuit to obtain a first relational expression; the base body includes a first base body, an upper base body, and a lower base body.

The first relation determining module 203 specifically includes:

the equivalent impedance determining unit of the first RC parallel circuit of the first area is used for determining the equivalent impedance of the first RC parallel circuit of the first area by adopting the following formula according to the parameters of the first RC parallel circuit:

wherein the content of the first and second substances,

in the formula,. DELTA.Z₁Is as followsEquivalent resistance, Δ R, of a first RC parallel circuit of a region₁Is the equivalent resistance, Δ C, of the first RC parallel circuit of the first region₁Is the equivalent capacitance of the first RC parallel circuit in the first region, omega is angular frequency, epsilon'_mIs the real part of the complex permittivity of the matrix at a frequency corresponding to the angular frequency omega, epsilon'_mIs the imaginary part of the complex dielectric constant of the matrix under the frequency corresponding to the angular frequency omega, a is the side length of the cubic unit, and deltas is the area of the infinitesimal base of the first area which is discretized into a plurality of infinitesimal;

the equivalent impedance determining unit of the second sub-area is used for determining the equivalent impedance of the second sub-area by adopting the following formula according to the parameters of the second RC parallel circuit, the parameters of the third RC parallel circuit and the parameters of the fourth RC parallel circuit:

ΔZ₂＝Z_2a+Z_2m+Z_2b

wherein the content of the first and second substances,

in the formula,. DELTA.Z₂Is the equivalent impedance of the second subregion, Z_2aIs an upper base equivalent impedance, Z_2bIs lower base equivalent impedance, Δ R_2aIs the equivalent resistance of the upper substrate, Δ R_2bIs the equivalent resistance of the lower substrate, Δ C_2aIs the equivalent capacitance of the upper substrate, Δ C_2bIs the equivalent capacitance of the lower substrate, R is the radius of the filler, R is the distance from any point on the cross section of the second region to the center of the cross section, R<R，Z_2mΔ R being equivalent resistance of the filler_2mIs the equivalent resistance, Δ C, of the filler_2mIs the equivalent capacitance of the filler, epsilon'_fIs the real part of the dielectric constant, epsilon'_fIs the imaginary part of the dielectric constant of the filler;

the first relational expression determining unit is used for determining the equivalent impedance of the cubic unit by adopting the following formula according to the equivalent impedance of the first RC parallel circuit in the first area and the equivalent impedance of the second subregion to obtain a first relational expression:

in the formula, Z_eqIs the equivalent impedance of a cubic cell.

And a second relation determining module 204, configured to establish a relation among the matrix dielectric constant, the filler dielectric constant, and the composite dielectric constant according to the first relation, so as to obtain a second relation.

The second relation determining module 204 specifically includes:

the equivalent impedance decomposition unit is used for decomposing the equivalent impedance of the cube unit by adopting the following formula to obtain the equivalent resistance of the cube unit and the equivalent capacitance of the cube unit:

wherein the content of the first and second substances,

Z_eq＝Z'_eq-jZ”_eq

in the formula, C_eqEquivalent capacitance being a cubic unit, R_eqIs the equivalent resistance of a cubic cell, Z'_eqIs the real part of the equivalent impedance of a cubic unit, Z "_eqIs the equivalent impedance imaginary part of the cubic unit;

the second relational expression determining unit is used for calculating the dielectric constant of the composite material by adopting the following formula according to the equivalent resistance of the cubic unit and the equivalent capacitance of the cubic unit to obtain a second relational expression:

in the formula (II) is epsilon'_effIs the real part of the dielectric constant, epsilon'_effIs the imaginary part of the dielectric constant of the composite material.

And the dielectric constant calculation module 205 is configured to obtain dielectric constant spectrums of any two of the three materials, namely the matrix, the filler and the composite material, and determine the dielectric constant spectrum of the other material by using a least square method according to the second relational expression.

For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.

The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In summary, this summary should not be construed to limit the present invention.