CN105259450A - Magnetic shielding effectiveness evaluation method - Google Patents

Abstract

The invention provides a magnetic shielding effectiveness evaluation method. The magnetic shielding effectiveness evaluation method comprises the steps: 1) establishing a model with applied static magnetic field for a shield at will; 2) performing mesh generation; 3) setting boundary conditions; 4) selecting a node to calculate a mean value; and 5) calculating the shielding effectiveness.

Description

A kind of magnetic shielding usefulness evaluation method

Technical field

Technology described in the invention relates to a kind of high stability D.C. high-current calibration system, particularly relates to a kind of shield effectiveness evaluation method of current comparator.

Background technology

Magnetic modulation iron core is the core component of current comparator, the performance of magnetic modulator iron core directly affects the technical indicator of current comparator, and magnetic modulation iron core is easily by magnetic interference, and current comparator in use inevitably also exists magnetic field around, so magnetic modulation iron core generally needs conductively-closed.Take the method for experience to the design of Electromagnetic Shielding of current comparator for a long time always.Shield effectiveness estimation for current comparator shield has multiple diverse ways, than if any plane wave shielding theory, circuit approximation theory and the Field Analyze Method based on maxwell equation group.Because the size of the effect of electromagnetic screen and shield is as shape, the many factors such as material are relevant, and the frequency band distribution difference of interfere with electromagnetic field also can have influence on shield effectiveness, and the shield shape of current comparator is relatively complicated, if calculated with several method above-mentioned, have to adopt a large amount of being similar to, the reliability of result of calculation is reduced, cause the electromagnetic screen that designs thus or effect bad, or bulky, cause unnecessary the economic loss even failure of research work.So, calculate comparatively reliably in the urgent need to a kind of comparatively accurate shield effectiveness of method to shield.

Summary of the invention

The object of the invention is to be for the deficiencies in the prior art, propose a kind of current comparator shield effectiveness evaluation method based on finite element analysis, and be applied in the design of current comparator shield.

The invention provides a kind of magnetic shielding usefulness evaluation method, specifically comprise the steps: 1) set up the model of any additional static magnetic field of shield; 2) mesh generation; 3) boundary condition is set; 4) node calculate mean value is chosen; 5) shield effectiveness is calculated.

Further, wherein, in step 3), 4) between also have the step of calculating magnetic field intensity distributions.

Further, wherein saidly set up in the model process of any additional static magnetic field of shield, externally-applied magnetic field is resolved into additional axial magnetic field and additional radial magnetic field, wherein, under the condition of the additional uniform magnetic field of axis, three-dimensional model can be simplified to two dimensional model.

Further, scalar magnetic potential is introduced in the calculation with vector magnetic potential A, in two-dimentional computational problem, use vector magnetic potential A, use scalar magnetic potential when three-dimensional computations

Further, wherein field domain is a passive system, describes by scalar magnetic potential, then:

Represent by vector magnetic potential, then:

$\left\{\begin{array}{c}{\▿}^{2}A=\frac{{\∂}^{2}A}{\∂x^2}+\frac{{\∂}^{2}A}{\∂y^2}=0\\ A_i{|}_1=f\left(c_i\right)\end{array}\right.---\left(2\right)$

In formula (1), (2), ci (i=1,2,3,4) 4 borders in magnetic shield cross section are referred to, l refers to the interior semi-ring length of magnetic shield, formula (1) is substantially identical with the solution of (2), a two formulas unified form is represented, more generally be described as: set Ω as field region, its boundary condition is made up of first kind condition s1 and second kind boundary condition s2, and region itself is divided into Ω a and Ω b by medium separatrix l, and be defined in the normal direction of medium separatrix l and the direction of n and point to Ω b from Ω a, then:

$\left\{\begin{array}{c}{\▿}^2=\frac{{\∂}^{2}u}{\∂x^2}+\frac{{\∂}^{2}u}{\∂y^2}=-\frac{f}{\mathrm{\β}}\\ s_1:u=u_0\\ s_2=\frac{\∂u}{\∂n}=\frac{q}{\mathrm{\β}}\\ l:{\mathrm{\β}}_a\frac{\∂u}{\∂n}={\mathrm{\β}}_b\frac{\∂u}{\∂n}\end{array}\right.---\left(3\right)$

The first row of above formula is rewritten into:

$\frac{\∂}{\∂x}\[\mathrm{\β}\frac{\∂u}{\∂x}\]+\frac{\∂}{\∂y}\[\mathrm{\β}\frac{\∂u}{\∂y}\]=-f---\left(4\right)$

Variation δ u is multiplied by its two ends, and to x, y double integral in Ω:

$\∫\∫\[\frac{\∂}{\∂x}\[\mathrm{\β}\frac{\∂u}{\∂x}\]+\frac{\∂}{\∂y}\[\mathrm{\β}\frac{\∂u}{\∂y}\]\]\mathrm{\δ}udxdy=-\∫\∫\mathrm{\δ}udxdy---\left(5\right)$

Utilize Gaussian integrating formula, can obtain:

Consider every integral domain, can obtain:

Wherein x, y, z is the variable of function in three coordinate axis, and q is the quantity of electric charge, and B is magnetic induction density, and n, u are integration variable.

Further, wherein said node calculate mean value of choosing is specially: for additional axial magnetic field, in inner air gap, around geometric center, get several nodes, calculate the magnetic field intensity of each point, then average as the magnetic field intensity of inner air gap under additional axial magnetic field condition.

Further, wherein said node calculate mean value of choosing is specially: for additional radial magnetic field, in shield cavity, intercept xsect, around shield geometric center, get several nodes and form a path, node separation is 2mm, on calculating path, the magnetic field intensity of each point, then averages.

Further, the method wherein arranging boundary condition is, in shield cavity, arrange border around geometric center, gets several nodes, calculates the magnetic field intensity of each point, then averages.

Further, the method wherein calculating shield effectiveness is, in shield cavity, around geometric center, get several nodes and form a path, the magnetic field intensity of each point on calculating path, then average as under this magnetic field condition, the magnetic field intensity of inner air gap.

Technique effect:

In the analysis and estimation process of shield effectiveness, the structural parameters of shield effectiveness and shield, as the material of shield, thickness, the xsect length of side and internal diameter have certain relation, but this relation is not simple monotone increasing or relation of successively decreasing.Apply technology of the present invention, in shield actual design, set up the complex relationship between shield effectiveness and shield structural parameters, and then obtain optimum shield design proposal, to adapt to specific on-the-spot characteristic, obtain best shield effectiveness.

Application of the present invention is the current comparator amplifying double check principle based on magnetic modulation and magnetic, uses the magnetic shielding usefulness of finite element method to current comparator analyze and estimate.In analytic process, externally-applied magnetic field is decomposed into additional axial magnetic field and additional radial magnetic field, respectively the shield effectiveness under two kinds of different externally-applied magnetic fields is estimated, and result estimation result and Magnetic Circuit Method being calculated gained compares, the results contrast of the two is close, as can be seen here, the estimation of technical solution of the present invention to magnetic shielding usefulness has important reference significance application prospect widely.

Accompanying drawing explanation

Fig. 1 is the cut-open view of magnetic shield of the present invention

Fig. 2 is the usefulness estimation flow process of magnetic shield of the present invention

Magnetic line of force distribution when Fig. 3 is the present invention's additional axial magnetic field

Magnetic shield structure when Fig. 4 is the present invention's additional axial magnetic field

Axial magnetic field simulation drawing when Fig. 5 is Finite element arithmetic of the present invention

Fig. 6 is the distribution plan of shield of the present invention magnetic line of force when being placed in radial magnetic field

Fig. 7 is magnetic shield model in radial magnetic field of the present invention

Fig. 8 is the Three-dimensional CAD of the magnetic shield that finite element analysis software of the present invention generates

Fig. 9 is boundary condition of the present invention and node selection figure

Figure 10 is the present invention's Distribution of Magnetic Field cloud atlas in air when not adding shield

Figure 11 is that the present invention adds Distribution of Magnetic Field cloud atlas after shield

Embodiment

In order to make the art personnel better understand the present invention, below in conjunction with accompanying drawing and implementation method, the present invention is described in further detail.

See Fig. 1, show the cut-open view of the general structure of current comparator magnetic shield of the present invention, it is cavity circular ring structure, and cavity cross section is rectangle or the positive dirction structure with certain wall thickness, can certainly be other shapes.

See Fig. 2, show the usefulness estimation flow process of current comparator magnetic shield of the present invention, specifically comprise the steps: 1) Modling model; 2) mesh generation; 3) boundary condition is set; 4) calculating magnetic field intensity distributions; 5) node calculate mean value is chosen; 6) shield effectiveness is calculated: be shield effectiveness by the magnetic field intensity in cavity after adding magnetic shield compared with magnetic field intensity when not shielding.Wherein, the 4th) step according to circumstances can dispense.

Specifically, externally-applied magnetic field is decomposed into additional axial magnetic field and additional radial magnetic field by the present invention, and analyzes the magnetic shielding usefulness under both direction and estimate respectively.First modeling is carried out.The final purpose of finite element analysis sets up the mathematical model of Practical Project problem.Broadly, model should comprise all nodes, element, material behavior, boundary condition etc., and the feature of all reflection physical systems.In finite element analysis software, the implication of Modling model wants narrow a lot, only refers to and sets up spatial model.In conjunction with particular problem of the present invention, solid modelling (SolidModeling) is only discussed, and does not relate to and directly generate finite element model (DirectModeling).For two-dimensional problems, finite element analysis software provides enough graphic hotsopt and graphic operation ability, and in addition required model is regular shape, and therefore problem is fairly simple.When adopting three-dimensional model to calculate, model set up more complicated, can select finite element analysis software itself with graphing capability, also mapping software can be used to create geometric model, then utilize the graphic interface of itself and finite element analysis software to be imported in finite element analysis software and carry out FEM (finite element) calculation.

When additional axial magnetic field, due to the symmetry of shield structure, be two-dimentional modeling by Solid Model Simplification; When additional radial magnetic field, can not simplify, need three-dimensional modeling be adopted.After completing modeling, the method for finite element analysis is adopted to carry out mesh generation to model, the distribution of boundary condition and calculating magnetic field intensity is set.Then, in inner air gap, choose node, ask for the mean value of multiple node magnetic field intensity, using the magnetic field intensity of this mean value as inner air gap.Finally, according to the shield effectiveness of shield effectiveness computing formula estimation shield.

Be specifically described for above-mentioned six steps below:

1) finite element model of any additional static magnetic field of current comparator shield is set up.

In model process of establishing, externally-applied magnetic field is resolved into additional axial magnetic field and additional radial magnetic field, respectively to the shield effectiveness analysis under two different directions externally-applied magnetic fields, thus reach the simply detailed estimation to any externally-applied magnetic field shield effectiveness.Therefore, there are two kinds of situations, a) under the condition of the additional uniform magnetic field of axis, three-dimensional model can be simplified to two dimensional model; B) when additional radial magnetic field, three-dimensional model can not be equivalent to two dimensional model, therefore adopts three-dimensional model when shield effectiveness is estimated.

When analysis and calculation comparator electromagnetic problems, in order to obtain the relation between field amount and field source, refer to bit function in the present invention and calculating as auxiliary quantity, specifically, introducing scalar magnetic potential with vector magnetic potential A, b=-▽ × A.Use vector magnetic potential A when two dimension calculates, use scalar magnetic potential when three-dimensional computations

See Fig. 4, suppose that the thickness of magnetic shield is a, the magnetic shield cross section length of side is c, and the interior semi-ring length of magnetic shield is l.For the situation described by Fig. 4, field domain is a passive system, uses scalar magnetic potential describing, is then following formula:

In formula (1), c _i(i=1,2,3,4) refer to 4 borders in magnetic shield cross section, and l refers to semi-ring length in magnetic shield.

Representing with vector magnetic potential A, is then following formula:

$\left\{\begin{array}{c}{\▿}^{2}A=\frac{{\∂}^{2}A}{\∂x^2}+\frac{{\∂}^{2}A}{\∂y^2}=0\\ A_i{|}_1=f\left(c_i\right)\end{array}\right.---\left(2\right)$

When utilizing Finite element arithmetic magnetic field, formula (1) is substantially identical with the solution of (2), a two formulas unified form can be represented, then more generally be described as: set Ω as field region, its boundary condition is by first kind condition s ₁with second kind boundary condition s ₂composition, region itself is divided into Ω by medium separatrix l _aand Ω _b, and the direction of the normal direction and n that are defined in medium separatrix l is from Ω _apoint to Ω _b, as shown in Figure 5.

The mathematical description in this region is following formula

$\left\{\begin{array}{c}{\▿}^2=\frac{{\∂}^{2}u}{\∂x^2}+\frac{{\∂}^{2}u}{\∂y^2}=-\frac{f}{\mathrm{\β}}\\ s_1:u=u_0\\ s_2=\frac{\∂u}{\∂n}=\frac{q}{\mathrm{\β}}\\ l:{\mathrm{\β}}_a\frac{\∂u}{\∂n}={\mathrm{\β}}_b\frac{\∂u}{\∂n}\end{array}\right.---\left(3\right)$

The first row of above formula is rewritten into:

$\frac{\∂}{\∂x}\[\mathrm{\β}\frac{\∂u}{\∂x}\]+\frac{\∂}{\∂y}\[\mathrm{\β}\frac{\∂u}{\∂y}\]=-f---\left(4\right)$

Variation δ u is multiplied by its two ends, and to x, y double integral in Ω:

$\∫\∫\[\frac{\∂}{\∂x}\[\mathrm{\β}\frac{\∂u}{\∂x}\]+\frac{\∂}{\∂y}\[\mathrm{\β}\frac{\∂u}{\∂y}\]\]\mathrm{\δ}udxdy=-\∫\∫\mathrm{\δ}udxdy---\left(5\right)$

Utilize Gaussian integrating formula, can obtain:

Consider every integral domain, can obtain:

Wherein x, y, z is the variable of function in three coordinate axis, and q is the quantity of electric charge, and B is magnetic induction density, and n, u are integration variable.

A) additional axial magnetic field

When outer magnetic field direction is consistent with the axis direction of magnetic shield, namely there is a homogeneous static magnetic field H in its outside ₀along with cross-section parallel and the direction vertical on one side with cross section flows to cylinder, the magnetic field in magnetic shield is uniform, and the magnetic shielding usefulness of each point is identical.Like this, the three-dimensional problem in space is just reduced to two dimensional field problem.Three-dimensional conditional problem of variation can be obtained equally by the method for the conditional problem of variation of derivation two-dimensional magnetic SHIELDING CALCULATION model.See Fig. 3, Fig. 4, magnetic line of force distribution when showing the additional axial magnetic field of the present invention and the structure of magnetic shield.

Because the magnetoconductivity of magnetic shielding material is than the large decades of times of the magnetoconductivity of air and even thousands of times, magnetic line of force major part is passed through along shielding wall, penetrates shield inner chamber air gap and arrives direct current transducer to detect the magnetic line of force unshakable in one's determination little.The magnetic permeability of shield is higher, or parietal layer is thicker, and magnetic shunt path effect is further obvious, and shield effectiveness better.

B) additional radial magnetic field

When the axes normal of outer magnetic field direction and magnetic shield, namely during additional radial magnetic field, in shield, Distribution of Magnetic Field is uneven.See Fig. 6, Fig. 7, show distribution situation and the magnetic shield model of magnetic line of force when shield that a high-permeability material makes is placed in radial magnetic field.

Wherein, act on that magnetic flux on semi-ring magnetic shield is half side from a left side to be flow to, the half side outflow from the right side.Assuming that magnetic shield sectional area is square, the length of side is c, and wall thickness is a, and the length of air-gap is 2b.If within semi-ring magnetic shield, the length of semicircular ring is l, magnetic flux Ф ₀middle most of magnetic flux Ф s passes through along shielding wall, as above in figure shown in dotted line, only has little magnetic flux Ф _tfrom shielding wall through arriving air-gap.

When adopting three-dimensional model to calculate, model set up more complicated, can select finite element analysis software itself with graphing capability or use mapping software to create geometric model, then utilize the graphic interface of itself and finite element analysis software to be imported in finite element analysis software and carry out FEM (finite element) calculation.With finite element analysis software itself set up the illustraton of model identical with Fig. 1 with graphing capability, the Three-dimensional CAD generated subsequently is as shown in Figure 8.

2) mesh generation;

Mesh generation is carried out to whole model selected after the shield of additional axial magnetic field, radial magnetic field respectively Modling model, adopt finite element analysis software itself with mesh generation function, shield inner air gap is comprised to shield Three-dimensional CAD, shielding wall carries out subdivision.

3) boundary condition is set;

See Fig. 9, in order to calculate shield effectiveness, adopt finite element analysis software, in shield cavity, border is set around geometric center, gets several nodes, this place's node be chosen as one of difficult point of usefulness evaluation method, here the method adopting theoretical analysis to combine with test carries out boundary condition setting, and the contrast verification according to final calculation result and actual conditions is further improved design.Such as, the contrast degree of conformity of final calculation result and actual conditions more than 90%, then can be approved result of calculation, be more preferably more than 95.

4) calculating magnetic field intensity distributions;

See Figure 10, when it is not for adding shield, the cloud atlas of Distribution of Magnetic Field in the air adopting finite element analysis software to make, Tu11Wei, adds Distribution of Magnetic Field cloud atlas after shield.

In other scheme, the calculating of this step magnetic field distribution can not be carried out, but the 3rd) after step executes, leap to the 5th) step chooses node calculate mean value.

5) node calculate mean value is chosen;

A. additional uneven axial magnetic field

Due to factor impact in many ways, after additional axial magnetic field, the magnetic field of shield inner air gap is not uniform, and therefore, the present invention adopts the method for average when estimating the magnetic shielding usefulness of shield.Be specially in inner air gap, around the geometric center of shield, get several nodes, sensor selection problem herein adopts averaging method, several nodes are evenly chosen in certain region, general 6 ~ 10 of the selection of node is advisable, node selection its average very few cannot characterize this regional magnetic field intensity, it is excessive that node selection crosses calculated amount follow-up at most, calculate the magnetic field intensity of each point, then average as under additional axial magnetic field condition, the magnetic field intensity of inner air gap, from then on estimates magnetic shielding usefulness.Choosing as shown in Figure 3 of node.

B. additional uneven radial magnetic field

Extraneous air magnetic field is radial and intensity non-uniform Distribution, but carries out modeling at the center of outside air layer, can be equivalent to uniform magnetic field.Still the method for average is adopted when estimating the magnetic shielding usefulness of shield.In shield cavity, intercept xsect, around the geometric center of shield, get several nodes, general 6 ~ 10 of the selection of point is advisable, and node selection its average very few cannot characterize this regional magnetic field intensity, and it is excessive that node selection crosses calculated amount follow-up at most, form a path, node separation is 2mm.The node of calculating path as shown in Figure 5.On calculating path, the magnetic field intensity of each point, then averages, as under radial magnetic field condition, and the magnetic field intensity of inner air gap,

6) shield effectiveness is calculated

In order to calculate shield effectiveness, in shield cavity, around geometric center, getting several nodes and forming a path, the magnetic field intensity of each point on calculating path, then average as under this magnetic field condition, the magnetic field intensity of inner air gap.

In order to check the validity of magnetic shielding usefulness, shield effectiveness is calculated under the physical dimension of different shielding material and shield, and compared with the result of calculation of Magnetic Circuit Method, found that, when the shielding material magnetic permeability of shield is less than 1000, along with magnetic permeability increases, shield effectiveness, in the trend increased, matches with the result of Magnetic Circuit Method; And along with magnetic permeability continuation increase, shield effectiveness increases slowly, until when magnetic permeability is increased to 2000, shield effectiveness starts to decline, and this point is close with actual conditions.Because after the magnetic permeability of shielding material increases to certain value, this shield is saturated, an interference magnet can be become, and then affect shield effectiveness.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.In addition, although employ some specific terms in this instructions, these terms are only used to convenient explanation, do not form any restriction to the present invention.

Claims (9)

1. a magnetic shielding usefulness evaluation method, specifically comprises the steps: 1) set up the model of any additional static magnetic field of shield; 2) mesh generation; 3) boundary condition is set; 4) node calculate mean value is chosen; 5) shield effectiveness is calculated.

2. evaluation method according to claim 1, is characterized in that: in step 3), 4) between also have the step of calculating magnetic field intensity distributions.

3. evaluation method according to claim 1 and 2, it is characterized in that: describedly set up in the model process of any additional static magnetic field of shield, externally-applied magnetic field is resolved into additional axial magnetic field and additional radial magnetic field, wherein, under the condition of the additional uniform magnetic field of axis, three-dimensional model can be simplified to two dimensional model.

4. evaluation method according to claim 3, is characterized in that: in the calculating of Modling model, introduce scalar magnetic potential with vector magnetic potential A, in two-dimentional computational problem, use vector magnetic potential A, use scalar magnetic potential when three-dimensional computations.

5. evaluation method according to claim 4, is characterized in that: the field domain in described magnetic field is a passive system, describes by scalar magnetic potential, then:

Represent by vector magnetic potential, then:

$\left\{\begin{array}{c}{\▿}^{2}A=\frac{{\∂}^{2}A}{\∂x^2}+\frac{{\∂}^{2}A}{\∂y^2}=0\\ A_i{|}_1=f\left(c_i\right)\end{array}\right.---\left(2\right)$

In formula (1), (2), c _i(i=1,2,3,4) refer to 4 borders in magnetic shield cross section, and l refers to the interior semi-ring length of magnetic shield,

Formula (1) is substantially identical with the solution of (2), a two formulas unified form is expressed as: set Ω as field region, its boundary condition is made up of first kind condition s1 and second kind boundary condition s2, region itself is divided into Ω a and Ω b by medium separatrix l, and be defined in the normal direction of medium separatrix l and the direction of n and point to Ω b from Ω a, then:

$\left\{\begin{array}{c}{\▿}^2=\frac{{\∂}^{2}u}{\∂x^2}+\frac{{\∂}^{2}u}{\∂y^2}=-\frac{f}{\mathrm{\β}}\\ s_1:u=u_0\\ s_2=\frac{\∂u}{\∂n}=\frac{q}{\mathrm{\β}}\\ l:{\mathrm{\β}}_a\frac{\∂u}{\∂n}={\mathrm{\β}}_b\frac{\∂u}{\∂n}\end{array}\right.---\left(3\right)$

The first row of above formula is rewritten into:

$\frac{\∂}{ex}\[\mathrm{\β}\frac{\∂u}{ex}\]+\frac{\∂}{ey}\[\mathrm{\β}\frac{\∂u}{ey}\]=-f---\left(4\right)$

Variation δ u is multiplied by its two ends, and to x, y double integral in Ω:

$\∫\∫\[\frac{\∂}{\∂x}\[\mathrm{\β}\frac{\∂u}{\∂x}\]+\frac{\∂}{\∂y}\[\mathrm{\β}\frac{\∂u}{\∂y}\]\mathrm{\δ}udxdy=-\∫\∫\mathrm{\δ}udxdy---\left(5\right)$

Utilize Gaussian integrating formula, can obtain:

Consider every integral domain, can obtain:

Wherein x, y, z is the variable of function in three coordinate axis, and q is the quantity of electric charge, and B is magnetic induction density, and n, u are integration variable.

6. evaluation method according to claim 5, it is characterized in that: described in choose node calculate mean value and be specially: for additional axial magnetic field, in inner air gap, around geometric center, get several nodes, preferably select 6-10 node, calculate the magnetic field intensity of each point, then average as the magnetic field intensity of inner air gap under additional axial magnetic field condition.

7. evaluation method according to claim 6, it is characterized in that: described in choose node calculate mean value and be specially: for additional radial magnetic field, in shield cavity, intercept xsect, around shield geometric center, get several nodes and form a path, preferably select 6-10 node, node separation is 2mm, and on calculating path, the magnetic field intensity of each point, then averages.

8. evaluation method according to claim 1 and 2, it is characterized in that: the method arranging boundary condition is, in shield cavity, around geometric center, border is set, get several nodes, calculate the magnetic field intensity of each point, and the method adopting theoretical analysis to combine with test carries out boundary condition setting, contrast verification according to final calculation result and actual conditions is further improved, and such as degree of conformity approves this border result more than 90%.

9. evaluation method according to claim 1 and 2, it is characterized in that: the method calculating shield effectiveness is, in shield cavity, around geometric center, get several nodes and form a path, the magnetic field intensity of each point on calculating path, then averages as under this magnetic field condition, the magnetic field intensity of inner air gap.