CN101968517A - Mutual inductor measuring system and method for realizing uniform mutual inductance quantity vertical gradient - Google Patents

Abstract

The invention relates to a novel mutual inductor system and method for realizing highly uniform mutual inductance quantity vertical gradient in an annular region of a mutual inductor. The novel mutual inductor system is different from the traditional mutual inductor system, and the parameters of the coil and the relative positions of a primary winding and a secondary winding of the mutual inductor are reasonably configured. When the space R between an internal excitation coil and an external excitation coil and the distance H between the excitation coils and a suspension coil meet the equation R2=4/3H2 and the turns ratio of the internal excitation coil to the external excitation coil to the suspension coil meets 10000:2700:430, a toroidal magnetic field uniform region with 2 cm axial length can be produced near the symmetrical plane of a Joule balance magnetic field, and the mutual induction parameters of the coil system in the uniform region have four-order uniformity.

Description

Mutual inductor measuring system and realizing the method for even mutual induction amount vertical gradient

Technical field:

The invention belongs to the delicate metering fields of measurement, relate in particular to a kind of new method of setting up coefficient of mutual inductance between the precision measurement coil.

Background technology:

Between coil mutual inductance structure parameter M by the relative position between the geometric configuration of mutual inductor, size, the number of turn, the coil, whether fill magnetic medium, and the character of magnetic medium decision, and irrelevant with the electric current in the coil.The main cause that mutual induction amount M is difficult to accurately measure is that mutual inductor itself is exactly a undesired signal receiver.When measuring, in order to improve measuring-signal, just need to increase coil turn to improve coefficient of mutual inductance, this also means the enhancing of undesired signal receiving ability simultaneously.This also is one of reason of not making progress in decades of domestic and international measurement of mutual inductance technology.

The method of accurately measuring structure parameter mutual inductance M between the coil system can be divided into two classes.First kind method is " Compbell coil " method.The Compbell coil is by separated by a distance, structure duplicate two coaxial, the single-layer solenoid coil of series connection is formed elementary winding mutually, in the symmetrical plane of winding, it is zero annulus area that a field intensity is arranged, in this annular region, place a several-layer solenoid coil composition secondary winding coaxial, as shown in Figure 1 with elementary winding.The result of Bu Zhiing is that the subtle change relation of the layout of magnetic flux chain and secondary winding of Compbell coil or straight warp is little like this, and its coil constant can be calculated with the highest accuracy.

The accuracy in computation of Compbell coil depends primarily on the processing and the accuracy of measurement of elementary winding, and it is little with the relation of secondary winding, this except because two elementary windings be symmetrical in secondary, also because secondary winding just is in the mutual inductance value place least responsive to the radius of secondary winding.When the axial location of secondary winding and radius respectively have a subtle change dC and dB, the mutual inductance main value M between the primary and secondary winding ₀Be changed to

${\mathrm{dM}}_0=\frac{\&PartialD;M_0}{\&PartialD;B}\mathrm{dB}+\frac{1}{2}[\frac{{\&PartialD;}^2{M}_0}{\&PartialD;C^2}{\mathrm{<figure-callout\; id="2C"\; label="d"\; filenames="HSA00000264330000011.png"\; state="\{\{state\}\}">d</figure-callout>}}^{2}C+\frac{{\&PartialD;}^2{M}_0}{{\&PartialD;B}^2}{\mathrm{<figure-callout\; id="2B"\; label="d"\; filenames="HSA00000264330000011.png"\; state="\{\{state\}\}">d</figure-callout>}}^{2}B]+......\left(1\right)$

If choose the radius B of secondary winding, make

$\frac{{\&PartialD;M}_0}{\&PartialD;B}=0---\left(2\right)$

The variation dC of the axial location of at this moment secondary several-layer solenoid coil and radius and dB are to M ₀Influence only be these variablees second order in a small amount, reduce requirement so greatly to secondary winding processing and accuracy of measurement, especially when secondary winding was the multilayer winding, advantage was just more outstanding.

" Compbell coil " method can be obtained the mutual induction amount under direct current or the low frequency state, and the restriction that is subjected to then is that actual coil has a lot of circles, and the physical dimension that relates to is various, and it is very big accurately to measure difficulty.And computing formula requires infinitely-great space outerpace, also difficult the realization.The basis of calculation mutual inductance that the P.W.HARRISON and G.H.RAYNE of Britain NPL adopted the Compbell coil to produce a 10mH in 1966, the uncertainty of result of calculation is 2 * 10 ^-6

Second class is to adopt " alternating current bridge method ", and mutual induction amount M is traceable to resistance and frequency quantity.Foster bridge, mutual inductance resonance bridge etc. all are the methods that can adopt.This in principle method also can reach very high accuracy, but the result who records is the mutual induction amount under the exchange status, and its value is subjected to the influence of mutual inductor winding inter-turn electric capacity.All use the circuit elements device to realize the right angle characteristic owing to traditional electric bridge in addition, and the imperfection of components and parts has limited the further raising of these scheme accuracy.

Summary of the invention:

The present invention has researched and developed the present invention in order to solve the technical matters that exists in the prior art, belongs to realize the high new method of mutual induction amount vertical gradient uniformly in annulus.The present invention solves in the prior art, and the coil system structure parameter mutual inductance M of design measured in the past, but by what calculate, its typical case's representative is Campbell's coil, and its uncertainty of calculating the back mutual inductance is 2 * 10 ^-6If, adopt the dash current method to measure, uncertainty can only reach 5 * 10 ^-4After adopting loop construction of the present invention, the mutual inductance parameter quite stable that becomes has been eliminated the space electromagnetic interference (EMI) greatly, makes uncertainty of measurement can reach 5 * 10 ^-7

The technical solution adopted in the present invention is,

A kind of mutual inductor measuring system, described system comprises the internal motivation coil, external drive coil and moving coil; Described internal motivation coil comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again, is used to produce uniform radial magnetic field;

Described external drive coil also comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again;

Described internal motivation coil is coaxial to be arranged in the described external drive coil; Described internal motivation coil is coaxial to be arranged in the described external drive coil; Internal motivation coil and external drive coil are by the discrete mutual electric insulation of insulation sleeve, and the material that insulation sleeve adopts is an organic glass.

Described moving coil is movably arranged on described external drive coil middle part, and its distance that moves up and down is controlled in the 2cm scope.

During measurement, described internal motivation coil and external drive coil load same steady current, drive coil has been realized high uniform mutual induction amount vertical gradient in annulus, make that the Lorentz force that the current-carrying moving coil is subjected in this annulus is constant in vertical direction.

In the concrete enforcement, described internal motivation coil is made up of 4 the same coils of size, forward connects for one group in twos, and two groups of coil winding after the series connection are differential concatenation again; Described external drive coil is made up of 4 the same coils of size equally, forward connects for one group in twos, and two groups of coil winding after the series connection are differential concatenation again;

Described measuring system comprises suspension, and described moving coil is arranged on outside the described external drive coil by fixing suspension.

When the spacing R of described internal motivation coil of mutual inductor system and external drive coil and the distance H of external drive coil and moving coil satisfy R ²=4/3H ²Internal motivation coil, external drive coil, moving coil turn ratio satisfied 10000: 2700: 430 o'clock, can form axial length near mutual inductor system symmetrical plane is the toroidal magnetic field homogeneity range of 2cm, has the quadravalence homogeneity in this homogeneity range coil system mutual inductance parameter.

In specific embodiment, described internal motivation internal coil diameter: 60-110mm, external diameter: 200-250mm, the number of turn: 10000;

External drive internal coil diameter: 200-250mm, external diameter: 300-330mm, the number of turn: 2700;

Moving coil internal diameter: 270-300mm, the number of turn: 430.

The present invention is according to the mutual inductor system of building, also researched and developed and in the mutual inductor annulus, realized the high method of mutual induction amount vertical gradient uniformly, promptly in order to realize high mutual induction amount vertical gradient uniformly in the mutual inductor annulus, it is constant in vertical direction to reach the Lorentz force that moving coil is subjected in annulus; Described method comprises the steps:

Step 1 is analyzed the external drive coil, internal motivation coil and moving coil relation;

Step 2 physical model that theorizes: establishing the drive coil system is the endless lead, near the center (x z) locates to put a lead as moving coil again; When adjust between drive coil system and the moving coil spatial relation, be to make up an annular region, in this regional mutual induction amount vertical gradient

Be almost constant; Promptly in the mutual induction amount vertical gradient at initial point place

Will be very insensitive: mutual induction amount vertical gradient in a border circular areas that with the initial point is the center with the subtle change of coordinate

Be almost constant:

z ₀ ²＝3x ₀ ² (16)

Then

$\frac{{\&PartialD;}^{3}M}{{\&PartialD;Z}^3}=0,$ $\frac{{\&PartialD;}^{3}M}{\&PartialD;Z\&PartialD;x^2}=0---\left(17\right)$

Step 3 design actual measurement coil physical parameter:

The relation of the geometric position and the number of turn satisfies between the drive coil group

${\left(\frac{r_3+r_4-r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}{2}\right)}^2=\frac{4}{3}{(h+l)}^2---\left(42\right)$

$\frac{N_1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}=\frac{10000}{2700}---\left(43\right)$

r ₁: the inside radius of internal motivation coil

r ₂: the external radius of internal motivation coil

r ₃: the inside radius of external drive coil

r ₄: the external radius of external drive coil

H: to half of top internal motivation coil axial distance,

L: the axial distance of drive coil winding,

N ₁: the internal motivation coil turn

N ₂: the external drive coil turn

There is an annular space in middle symmetric position in the drive coil group, in moving coil is in homogeneity range, and the mutual inductance vertical gradient between the coil groups

Single order, second order, three order derivative degree for the vertical direction displacement are very little, that is to say mutual induction amount vertical gradient in this annular space

Very even, be constant;

Step 4 is built the mutual inductor measuring system

Described internal motivation coil comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again, is used to produce the radial magnetic field to the top;

Described external drive coil also comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again;

Described internal motivation coil is coaxial to be arranged in the described external drive coil; Described internal motivation coil is coaxial to be arranged in the described external drive coil; Internal motivation coil and external drive coil are by the discrete mutual electric insulation of insulation sleeve, and the material that insulation sleeve adopts is an organic glass.

Described moving coil is movably arranged on described external drive coil middle part, and its distance that moves up and down is controlled in the 2cm scope.

During measurement, described internal motivation coil and external drive coil load same steady current, drive coil has been realized high uniform mutual induction amount vertical gradient in annulus, make that the Lorentz force that the current-carrying moving coil is subjected in this annulus is constant in vertical direction.

When the mutual inductance parameter of measuring between the coil groups, find externally drive coil middle part of moving coil, when its distance that moves up and down is controlled in the 2cm scope, the mutual inductance structure parameter is linear change really, it is 28.32H/m with the rate of change of z axle that first-order linear simulates the mutual inductance structure parameter, and standard deviation is 9.2726E-6.This result's proof is at the magnetic field homogeneity range of design, and the z axial gradient of mutual inductance structure parameter is approximate near constant between coil.

Description of drawings

Fig. 1 is a prior art Compbell coil;

Fig. 2 is mutual inductor of the present invention system;

Fig. 3 designs a model for mutual inductance drive coil of the present invention;

Fig. 4 is the variations of two coil mutual inductance structure parameters with coil-span;

Fig. 4-1 liang of coil mutual inductance structure parameter is with the variation (ρ≤1) of coil-span;

Fig. 4-2 liang of coil mutual inductance structure parameter is with the variation (ρ 〉=1) of coil-span

Fig. 5 is a mutual inductor system simplification synoptic diagram;

Fig. 6 is a mutual inductor system simplification synoptic diagram;

Fig. 7 is an actual mutual inductance drive coil geometric position distribution parameter;

Fig. 8 is a homogeneity range coil system coefficient of mutual inductance change curve;

Fig. 9 changes test curve relatively for the magnetic field of homogeneity range;

Below in conjunction with embodiment each width of cloth accompanying drawing is described.

1 is suspension among Fig. 2, and 2 is drive coil, and 3 is moving coil; 4 are the external drive coil among Fig. 3, and 5 is the internal motivation coil

Embodiment

The mutual inductor system comprises moving coil and fixing drive coil group two parts, sees accompanying drawing 2.Moving coil is a common rotational symmetry multilayer heavy wall coil, hangs over an arm of precision balance by suspension.What need emphasis consideration design is the drive coil group of fixing.This is one group of coaxial heavy wall coil of stationary shaft symmetry, provides uniform radial magnetic field, so that be in the moving coil of radial magnetic field can be subjected to vertical direction behind loading current Lorentz force.

$F=I_1{I}_2\frac{\&PartialD;M}{\&PartialD;z}---\left(3\right)$

The difficult point of coil system design is that the radial magnetic field that will guarantee the moving coil place keeps evenly in vertical direction.Like this, the moving coil that hangs over when measuring on the precision balance just needn't be too strict in the position of vertical direction, just do not change when suffered electromagnetic force can a little not change because of the position of moving coil on the moving coil, destroys the equilibrium state of precision balance.In addition, should guarantee also during design drive coil group that the position of moving coil is stressed when radially changing also remains unchanged substantially, just guarantee between moving coil and the drive coil group mutual inductance structure parameter M (ρ, z) all insensitive to the variation of axial direction and radial direction.Abstract is mathematical concept, just require moving coil axially and variation d ρ radially and dz (ρ is z) in the gradient of vertical direction to mutual inductance M

Influence only be these variable quantities high-order in a small amount.Can accomplish this two requirements, the work that precision balance just can be stable.

When the axial location of moving coil and radial position respectively had a subtle change d ρ and dz, (ρ was z) in the gradient of vertical direction for mutual inductance M

Variable quantity is

$d\left(\frac{\&PartialD;M(\mathrm{\&rho;},z)}{\&PartialD;z}\right)=\frac{{\&PartialD;}^{2}M(\mathrm{\&rho;},z)}{\&PartialD;\mathrm{\&rho;}\&PartialD;z}\mathrm{d\&rho;}+\frac{{\&PartialD;}^{2}M(\mathrm{\&rho;},z)}{{\&PartialD;}^{2}z}\mathrm{dz}+$

$\frac{1}{2!}(\frac{{\&PartialD;}^{3}M(\mathrm{\&rho;},z)}{{\&PartialD;}^2\mathrm{\&rho;}\&PartialD;\mathrm{<figure-callout\; id="2"\; label="z\; d"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">z</figure-callout>}}{d}^{}{}^2\mathrm{\&rho;}+\frac{{\&PartialD;}^{3}M(\mathrm{\&rho;},z)}{{\&PartialD;}^{3}z}{d}^{2}z)+...$

$+\frac{1}{(n-1)!}(\frac{{\&PartialD;}^{n}M(\mathrm{\&rho;},z)}{{\&PartialD;}^{n-1}\mathrm{\&rho;}\&PartialD;z}{d}^{n-1}\mathrm{\&rho;}+\frac{{\&PartialD;}^{n}M(\mathrm{\&rho;},z)}{{\&PartialD;}^{n}z}{d}^{n}z)+R(x,z)$

If the geometric space parameter of reasonable disposition mutual inductor system makes

$\frac{{\&PartialD;}^{2}M(\mathrm{\&rho;},z)}{\&PartialD;\mathrm{\&rho;}\&PartialD;z}=0;$ $\frac{{\&PartialD;}^{2}M(\mathrm{\&rho;},z)}{{\&PartialD;}^{2}z}=0;$ $\frac{{\&PartialD;}^{3}M(\mathrm{\&rho;},z)}{{\&PartialD;}^2\mathrm{\&rho;}\&PartialD;z}=0;$ $\frac{{\&PartialD;}^{3}M(\mathrm{\&rho;},z)}{{\&PartialD;}^{3}z}=0---\left(4\right)$

The axial coordinate position of moving coil and variation d ρ radially so, dz is right Influence only be these variable quantities high-order in a small amount.To lower greatly like this balance suspension and the requirement balance degree of stability, especially working as moving coil is the multilayer winding, when weight was heavier, the mutual inductor system had only and keeps above-mentioned design feature could guarantee that the mutual inductance parameter of different spatial can accurately measure.

Measure the mutual inductance gradient accurately

Need mutual inductance drive coil system to provide in the annular magnetic place, mutual induction amount is linear change with vertical direction in this zone, make when moving coil is in this annulus, the Lorentz force that produces behind the loading current is constant substantially in vertical direction, and makes the suffered Lorentz force of the moving coil that is in this annular space insensitive to the small variations of moving coil geometric position.According to above-mentioned requirements, this patent has designed one group of drive coil group, ingenious arrangement by its locus geometric relationship, can realize above-mentioned needed Distribution of Magnetic Field, the synoptic diagram of mutual inductance drive coil group xsect satisfies R in the distance H of the spacing R that satisfies internal motivation coil and external drive coil and drive coil and moving coil as shown in Figure 3 ²=4/3H ²The proportionate relationship of locus after, the mutual inductance gradient

Has the quadravalence uniformity coefficient in coil groups symcenter position.

The mutual inductance drive coil field system synoptic diagram of reduced graph 3 owing to symmetry, can only be considered the situation of left half-plane earlier.Complex calculation for fear of elliptic integral, make things convenient for mathematical derivation, might as well be at first drive coil and moving coil be assumed to be the straight lead of single turn endless, the straight lead of so-called endless, in fact can regard the part on the very big circular loop as, but other parts in loop are all in far place, and they can be ignored the influence that is studied a question, and simplifying the benefit of handling on the mathematics like this is the analytical expression that obtains the mutual inductance of mutual inductor system easily.Suppose that the drive coil current element is symmetrically distributed, position coordinates is respectively (x ₀, z ₀), (x ₀, z ₀), (x ₀,-z ₀), (x ₀,-z) located.The drive coil current element current density that wherein is in the first quartile and second quadrant is j, is in the 3rd limit and four-quadrant drive coil current element electric current to be-j.

Consider such two-dimensional ideal situation, the mutual inductance drive coil system physical model of simplifying just becomes four endless leads perpendicular to paper, hypothesis is at (the x near the center now, z) locate to put again a lead as moving coil, obtain four current carrying conductors to (x, z) the mutual inductance summation of locating the lead that newly adds is:

$M=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\ln \frac{\sqrt{{(z_0-z)}^2+{(x_0-x)}^2}\sqrt{{(z_0-z)}^2+{(x_0+x)}^2}}{\sqrt{{(z_0+z)}^2+{(x_0-x)}^2}\sqrt{{(z_0+z)}^2+{(x_0+x)}^2}}---\left(5\right)$

Consider of the variation of mutual inductance structure parameter at the z axle

$\frac{\&PartialD;M}{\&PartialD;z}=\frac{u_0}{2\mathrm{\&pi;}}\left\{\begin{array}{c}-\frac{z_0-z}{{(z_0-z)}^2+{(x_0-x)}^2}-\frac{z_0-z}{{(z_0-z)}^2+{(x_0+x)}^2}\\ -\frac{z_0+z}{{(z_0+z)}^2+{(x_0-x)}^2}-\frac{z_0+z}{{(z_0+z)}^2+{(x_0+x)}^2}\end{array}\right\}---\left(6\right)$

Gradient with mutual inductance z axle Locate to carry out Taylor series expansion in (0,0)

$\frac{\&PartialD;M(x,z)}{\&PartialD;z}=\frac{\&PartialD;M\left(\mathrm{0,0}\right)}{\&PartialD;z}+\frac{{\&PartialD;}^{2}M\left(\mathrm{0,0}\right)}{\&PartialD;z\&PartialD;x}\frac{{\&PartialD;}^{2}M\left(\mathrm{0,0}\right)}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">z</figure-callout>}}^2}\mathrm{xz}+\frac{1}{2!}\frac{{\&PartialD;}^{3}M\left(\mathrm{0,0}\right)}{\&PartialD;z\&PartialD;x^2}\frac{{\&PartialD;}^{3}M\left(\mathrm{0,0}\right)}{\&PartialD;z^3}{x}^2{z}^2---\left(7\right)$

$+...+\frac{1}{n!}\frac{{\&PartialD;}^{n}M\left(\mathrm{0,0}\right)}{\&PartialD;z\&PartialD;x^{n-1}}\frac{{\&PartialD;}^{n}M\left(\mathrm{0,0}\right)}{{\&PartialD;z}^n}{x}^{n-1}{z}^{n-1}+R(x,z)$

Wherein

$\frac{{\&PartialD;}^{2}M}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">z</figure-callout>}}^2}=\frac{u_0}{2\mathrm{\&pi;}}\left\{\begin{array}{c}-\frac{{(z_0-z)}^2-{(x_0-x)}^2}{{[{(z_0-z)}^2+{(x_0-x)}^2]}^2}-\frac{{(z_0-z)}^2-{(x_0+x)}^2}{{[{(z_0-z)}^2+{(x_0+x)}^2]}^2}\\ +\frac{{(z_0+z)}^2-{(x_0-x)}^2}{{[{(z_0+z)}^2+{(x_0-x)}^2]}^2}+\frac{{(z_0+z)}^2-{(x_0+x)}^2}{{[{(z_0+z)}^2+{(x_0+x)}^2]}^2}\end{array}\right\}---\left(8\right)$

$\frac{{\&PartialD;}^{2}M}{\&PartialD;z\&PartialD;x}=\frac{u_0}{\mathrm{\&pi;}}\left\{\begin{array}{c}-\frac{-(z_0-z)\&CenterDot;\left(x_0-x\right)}{{[{(z_0-z)}^2+{(x_0-x)}^2]}^2}-\frac{(z_0-z)\&CenterDot;(x_0+x)}{{[{(z_0-z)}^2+{(x_0+x)}^2]}^2}\\ -\frac{(z_0+z)\&CenterDot;(x_0-x)}{{[{(z_0+z)}^2+{(x_0-x)}^2]}^2}+\frac{(z_0+z)\&CenterDot;(x_0+x)}{{[{(z_0+z)}^2+{(x_0+x)}^2]}^2}\end{array}\right\}---\left(9\right)$

$\frac{{\&PartialD;}^{3}M}{\&PartialD;z{\&PartialD;x}^2}=-\frac{u_0}{\mathrm{\&pi;}}\left\{\begin{array}{c}\frac{(z_0-z)[{(z_0-z)}^2-{3(x_0-x)}^2]}{{[{(z_0-z)}^2+{(x_0-x)}^2]}^3}+\frac{(z_0-z){[(z_0-z)}^2-{3(x_0+x)}^2]}{{[{(z_0-z)}^2+{(x_0+x)}^2]}^3}+\\ \frac{(z_0+z)[{(z_0+z)}^2-3{(x_0-x)}^2]}{{[{(z_0+z)}^2+{(x_0-x)}^2]}^3}+\frac{(z_0+z)[{(z_0+z)}^2-{3(x_0+x)}^2]}{{[{(z_0+z)}^2+{(x_0+x)}^2]}^3}\end{array}\right\}---\left(10\right)$

$\frac{{\&PartialD;}^{3}M}{{\&PartialD;x}^3}=-\frac{u_0}{\mathrm{\&pi;}}\left\{\begin{array}{c}\frac{(z_0-z)[{(z_0-z)}^2-{3(x_0-x)}^2]}{{[{(z_0-z)}^2+{(x_0-x)}^2]}^3}+\frac{(z_0-z){[(z_0-z)}^2-{3(x_0+x)}^2]}{{[{(z_0-z)}^2+{(x_0+x)}^2]}^3}+\\ \frac{(z_0+z)[{(z_0+z)}^2-3{(x_0-x)}^2]}{{[{(z_0+z)}^2+{(x_0-x)}^2]}^3}+\frac{(z_0+z)[{(z_0+z)}^2-{3(x_0+x)}^2]}{{[{(z_0+z)}^2+{(x_0+x)}^2]}^3}\end{array}\right\}---\left(11\right)$

In true origin, i.e. z=0, the situation at x=0 place, as can be known:

$M=\frac{{\&PartialD;}^{2}M}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">z</figure-callout>}}^2}=\frac{{\&PartialD;}^{2}M}{\&PartialD;z\&PartialD;x}=0---\left(12\right)$

In view of the symmetry that current carrying conductor is arranged, perseverance has on the x axle

Therefore on whole x axle M and M inevitable to the all-order derivative of x all be zero.Simultaneously, because symmetry, M is an even function for the z coordinate, thus on whole x axle M to each rank even derivative of z,

$\frac{{\&PartialD;}^{2}M}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">z</figure-callout>}}^2}{|}_{z=0}\&equiv;0,$ $\frac{{\&PartialD;}^{4}M}{\&PartialD;{\mathrm{<figure-callout\; id="4"\; label="z"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">z</figure-callout>}}^4}{|}_{z=0}\&equiv;0,$ $......,\frac{{\&PartialD;}^{2n}M}{\&PartialD;z^{2n}}{|}_{z=0}\&equiv;0---\left(13\right)$

But

$\frac{{\&PartialD;}^{3}M}{\&PartialD;Z^3}=-\frac{4u_0}{\mathrm{\&pi;}}\frac{z_0({z_0}^2-3{x_0}^2)}{{({z_0}^2+{x_0}^2)}^3}\&NotEqual;0---\left(14\right)$

$\frac{{\&PartialD;}^{3}M}{\&PartialD;{z\&PartialD;x}^2}=-\frac{4u_0}{\mathrm{\&pi;}}\frac{z_0({z_0}^2-3{x_0}^2)}{{({z_0}^2+{x_0}^2)}^3}\&NotEqual;0---\left(15\right)$

If satisfy

z ₀ ²＝3x ₀ ² (16)

Then

$\frac{{\&PartialD;}^{3}M}{{\&PartialD;Z}^3}=0,$ $\frac{{\&PartialD;}^{3}M}{{\&PartialD;Z\&PartialD;x}^2}=0---\left(17\right)$

From top as can be seen various, at the initial point place, i.e. z=0, x=0,

Near initial point, do not change among a small circle, have only with the single order of x

Second derivative to z

Second derivative to x

And it is non-vanishing.If but suitable the distance between the drive coil according to (16) formula arrangement, just can make the initial point place

Also be zero.Like this, mutual induction amount vertical gradient

Single order and second derivative at the initial point place all are zero.Consider also initial point as can be known from symmetry

Also be zero.According to mutual inductance z axial gradient

The taylor series expansion of locating in (0,0) just can obtain following conclusion, the mutual induction amount vertical gradient at the initial point place

Will be very insensitive to the subtle change of coordinate.The axial coordinate position of moving coil and variation d ρ radially in a border circular areas that with the initial point is the center, dz is right

Influence only be these variable quantities high-order in a small amount.

Although the derivation of the geometry site of top relevant mutual inductance drive coil system is owing to approximate reason, in mathematical derivation is undemanding, if but proved really adjust between drive coil system and the moving coil spatial relation, be to make up an annular region, in this regional mutual induction amount vertical gradient

Be almost constant.Promptly just can obtain conclusion like this, mutual induction amount vertical gradient at the initial point place

Will be very insensitive with the subtle change of coordinate.Mutual induction amount vertical gradient in a border circular areas that with the initial point is the center Be almost constant.(16) formula is exactly a main innovate point of the present invention.

Above-mentioned only is a kind of ideal situation.The difference of actual conditions and ideal situation mainly contains 2 points.At first, actual coil diameter is limited, can not be infinitely great.Simultaneously, lead can not be unlimited thin yet, is not a circle but multiturn toward contact.Consider that actual coil is the limited circular coil of diameter.The radius of supposing two circular coils is respectively R ₁And R ₂, coil plane is parallel to each other and perpendicular to the axis that connects two coil centers of circle, the distance between the coil plane is h, and then the mutual induction amount M between these two coils is

$M_l=u_0\sqrt{R_1{R}_2}[(\frac{2}{k}-k)K\left(k\right)-\frac{2}{k}E\left(k\right)]=u_0\sqrt{R_1{R}_2}f\left(k\right)---\left(18\right)$

In order to investigate the dependence of coefficient of mutual inductance and physical dimension between the coaxial circle coil, for the design of drive coil and moving coil radial dimension provides reference, seek drive coil and moving coil radial dimension optimal proportion, make moving coil mobile phase same distance, mutual inductance structure parameter between the coil groups can reach maximum variable quantity, need change the coil mutual inductance under the different radial dimensions ratios to analyze.For convenience relatively, can do dimensionless to formula (18) and handle, suppose

M ₀＝u ₀R ₂ (19)

Then

$M_l=M_0\sqrt{\frac{R_1}{R_2}}[(\frac{2}{k}-k)K\left(k\right)-\frac{2}{k}E\left(k\right)]---\left(20\right)$

Radius ratio r=R when two coils ₁/ R ₂Be respectively 0.1,0.3,0.5,0.7,0.9,0.95,1.0,2.0,3.0,4.0,5.0 o'clock, can be depicted under these physical dimensions with Origin 7.0, the mutual inductance structure parameter is with the variation of two coil distance h, as shown in Figure 4.As can be seen from Figure 4, if two circular coils distance is very near, it is more little that coil radius differs, and coefficient of mutual inductance is big more; If two circular coils distance is far away, as long as surpass R ₂/ 2 distance is owing to the difference of two circular coil radiuses causes that the variation of coefficient of mutual inductance has not been too obvious.Therefore when the mutual inductor system design, the radial dimension of moving coil should be as far as possible near the radial dimension of drive coil.

Consider that then the mutual inductor system is a multiturn coil, coil has certain sectional area, can adopt equivalent circular ring coil method that its mutual inductance is analyzed.Coil is divided into fine rule loop, n unit, and when n was tending towards infinity, the mutual inductance between two coils can be expressed as

$M=\frac{1}{I_1{I}_2}{\&Integral;}_{S_2}d{I}_2{\&Integral;}_{S_1}{M}_{l}d{I}_1---\left(21\right)$

According to the spatial symmetry of mutual inductor system, can analyze the mutual inductance parameter between one of them drive coil and moving coil earlier, the mutual inductance parameter of whole winding can obtain by superposition principle.If drive coil and moving coil have N respectively ₁And N ₂The circle coil, the cross section is respectively S ₁And S ₂, the mutual inductance structure parameter between them then

$M=\frac{N_1{N}_2}{S_1{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">S</figure-callout>}}_2}{\&Integral;}_{S_2}\mathrm{<figure-callout\; id="2"\; label="d\; S"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">d</figure-callout>}{S_{}}^{}{{}_2}^{\&prime;}{\&Integral;}_{S_1}{M}_{\mathrm{<figure-callout\; id="1"\; label="l\; d\; S"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">l</figure-callout>}}d{S_{}}^{}{{}_1}^{\&prime;}---\left(22\right)$

To integral domain S ₁And S ₂Adopt the approximate formula of double integral

$M=N_1{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{\mathrm{\&omega;}}_j{M}_{\mathrm{ij}}---\left(23\right)$

The geometric relationship analytical expression that need satisfy with the variation derivation toroidal magnetic field homogeneous area of spacing h with the mutual inductance parameter between a pair of drive coil and moving coil.When drive coil group 1 and moving coil 3 about magnetic field symcenter plane symmetry, and when moving coil was in the symcenter plane of field system, as shown in Figure 5, the mutual inductance expression formula between drive coil group 1 and the moving coil 3 was

${\mathrm{<figure-callout\; id="13"\; label="M"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">M</figure-callout>}}_{13}=u_0{N}_1{N}_2\sqrt{R_1{R}_2}[(\frac{2}{k}-k)K\left(k\right)-\frac{2}{k}E\left(k\right)]---\left(24\right)$

Mutual inductance expression formula between drive coil group 2 and the moving coil 3 is

$M_{23}=u_0{N}_1{N}_2\sqrt{R_1{R}_2}[(\frac{2}{k}-k)K\left(k\right)-\frac{2}{k}E\left(k\right)]---\left(25\right)$

The exciting current direction of considering the drive coil group is opposite, the mutual inductance expression formula between whole drive coil group and the moving coil

M _12-3＝M ₁₃-M ₂₃＝0 (26)

When moving coil moves to h at the magnetic field homogeneity range ₀, the mutual inductance expression formula between drive coil group 1 and the moving coil 3 is

${\mathrm{<figure-callout\; id="13"\; label="M"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">M</figure-callout>}}_{13}=u_0{N}_1{N}_2\sqrt{R_1{R}_2}[(\frac{2}{k_{13}}-k_{13})K\left(k_{13}\right)-\frac{2}{k_{13}}E\left(k_{13}\right)]---\left(27\right)$

Wherein

${\mathrm{<figure-callout\; id="13"\; label="k"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">k</figure-callout>}}_{13}=\frac{2\sqrt{R_1{R}_2}}{\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+R_2)}^2+{(h-h_0)}^2}}---\left(28\right)$

Mutual inductance expression formula between drive coil group 2 and the moving coil 3 is

$M_{23}=u_0{N}_1{N}_2\sqrt{R_1{R}_2}[(\frac{2}{k_{23}}-k_{23})K\left(k_{23}\right)-\frac{2}{k_{23}}E\left(k_{23}\right)]---\left(29\right)$

Wherein

$k_{23}=\frac{2\sqrt{R_1{R}_2}}{\sqrt{{({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+R_2)}^2+{(h+h_0)}^2}}---\left(30\right)$

Mutual inductance expression formula between whole drive coil group and the moving coil

$M_{12-3}=u_0\sqrt{R_1{R}_2}[(\frac{2}{k_{13}}-k_{13})K\left(k_{13}\right)-\frac{2}{k_{13}}E\left(k_{13}\right)-(\frac{2}{k_{23}}-k_{23})K\left(k_{23}\right)+\frac{2}{k_{23}}E\left(k_{23}\right)]---\left(31\right)$

Consider that following formula to the sensitivity that spacing h changes, in fact can regard the variable quantity of the coefficient of mutual inductance mutual inductance under the disturbance of Δ h between drive coil and moving coil as, therefore can come approximate solution for the pluriderivative of spacing h by finding the solution coefficient of mutual inductance.

Consider

$\frac{\mathrm{df}\left(k\right)}{\mathrm{dh}}=\frac{\mathrm{df}\left(k\right)}{\mathrm{dk}}\frac{\mathrm{dk}}{\mathrm{dh}}=\frac{1}{k^2}[-2K\left(k\right)+\frac{2-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{1-k^2}E\left(k\right)]\frac{\mathrm{dk}}{\mathrm{dh}}---\left(32\right)$

$=\frac{h}{[{({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+R_2)}^2+h^2]k}[2K\left(k\right)-\frac{2-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{1-k^2}E\left(k\right)]$

$\frac{\mathrm{dE}\left(k\right)}{\mathrm{dh}}=\frac{\mathrm{dE}\left(k\right)}{\mathrm{dk}}\frac{\mathrm{dk}}{\mathrm{dh}}=[K\left(k\right)-E\left(k\right)]\frac{h}{{({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+R_2)}^2+h^2}---\left(33\right)$

$\frac{\mathrm{dk}}{\mathrm{dh}}=-\frac{\mathrm{kh}}{{({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+R_2)}^2+h^2}---\left(34\right)$

$\frac{\&PartialD;M}{\&PartialD;h}=-u_0{N}_1{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_2\frac{\mathrm{hk}}{A}[-G\left(k\right)+\mathrm{DE}\left(k\right)]---\left(35\right)$

$\frac{\mathrm{dK}\left(k\right)}{\mathrm{dh}}=(\frac{E\left(k\right)}{k(1-k^2)}-\frac{K\left(k\right)}{k})\frac{\mathrm{dk}}{\mathrm{dh}}=\frac{h[E\left(k\right)-K\left(k\right)(1-k^2)]}{(k^2-1)[{({\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000264330000022.png,HSA00000264330000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_1+R_2)}^2+h^2]}---\left(36\right)$

In like manner can get

$\frac{{\&PartialD;}^{2}M}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}==\frac{u_0{w}_1{\mathrm{<figure-callout\; id="2C"\; label="w"\; filenames="HSA00000264330000011.png"\; state="\{\{state\}\}">w</figure-callout>}}_2}{C^3}[(B-{\mathrm{Dh}}^2)G\left(k\right)+(4{\mathrm{Dh}}^2-B)\mathrm{DE}\left(k\right)]---\left(37\right)$

$\frac{{\&PartialD;}^{3}M}{\&PartialD;h^3}=-u_0{N}_1{N}_2\frac{h}{C^5}\left\{\right[(3+D)B+2D{C}^2-D{h}^2(3+4D+\frac{4D}{k^2})]G\left(k\right)$

$+(10{\mathrm{Dh}}^2-B-8D{C}^2-\frac{4\mathrm{<figure-callout\; id="2"\; label="DB\; k"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">DB</figure-callout>}}{k^{}}+\frac{32D^2{h}^2}{k^2})\mathrm{DE}\left(k\right)\}---\left(38\right)$

Wherein

B＝(R ₁+R ₂) ²，

G(k)＝K(k)-E(k)

According to a certain position h of homogeneity range ₀The Taylor expansion of coefficient of mutual inductance

$M\left(h\right)=M\left(h_0\right)+\frac{\mathrm{dM}\left(0\right)}{\mathrm{dh}}(h-h_0)+\frac{1}{2!}\frac{d^{2}M\left(0\right)}{d{h}^2}{(h-h_0)}^2+...$

$+\frac{1}{n!}\frac{d^{n}M\left(0\right)}{d{h}^n}{(h-h_0)}^n+R\left(h\right)---\left(40\right)$

The condition that mutual inductor system magnetic field homogeneity range must satisfy is

$\frac{\&PartialD;M}{\&PartialD;h}=\frac{(h-h_0)k_{13}}{A}[-G\left(k_{13}\right)+D_{13}E\left(k_{13}\right)]-\frac{(h+h_0)k_{23}}{A}[-G\left(k_{23}\right)+D_{23}E\left(k_{23}\right)]\&ap;0$

$\frac{{\&PartialD;}^{2}M}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}=\frac{1}{{{\mathrm{<figure-callout\; id="13"\; label="C"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">C</figure-callout>}}_{13}}^3}[(B-D_{13}{(h-h_0)}^2)G\left(k_{13}\right)+(4D_{13}{(h-h_0)}^2-B)D_{13}E\left(k_{13}\right)]$

$-\frac{1}{{C_{23}}^3}[(B-D_{23}{(h+h_0)}^2)G\left(k_{23}\right)+(4D_{23}{(h+h_0)}^2-B)D_{23}E\left(k_{23}\right)]$

$\&ap;0$

$\frac{{\&PartialD;}^{3}M}{{\&PartialD;h}^3}=\frac{(h-h_0)}{{{\mathrm{<figure-callout\; id="13"\; label="C"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">C</figure-callout>}}_{13}}^5}\left\{\right[(3+D_{13})B+2D_{13}{{\mathrm{<figure-callout\; id="13"\; label="C"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">C</figure-callout>}}_{13}}^2-D_{13}{(h-h_0)}^2(3+4{\mathrm{<figure-callout\; id="13"\; label="D"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">D</figure-callout>}}_{13}+\frac{4D_{13}}{{{\mathrm{<figure-callout\; id="13"\; label="k"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">k</figure-callout>}}_{13}}^2})]G\left(k_{13}\right)$

$+(10D_{13}{(h-h_0)}^2-B-8D_{13}{{\mathrm{<figure-callout\; id="13"\; label="C"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">C</figure-callout>}}_{13}}^2-\frac{4D_{13}\mathrm{<figure-callout\; id="13"\; label="B\; k"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">B</figure-callout>}}{{k_{}}^{}}+\frac{32{{\mathrm{<figure-callout\; id="13"\; label="D"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">D</figure-callout>}}_{13}}^2{(h-h_0)}^2}{{{\mathrm{<figure-callout\; id="13"\; label="k"\; filenames="HSA00000264330000041.png"\; state="\{\{state\}\}">k</figure-callout>}}_{13}}^2})D_{13}E\left(k_{13}\right)\}$

$-\frac{(h+h_0)}{{C_{23}}^5}\left\{\right[(3+D_{23})B+2D_{23}{C_{23}}^2-D_{23}{(h+h_0)}^2(3+4D_{23}+\frac{4D_{23}}{{k_{23}}^2})]G\left(k_{23}\right)$

$+(10D_{23}{(h+h_0)}^2-B-8D_{23}{C_{23}}^2-\frac{4D_{23}B}{{k_{23}}^2}+\frac{32{D_{23}}^2{(h+h_0)}^2}{{k_{23}}^2})D_{23}E\left(k_{23}\right)\}$

$\&ap;0---\left(41\right)$

The calculating of above-mentioned condition can be adopted LabVIEW language compilation computer program, seeks the magnetic field homogeneity range that satisfies above-mentioned condition by method of interpolation.By computer solving, can find to work as the size of drive coil and arrange that as shown in Figure 6, wherein the relation of the geometric position and the number of turn satisfies between the drive coil group

${\left(\frac{r_3+r_4-r_1-{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}{2}\right)}^2=\frac{4}{3}{(h+l)}^2---\left(42\right)$

$\frac{N_1}{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000264330000012.png,HSA00000264330000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_2}=\frac{10000}{2700}---\left(43\right)$

There is an annular space really in middle symmetric position in the drive coil group, in moving coil is in homogeneity range, and the mutual inductance vertical gradient between the coil groups Single order, second order, three order derivative degree for the vertical direction displacement are very little, that is to say mutual induction amount vertical gradient in this annular space

Very even, be almost constant.

According to summary of the invention, the patent applicant has built actual mutual inductor system, and wherein the geometric parameter of the drive coil situation of twining according to ideal is set to: internal layer drive coil number of turn n=10000 circle, and mean radius is 62.5mm; Outside drive coil number of turn n=2700 circle, mean radius is 140mm.According to actual mutual inductance drive coil geometric position distribution parameter shown in Figure 7, physical dimension satisfies homogeneity range computing formula (42), (43) between the drive coil system, measure the coil system coefficient of mutual inductance at homogeneity range and change as shown in Figure 8, the magnetic field of homogeneity range changes as shown in Figure 9 relatively.

From the coefficient of mutual inductance of homogeneity range coil system shown in the accompanying drawing 8 measurement result, find externally drive coil middle part of moving coil, when its distance that moves up and down is controlled in the 2cm scope, the mutual inductance structure parameter is linear change really, it is 28.32H/m with the rate of change of z axle that first-order linear simulates the mutual inductance structure parameter, and standard deviation is 9.2726E-6.This result's proof is at the magnetic field homogeneity range of design, and the z axial gradient of mutual inductance structure parameter is approximate near constant between coil.

From the relative change curve of the magnetic induction density of magnetic field homogeneity range shown in the accompanying drawing 9, magnetic field homogeneity range and theoretical analysis basically identical, at the magnetic field homogeneity range, the maximal phase in magnetic field exists some asymmetric to changing 0.5 ‰ slightly.Analyze reason, should be that drive coil is in assembling process, because the coaxiality of whole winding group is to rely on insulation sleeve to guarantee, coil is because deadweight exists stress deformation, therefore the drive coil winding coaxiality on the deviation theory to a certain extent influences the symmetry of magnetic field homogeneity range axial magnetic induction to a certain extent.

Technique scheme is one embodiment of the present invention, for those skilled in the art, on the basis that the invention discloses application process and principle, be easy to make various types of improvement or distortion, and be not limited only to the described method of the above-mentioned embodiment of the present invention, therefore previously described mode is a specific embodiment, and does not have restrictive meaning.

Claims (6)

1. mutual inductor measuring system, described system comprises the internal motivation coil, external drive coil and moving coil; It is characterized in that,

Described internal motivation coil comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again, is used to produce uniform radial magnetic field;

Described external drive coil also comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again;

Described internal motivation coil is coaxial to be arranged in the described external drive coil; Described internal motivation coil and external drive coil are by the discrete mutual electric insulation of insulation sleeve, and the material that insulation sleeve adopts is an organic glass;

Described moving coil is movably arranged on described external drive coil middle part, and its distance that moves up and down is controlled in the 2cm scope;

During measurement, described internal motivation coil and external drive coil load same steady current, drive coil has been realized high uniform mutual induction amount vertical gradient in annulus, make that the Lorentz force that the current-carrying moving coil is subjected in this annulus is constant in vertical direction.

2. a kind of mutual inductor measuring system according to claim 1 is characterized in that,

Described internal motivation coil is made up of 4 the same coils of size, forward connects for one group in twos, and two groups of coil winding after the series connection are differential concatenation again; Described external drive coil is made up of 4 the same coils of size equally, forward connects for one group in twos, and two groups of coil winding after the series connection are differential concatenation again;

Described measuring system comprises suspension, and described moving coil is arranged on outside the described external drive coil by fixing suspension.

3. a kind of mutual inductor measuring system according to claim 1 and 2 is characterized in that,

When the spacing R of described internal motivation coil of mutual inductor system and external drive coil and the distance H of external drive coil and moving coil satisfy R ²=4/3 H ²Internal motivation coil, external drive coil, moving coil turn ratio satisfied 10000: 2700: 430 o'clock, can form axial length near mutual inductor system symmetrical plane is the toroidal magnetic field homogeneity range of 2cm, has the quadravalence homogeneity in this homogeneity range coil system mutual inductance parameter.

4. a kind of mutual inductor measuring system according to claim 1 and 2 is characterized in that,

Described internal motivation internal coil diameter: 60-110mm, external diameter: 200-250mm, the number of turn: 10000; External drive internal coil diameter: 200-250mm, external diameter: 300-330mm, the number of turn: 2700; Moving coil internal diameter: 270-300mm, the number of turn: 430.

5. adopt the system of one of claim 1-4, in the mutual inductor annulus, realize the high method of mutual induction amount vertical gradient uniformly, it is characterized in that: in order to realize high mutual induction amount vertical gradient uniformly in the mutual inductor annulus, it is constant in vertical direction to reach the Lorentz force that moving coil is subjected in annulus; Described method comprises the steps:

Step 1 is analyzed the external drive coil, internal motivation coil and moving coil relation;

Step 2 physical model that theorizes: establishing the drive coil system is the endless lead, near the center (x z) locates to put a lead as moving coil again; When adjust between drive coil system and the moving coil spatial relation, be to make up an annular region, in this regional mutual induction amount vertical gradient Be almost constant; Promptly in the mutual induction amount vertical gradient at initial point place

Will be very insensitive: mutual induction amount vertical gradient in a border circular areas that with the initial point is the center with the subtle change of coordinate Be almost constant:

z ₀ ²＝3x ₀ ² (16)

Then

$\frac{{\&PartialD;}^{3}M}{{\&PartialD;Z}^3}=0,$ $\frac{{\&PartialD;}^{3}M}{\&PartialD;Z\&PartialD;x^2}=0---\left(17\right)$

Step 3 design actual measurement coil physical parameter:

The relation of the geometric position and the number of turn satisfies between the drive coil group

${\left(\frac{r_3+r_4-r_1-r_2}{2}\right)}^2=\frac{4}{3}{(h+l)}^2---\left(42\right)$

$\frac{N_1}{N_2}=\frac{10000}{2700}---\left(43\right)$

Wherein, r ₁: the inside radius of internal motivation coil; r ₂: the external radius r of internal motivation coil ₃: the inside radius of external drive coil; r ₄: the external radius h of external drive coil: to half of top internal motivation coil axial distance; L: the axial distance of drive coil winding, N ₁: the internal motivation coil turn; N ₂: the external drive coil turn;

There is an annular space in middle symmetric position in the drive coil group, in moving coil is in homogeneity range, and the mutual inductance vertical gradient between the coil groups

Single order, second order, three order derivative degree for the vertical direction displacement are very little, that is to say mutual induction amount vertical gradient in this annular space

Very even, be constant;

Step 4 is built the mutual inductor measuring system

Described internal motivation coil comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again, is used to produce the radial magnetic field to the top;

Described external drive coil also comprises one group of coil, forward connects for one group in twos, and the coil winding after the series connection is differential concatenation again;

Described internal motivation coil is coaxial to be arranged in the described external drive coil; Described internal motivation coil is coaxial to be arranged in the described external drive coil; Internal motivation coil and external drive coil are by the discrete mutual electric insulation of insulation sleeve, and the material that insulation sleeve adopts is an organic glass;

Described moving coil is movably arranged on described external drive coil middle part, and its distance that moves up and down is controlled in the 2cm scope;

During measurement, described internal motivation coil and external drive coil load same steady current, drive coil has been realized high uniform mutual induction amount vertical gradient in annulus, make that the Lorentz force that the current-carrying moving coil is subjected in this annulus is constant in vertical direction.

6. method as claimed in claim 5 is characterized in that:

When the spacing R of described internal motivation coil of mutual inductor system and external drive coil and the distance H of external drive coil and moving coil satisfy R ²=4/3H ²Internal motivation coil, external drive coil, moving coil turn ratio satisfied 10000: 2700: 430 o'clock, can form axial length near mutual inductor system symmetrical plane is the toroidal magnetic field homogeneity range of 2cm, has the quadravalence homogeneity in this homogeneity range coil system mutual inductance parameter.

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