CN113251911A - Non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection - Google Patents

Non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection Download PDF

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CN113251911A
CN113251911A CN202110485736.2A CN202110485736A CN113251911A CN 113251911 A CN113251911 A CN 113251911A CN 202110485736 A CN202110485736 A CN 202110485736A CN 113251911 A CN113251911 A CN 113251911A
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coil
metal conductor
spherical metal
eddy current
impedance
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CN113251911B (en
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金仲文
秦刚华
郑渭建
熊磊
李炳辰
许云良
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Zhejiang Zheneng Digital Technology Co Ltd
Zhejiang Energy Group Research Institute Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/02—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring length, width or thickness
    • G01B7/06—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring length, width or thickness for measuring thickness
    • G01B7/10—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring length, width or thickness for measuring thickness using magnetic means, e.g. by measuring change of reluctance
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/12—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring diameters
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
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Abstract

The invention relates to a non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection, which comprises the following steps: connecting an output port of an impedance analyzer to two ends of the excitation coil, and connecting a receiving port of the impedance analyzer to two ends of the receiving coil; an output port of the impedance analyzer generates alternating current, a digital synthesis module of an FPGA module in the impedance analyzer generates an excitation signal, and an excitation source of an electromagnetic eddy current signal is provided for the excitation coil. The invention has the beneficial effects that: the invention utilizes the skin effect that electromagnetic eddy current signals are only transmitted on the near surface of the pipe wall, combines the single-frequency electromagnetic eddy current detection technology to inhibit the nonlinear change caused by the lift-off effect, and realizes the high-precision and high-performance related parameter detection of the spherical metal conductor in the industry, such as the detection of the thickness of the plane of the metal conductor. The invention is mainly suitable for spherical metal parts which have high precision requirements and need to be subjected to nondestructive testing.

Description

Non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection
Technical Field
The invention belongs to the technical field of non-contact size measurement by using electromagnetic eddy current, and particularly relates to a non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection.
Background
Spherical metal conductors are widely used in industrial production processes, metal spheres can be used as bearings for robots, airplanes, automobiles and medical cuttings, and can also be used as transport containers or storage containers for gas and oil, and hollow metal sphere shells play an important role in shielding electromagnetic interference. The safety of such metal spheres is determined in large part by the size of the sphere and the integrity of the surface, and therefore there is a need in the industry for a non-destructive, non-contact metal sphere sizing technique.
Most of the existing metal sphere size measurement technologies realize non-contact measurement of the radius of a metal sphere based on optical methods such as optical path layout or Fizeau interference, and the existing metal sphere size measurement technologies are high in cost of test tools, can only detect the radius after a spherical contour is calculated, and cannot detect parameter information such as the wall thickness of a spherical element and the thickness, the conductivity and the magnetic conductivity of the surface layer of the metal sphere. The method has high limitation in industrial application, and the test environment is harsh, so that the wide test is difficult to realize.
The electromagnetic eddy current detection has high sensitivity and wide adaptability to a test object, can maintain the characteristics of high precision and low response time delay while detecting the conductivity and the magnetic conductivity of a material and evaluating the thickness of a metal shell, can be used for detecting the integrity of a spherical surface and the radius of a sample, and can meet the test requirement on a spherical metal conductor in industrial production. Therefore, it is very important to provide a non-contact spherical metal conductor characteristic parameter measurement method based on electromagnetic eddy current detection.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection.
The non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection comprises the following steps:
step 1, connecting an output port (current port) of an impedance analyzer to two ends of an excitation coil, and connecting a receiving port (sampling port) of the impedance analyzer to two ends of a receiving coil;
step 2, an output port of the impedance analyzer generates alternating current, a digital synthesis module (DDS) of an FPGA module in the impedance analyzer generates an excitation signal, and an excitation source of an electromagnetic eddy current signal is provided for an excitation coil; the excitation coil generates various electromagnetic eddy current signals, and the electromagnetic eddy current signals are transmitted to the receiving coil through the surface of the spherical metal conductor of the sample to be detected and are used for detecting the integrity of the metal spherical surface; the receiving coil receives electromagnetic eddy current signals generated by the exciting coil on the surface of the spherical metal conductor of the sample to be detected and generated variable impedance, and monitors mutation signals when the electromagnetic eddy current signals are mutated in real time; a receiving port of the impedance analyzer collects receiving signals of a receiving coil under the control of the FPGA module, the collected signals are fed back to an analog-to-digital converter circuit (ADC), and the ADC circuit converts analog voltage signals into digital signals; the FPGA module demodulates the received digital signals through a digital I/Q demodulator, and the FPGA module exports effective data to a data processing terminal for data operation and analysis;
step 3, after obtaining the variable impedance delta Z generated by the electromagnetic eddy current signal in the step 2, finding the minimum value of the imaginary part of the impedance along with the variation of the excitation frequency according to the ratio relation between the variation of the impedance and the excitation frequency, and accurately obtaining a peak value frequency value:
[a，f]＝min(imag((ΔZ/jω)))
in the above formula, f is the peak frequency, a is the minimum value of the imaginary part of the impedance generated under the peak frequency f, imag () is an imaginary part formula, Δ Z is the varying impedance generated by the electromagnetic eddy current signal, j is an imaginary unit, and ω is the excitation angular frequency;
and 4, fitting a graph equation and deriving through the negative correlation linear relation between the peak frequency value obtained in the step 3 and the lift-off distance, finding that the slope characteristic presents different characteristics for spherical metal conductors with different radiuses, materials and surface thicknesses, and obtaining the radius, the material characteristic and the thickness information of the metal shell of the spherical metal conductor of the sample to be detected through slope information in a pre-stored database.
Preferably, step 2 specifically comprises the following steps:
2.1, the data processing terminal receives data from the impedance analyzer and reads the corrected sampling data; the corrected sampled data includes the receive coil impedance Z; by self-impedance Z of the receiving coil0Adding the variable impedance delta Z generated by the electromagnetic eddy current signal to obtain the impedance Z of the receiving coil:
Z＝Z0+ΔZ
in the above formula, Z is the impedance of the receiving coil, Z0For the self-impedance of the receiving coil, Δ Z is the varying impedance generated by the electromagnetic eddy current signal (the impedance variation with the geometric information of the spherical surface generated by the lift-off effect);
2.2, for the spherical metal conductor of the sample to be detected, expressing the variable impedance delta Z generated by the electromagnetic eddy current signal as follows:
Figure BDA0003050155410000021
in the above formula, Δ Z is the varying impedance generated by the electromagnetic eddy current signal, Δ R is the variation of the real part of the impedance, j is the imaginary unit, Δ X is the variation of the imaginary part, Z1The distance between the lower plane of the excitation coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of2The distance of the upper plane of the excitation coil from the horizontal axis of the spherical metal conductor of the sample to be tested; z is a radical of3The distance between the lower plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of4The distance between the upper plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; x is the number of1Is the inside radius of the receive coil; x is the number of2Is outside of the receiving coilA side radius; x is the number of3Is the inside radius of the field coil, x4The outside radius of the excitation coil; omega is the excitation angular frequency; n is a radical of1The number of exciting coil turns is set; n is a radical of2The number of turns of the receiving coil is; the gap between the adjacent metal layers t and t +1 is bt，bt 2n+1Is b istThe metal layer is positioned on the spherical metal conductor of the sample to be detected to the power of 2n + 1; n is the number of layers of the multi-layer metal surface, tthContaining electrical conductivity σtAnd relative magnetic permeability mut；VijNRepresenting the ith in the matrixthLine, jthA column element; pn，SIs a double integral which is simplified into polynomial integral and comprises a coil rectangular section; wherein:
NOMI＝in(aNbN)[(n+1)μN-1]-aNbNi′n(aNbN)
NOMK＝kn(aNbN)[(n+1)μN-1]-aNbNk′n(aNbN)
DENI＝in(aNbN)(nμN+1)+aNbNi′n(aNbN)
DENK＝kn(aNbN)(nμN+1)+aNbNk′n(aNbN)
in the above formula, in(aNbN) And kn(aNbN) Respectively representing a first Bessel function and a second Bessel function of the spherical metal conductor of the sample to be detected; mu.sNThe magnetic permeability of the outermost metal shell; i'n(aNbN) And k'n(aNbN) Respectively obtaining the derivation results of the first Bezier function and the second Bezier function;
combining data from an impedance analyzer with a skin effect formula to obtain impedance change caused by the spherical metal conductor of the sample to be detected, wherein the skin effect formula is as follows:
Figure BDA0003050155410000031
in the above formula, j is an imaginary unit, ω is an excitation angular frequency, μ0Is the permeability of the gap air, mutIs the relative permeability, σ, of the object to be measuredtIs the measured object conductivity;
obtaining the surface depth of the spherical metal conductor of the sample to be detected:
Figure BDA0003050155410000032
in the above formula, f0For the frequency of the excitation signal, mutIs the relative permeability of the measured object, mu0Permeability of the air being spaced, σtIs the measured object conductivity; j is an imaginary unit, atIs a skin effect formula;
double integral P comprising rectangular cross-section of coil simplified to polynomial integraln，SComprises the following steps:
Figure BDA0003050155410000033
in the above formula, θ is shown in FIGS. 9 and 621、θ12Is the boundary angle of the coil cross-section, ro2(θo)、ro1(θo) Is the distance from the center of the metal ball to the boundary of the lowest end of the electromagnetic sensor;
Figure BDA0003050155410000034
is a first order Legendre function, θoParameterizing the situation, and positioning different integration results at different relative positions;
the second order matrix V (N) is:
V(N)＝T(N，N-1)T(N-1，N-2)...T(2，1)
Figure BDA0003050155410000041
in the above formula, T is a second-order matrix between adjacent metal layers T and T +1, T11、T12、T21、T22Four parameters of the second order matrix T are respectively.
Preferably, the second order matrix T between adjacent metal layers T and T +1 in step 2.2 is the following:
when sigma ist+1Not equal to 0 and σtWhen not equal to 0:
Figure BDA0003050155410000042
Figure BDA0003050155410000043
Figure BDA0003050155410000044
Figure BDA0003050155410000045
when sigma ist+1Not equal to 0 and σtWhen the value is 0:
Figure BDA0003050155410000046
Figure BDA0003050155410000047
Figure BDA0003050155410000048
Figure BDA0003050155410000049
when sigma ist+10 and σtWhen not equal to 0:
Figure BDA00030501554100000410
Figure BDA00030501554100000411
Figure BDA00030501554100000412
Figure BDA00030501554100000413
in the above formula, DEN is:
Figure BDA00030501554100000414
T11、T12、T21、T22four parameters of a second-order matrix T are respectively set; t is the number of metal layers; the gap between the adjacent metal layers t and t +1 is bt；μtRelative magnetic permeability of the measured object; i.e. in(aNbN) And kn(aNbN) Respectively representing a first Bessel function and a second Bessel function of the spherical metal conductor of the sample to be detected; i'n(aNbN) And k'n(aNbN) Respectively are the derivation results of the Bessel function of the first kind and the Bessel function of the second kind.
Preferably, in step 2.2, P is doubly integratedn，SThe simplified process of (A) is as follows:
when n ≠ 2:
Figure BDA0003050155410000051
when n is 2:
Figure BDA0003050155410000052
in the above formula, θij＝arctan(xi/zi)，i＝1、2；z1Is the horizontal axis distance, z, of the lower plane of the excitation coil from the spherical metal conductor of the sample to be measured1Is equivalent to ro1(θo)；z2The distance of the upper plane of the excitation coil from the horizontal axis of the spherical metal conductor of the sample to be tested; z is a radical of3The distance, z, from the lower plane of the receiving coil to the horizontal axis of the spherical metal conductor of the sample to be measured3Is equivalent to ro2(θo)；z4The distance between the upper plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; x is the number of1Is the inside radius of the receive coil; x is the number of2The outside radius of the receiving coil; x is the number of3Is the inside radius of the field coil, x4The outside radius of the excitation coil; as shown in fig. 6 to 9, θijThe boundary angle of the coil cross-sectional view.
Preferably, the frequency of the alternating current generated at the output port of the impedance analyzer is 200Hz to 20kHz, and different conductor characteristics can be obtained through different frequencies.
Preferably, the database stored in advance in step 4 is a database simulated by simulation, and the database contains the relationship between the peak frequency generated by the output port of the impedance analyzer under the condition of different radii and metal materials and the lift-off distance.
The invention has the beneficial effects that: the invention utilizes the skin effect that electromagnetic eddy current signals are only transmitted on the near surface of the pipe wall, combines the single-frequency electromagnetic eddy current detection technology to inhibit the nonlinear change caused by the lift-off effect, and realizes the high-precision and high-performance related parameter detection of the spherical metal conductor in the industry, such as the detection of the thickness of the plane of the metal conductor. The invention is mainly suitable for spherical metal parts which have high precision requirements and need to be subjected to nondestructive testing.
Drawings
FIG. 1 is a schematic diagram of an overall test system architecture;
FIG. 2 is a schematic diagram of the design of the coil and mechanical structure;
FIG. 3 is a schematic diagram of the effect of the non-contact spherical metal conductor dimension measuring device based on electromagnetic eddy current testing on the implementation of spherical metal conductors with different radius dimensions;
FIG. 4 is a schematic diagram of the effect of a non-contact spherical metal conductor size measuring device based on electromagnetic eddy current testing on spherical metal conductors of different materials;
FIG. 5 is a schematic diagram of the effect of the non-contact spherical metal conductor dimension measuring device based on electromagnetic eddy current testing on spherical metal conductors with different thicknesses;
fig. 6 to 9 are schematic views of the sensor and the sample to be measured.
Description of reference numerals: the device comprises a data processing terminal 1, an impedance analyzer 2, a receiving coil 3, an excitation coil 4, a spherical metal conductor 5 of a sample to be detected and a sphere fixing mechanical structure 6.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for a person skilled in the art, several modifications can be made to the invention without departing from the principle of the invention, and these modifications and modifications also fall within the protection scope of the claims of the present invention.
Electromagnetic eddy current is generated on the surface of the spherical metal conductor, the receiving coil receives the mutation signal and generates impedance change, the impedance analyzer acquires the change, the signal is sampled, amplified, corrected, compensated and filtered, the effective signal is transmitted to the data processing terminal, and the radius, the material and the shell thickness information of the spherical metal conductor are analyzed by connecting the impedance information changed by the receiving coil and combining the lift-off effect and the signal excitation frequency.
Example 1:
as shown in FIG. 1, the present embodiment employs a method based on electromagnetic eddy currentThe size measuring device for the detected non-contact spherical metal conductor measures the size of the spherical metal conductor: the receiving coil is closer to the spherical metal conductor, as shown in fig. 6 to 9, the distance from the lower plane of the receiving coil to the surface tangent plane of the spherical metal conductor is z, and the distance from the lower plane of the receiving coil to the horizontal axis of the spherical metal conductor is z3The distance from the upper plane of the receiving coil to the horizontal axis of the spherical metal conductor is z4The radius of the inner side of the receiving coil is x1The outside radius of the receiving coil is x2The radius and thickness of the exciting coil are the same as those of the receiving coil, and the distance from the lower plane of the exciting coil to the horizontal axis of the spherical metal conductor is z1The distance of the upper plane of the exciting coil from the horizontal axis of the spherical metal conductor is z2The distance between the excitation coil and the receiving coil is g. The excitation coil generates an alternating magnetic field to generate vortex current on the surface of the spherical metal conductor, and the receiving coil can simultaneously receive a signal from the excitation coil and an electromagnetic vortex signal generated on the metal surface and monitor the signal when the electromagnetic vortex signal changes in real time;
an impedance analyzer 2 in the non-contact spherical metal conductor size measuring device based on electromagnetic eddy current detection is electrically connected with a data processing terminal 1, an output port (current port) of the impedance analyzer 2 is connected to two ends of an excitation coil 4, and a receiving port (sampling port) of the impedance analyzer 2 is electrically connected to two ends of a receiving coil 3; the frequency of alternating current generated by the output port is changed within 200Hz to 20kHz, and different conductor characteristics can be obtained through different frequencies; the receiving coil 3 and the excitation coil 4 are both positioned in the bottom area of the sphere fixing mechanical structure 6, the receiving coil 3 and the excitation coil 4 are fixed by a round tubular structure and a base of the sphere fixing mechanical structure 6, and the receiving coil 3 and the excitation coil 4 are coaxial and are both positioned at the axis of the round tubular structure; the receiving coil 3 is close to the spherical metal conductor 5 of the sample to be detected, and the excitation coil 4 is positioned right below the receiving coil 3; the radius and thickness of the exciting coil 4 are the same as those of the receiving coil 3; as shown in fig. 2, a support rod is welded on the base of the sphere fixing mechanical structure 6, a groove-shaped sliding shaft is arranged in the support rod, and the shape of the sliding block is matched with that of the sliding shaft; the slide shaft is internally provided with a slide block, and the slide block and a fixed part (a ring with thickness) form an integrated structure.
The excitation coil is used for generating various electromagnetic eddy current signals, transmitting the signals through the surface of the spherical metal conductor, detecting the integrity of a metal spherical surface and generating impedance change with geometric information of the spherical surface by using a lift-off effect. The receiving coil is coaxial with the excitation coil and positioned on the axis of the framework, and is used for simultaneously receiving electromagnetic eddy current signals generated by the excitation coil on the metal surface, monitoring sudden change signals when the electromagnetic eddy current signals suddenly change in real time, matching impedance change characteristics of the lift-off effect with a database (the relation between peak frequency and lift-off distance under the conditions of different radiuses, metal materials and the like) which is simulated in advance, so that geometrical information of the metal surface is obtained, and parameters such as the radiuses are calculated.
The sphere fixing mechanical structure is used for fixing the spherical metal conductor and the transmitting and receiving coil, ensures that the central axes of the exciting coil and the receiving coil pass through the center of a sphere, ensures that the metal sphere and the coil are kept in a fixed state in the measuring process and are always in the same relative position relation.
Example 2:
on the basis of embodiment 1, the non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection comprises the following steps:
step 1, connecting an output port of an impedance analyzer 2 to two ends of an excitation coil 4, and connecting a receiving port of the impedance analyzer 2 to two ends of a receiving coil 3;
step 2, an output port of the impedance analyzer 2 generates alternating current, a digital synthesis module of an FPGA module in the impedance analyzer 2 generates an excitation signal, and an excitation source of an electromagnetic eddy current signal is provided for the excitation coil 4; the excitation coil 4 generates an electromagnetic eddy current signal, and the electromagnetic eddy current signal is transmitted to the receiving coil 3 through the surface of the spherical metal conductor 5 of the sample to be detected; the receiving coil 3 receives electromagnetic eddy current signals and generated variable impedance generated by the exciting coil 4 on the surface of the spherical metal conductor 5 of the sample to be detected, and monitors mutation signals when the electromagnetic eddy current signals are mutated in real time; a receiving port of the impedance analyzer 2 collects a receiving signal of the receiving coil 3 under the control of the FPGA module, and feeds the collected signal back to the analog-to-digital converter circuit, and the analog-to-digital converter circuit converts an analog voltage signal into a digital signal; the FPGA module demodulates the received digital signals through a digital I/Q demodulator, and the FPGA module exports effective data to the data processing terminal 1 for data operation and analysis;
step 2.1, the data processing terminal 1 receives the data from the impedance analyzer 2 and reads the corrected sampling data; the corrected sampled data includes the receive coil impedance Z; by the self-impedance Z of the receiving coil 30Adding the variable impedance delta Z generated by the electromagnetic eddy current signal to obtain the impedance Z of the receiving coil:
Z＝Z0+ΔZ
in the above formula, Z is the impedance of the receiving coil, Z0Is the self impedance of the receiving coil, and Delta Z is the variable impedance generated by the electromagnetic eddy current signal;
2.2, for the spherical metal conductor of the sample to be detected, expressing the variable impedance delta Z generated by the electromagnetic eddy current signal as follows:
Figure BDA0003050155410000081
in the above formula, Δ Z is the varying impedance generated by the electromagnetic eddy current signal, Δ R is the variation of the real part of the impedance, j is the imaginary unit, Δ X is the variation of the imaginary part, Z1The distance between the lower plane of the excitation coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of2The distance of the upper plane of the excitation coil from the horizontal axis of the spherical metal conductor of the sample to be tested; z is a radical of3The distance between the lower plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of4The distance between the upper plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; x is the number of1Is the inside radius of the receive coil; x is the number of2The outside radius of the receiving coil; x is the number of3Is the inside radius of the field coil, x4The outside radius of the excitation coil; omega is the excitation angular frequency; n is a radical of1The number of exciting coil turns is set; n is a radical of2The number of turns of the receiving coil is; adjacent metal layer t andthe gap between t +1 is bt，bt 2n+1Is b ist2n +1 th power of (1); n is the number of layers of the multi-layer metal surface, tthContaining electrical conductivity σtAnd relative magnetic permeability mut；VijNRepresenting the ith in the matrixthLine, jthA column element; pn，sIs a double integral which is simplified into polynomial integral and comprises a coil rectangular section; wherein:
NOMI＝in(aNbN)[(n+1)μN-1]-aNbNi′n(aNbN)
NOMK＝kn(aNbN)[(n+1)μN-1]-aNbNk′n(aNbN)
DENI＝in(aNbN)(nμN+1)+aNbNi′n(aNbN)
DENK＝kn(aNbN)(nμN+1)+aNbNk′n(aNbN)
in the above formula, in(aNbN) And kn(aNbN) Respectively representing a first Bessel function and a second Bessel function of the spherical metal conductor of the sample to be detected; mu.sNThe magnetic permeability of the outermost metal shell; i'n(aNbN) And k'n(aNbN) Respectively obtaining the derivation results of the first Bezier function and the second Bezier function;
combining data from an impedance analyzer with a skin effect formula to obtain impedance change caused by the spherical metal conductor of the sample to be detected, wherein the skin effect formula is as follows:
Figure BDA0003050155410000091
in the above formula, j is an imaginary unit, ω is an excitation angular frequency, μ0For spacing airMagnetic permeability, mutIs the relative permeability, σ, of the object to be measuredtIs the measured object conductivity;
obtaining the surface depth of the spherical metal conductor of the sample to be detected:
Figure BDA0003050155410000092
in the above formula, f0For the frequency of the excitation signal, mutIs the relative permeability of the measured object, mu0Permeability of the air being spaced, σtIs the measured object conductivity; j is an imaginary unit, atIs a skin effect formula;
double integral P comprising rectangular cross-section of coil simplified to polynomial integraln，SComprises the following steps:
Figure BDA0003050155410000093
in the above formula, θ21、θ12Is the boundary angle of the coil cross-section, ro2(θo)、ro1(θo) Is the distance from the center of the metal ball to the boundary of the lowest end of the electromagnetic sensor;
Figure BDA0003050155410000094
is a first order Legendre function; double integral Pn，SThe simplified process of (A) is as follows:
when n ≠ 2:
Figure BDA0003050155410000095
when n is 2:
Figure BDA0003050155410000096
in the above formula, θij＝arctan(xi/zi)，i＝1、2；z1Is the lower plane of the excitation coilThe distance from the horizontal axis of the spherical metal conductor of the sample to be measured; z is a radical of2The distance of the upper plane of the excitation coil from the horizontal axis of the spherical metal conductor of the sample to be tested; z is a radical of3The distance between the lower plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of4The distance between the upper plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; x is the number of1Is the inside radius of the receive coil; x is the number of2The outside radius of the receiving coil; x is the number of3Is the inside radius of the field coil, x4The outside radius of the excitation coil; thetaijIs the boundary angle of the coil cross-sectional view;
the second order matrix V (N) is:
V(N)＝T(N，N-1)T(N-1，N-2)...T(2，1)
Figure BDA0003050155410000101
in the above formula, T is a second-order matrix between adjacent metal layers T and T +1, T11、T12、T21、T22Four parameters of a second-order matrix T are respectively set; the second order matrix T between adjacent metal layers T and T +1, has the following conditions:
when sigma ist+1Not equal to 0 and σtWhen not equal to 0:
Figure BDA0003050155410000102
Figure BDA0003050155410000103
Figure BDA0003050155410000104
Figure BDA0003050155410000105
when sigma ist+1Not equal to 0 and σtWhen the value is 0:
Figure BDA0003050155410000106
Figure BDA0003050155410000107
Figure BDA0003050155410000108
Figure BDA0003050155410000109
when sigma ist+10 and σtWhen not equal to 0:
Figure BDA00030501554100001010
Figure BDA00030501554100001011
Figure BDA00030501554100001012
Figure BDA0003050155410000111
in the above formula, DEN is:
Figure BDA0003050155410000112
T11、T12、T21、T22are respectively twoFour parameters of the order matrix T; t is the number of metal layers; the gap between the adjacent metal layers t and t +1 is bt；μtRelative magnetic permeability of the measured object; i.e. in(aNbN) And kn(aNbN) Respectively representing a first Bessel function and a second Bessel function of the spherical metal conductor of the sample to be detected; i'n(aNbN) And k'n(aNbN) Respectively obtaining the derivation results of the first Bezier function and the second Bezier function;
step 3, after obtaining the variable impedance delta Z generated by the electromagnetic eddy current signal in the step 2, finding the minimum value of the imaginary part of the impedance along with the variation of the excitation frequency through the ratio relation of the impedance variation and the excitation frequency to obtain a peak frequency value:
[a，f]＝min(imag((ΔZ/jω)))
in the above formula, f is the peak frequency, a is the minimum value of the imaginary part of the impedance generated under the peak frequency f, imag () is an imaginary part formula, Δ Z is the varying impedance generated by the electromagnetic eddy current signal, j is an imaginary unit, and ω is the excitation angular frequency;
and 4, obtaining the radius, the material characteristic and the metal shell thickness information of the spherical metal conductor of the sample to be detected through the negative correlation linear relation between the peak frequency value obtained in the step 3 and the lift-off distance and through slope information in a pre-stored database, wherein the pre-stored database is a simulation-simulated database and comprises the relation between the peak frequency generated by an output port of the impedance analyzer 2 and the lift-off distance under the conditions of different radii and metal materials.
Fig. 3 to 5 are graphs showing the relationship between the peak frequency and the slope of the change (obtained by plotting experimental data) of spherical metal conductors with different radii, different materials and different surface thicknesses, respectively, and the peak frequency decreases with the increase of the radius for the spherical metal conductors with different radii and different thicknesses. For spherical metal conductors of different materials, the slope of the peak frequency as a function of lift-off distance changes, with the logarithm of the peak frequency decreasing as the metal conductivity increases. For spherical metal conductors with different thicknesses, the slope of the peak frequency changes along with the change of the lift-off distance, and when the material and the size are consistent, the slope of the peak frequency of the thicker metal surface is smaller. The conductivity parameters of the sample spherical metal conductor are shown in table 1 below;
TABLE 1 conductivity parameter table of sample spherical metal conductor
Material Conductivity (Ms/m)
Copper (Cu) 58.00
Brass 25.00
Aluminium 36.00
Zinc 17.40
Titanium alloy 0.59
The measured impedance change is a complex number Δ Z ═ Δ R + Δ jX, which varies with the excitation frequency, and the impedance equation is separated into a real part Re (Δ L) and an imaginary part Im (Δ L), as follows:
Figure BDA0003050155410000121
Figure BDA0003050155410000122
wherein Z (f) represents the impedance of the spherical metal conductor due to electromagnetic eddy current fed back to the receiving coil, Z0(f) The self-impedance of the receiving coil is shown, and the configuration of the coil is shown in the following table 2;
TABLE 2 coil configuration table
Radius of inner circle (x)1) 17.5mm
Outer ring radius (x)2) 17.9mm
Excitation, receiving coil spacing (g) 5.0mm
Distance (z) between exciting coil and center of sphere1/z2) 65.3mm/71.3mm
Distance (z) between receiving coil and center of sphere3/z4) 52.3mm/60.3mm
Distance between receiving coil and spherical tangent plane (z) 2.0mm
Sample spherical Metal radius (b)n) 50.0mm
Coil turns ratio (N)1/N2) 20/20
In this embodiment, when measuring the radius, the conductivity of the spherical metal conductor used is 1.37MS/m, and the thickness of the stainless steel metal sphere is 1mm, and through practical measurement, the lift-off distance should be controlled within 30mm, and when the distance exceeds 30mm, a nonlinear change may occur, and for better detection performance, the lift-off distance should be controlled between 2mm and 6mm, and step by 1 mm.
For spherical metal conductors made of the same material and having the same thickness, the change of peak current is obvious when the sizes are different, and the relative relation is not influenced along with the change of the lifting distance, the radius of the metal sphere can be effectively measured by the method, the error is within 2 percent, and the using effect of the device is as shown in the following table 3:
table 3 table of using effect of non-contact type spherical metal conductor size measuring device based on electromagnetic eddy current testing
Figure BDA0003050155410000131

Claims (6)

1. A non-contact spherical metal conductor characteristic parameter measuring method based on electromagnetic eddy current detection is characterized by comprising the following steps:
step 1, connecting an output port of an impedance analyzer (2) to two ends of an excitation coil (4), and connecting a receiving port of the impedance analyzer (2) to two ends of a receiving coil (3);
step 2, an output port of the impedance analyzer (2) generates alternating current, a digital synthesis module of an FPGA module in the impedance analyzer (2) generates an excitation signal, and an excitation source of an electromagnetic eddy current signal is provided for the excitation coil (4); the excitation coil (4) generates an electromagnetic eddy current signal, and the electromagnetic eddy current signal is transmitted to the receiving coil (3) through the surface of the spherical metal conductor (5) of the sample to be detected; the receiving coil (3) receives electromagnetic eddy current signals and generated variable impedance generated by the exciting coil (4) on the surface of the spherical metal conductor (5) of the sample to be detected, and monitors mutation signals when the electromagnetic eddy current signals are mutated in real time; a receiving port of the impedance analyzer (2) collects a receiving signal of the receiving coil (3) under the control of the FPGA module, the collected signal is fed back to the analog-to-digital converter circuit, and the analog-to-digital converter circuit converts an analog voltage signal into a digital signal; the FPGA module demodulates the received digital signals through a digital I/Q demodulator, and the FPGA module exports effective data to a data processing terminal (1) for data operation and analysis;
step 3, after obtaining the variable impedance delta Z generated by the electromagnetic eddy current signal in the step 2, finding the minimum value of the imaginary part of the impedance along with the variation of the excitation frequency through the ratio relation of the impedance variation and the excitation frequency to obtain a peak frequency value:
[a,f]＝min(imag((ΔZ/jω)))
in the above formula, f is the peak frequency, a is the minimum value of the imaginary part of the impedance generated under the peak frequency f, imag () is an imaginary part formula, Δ Z is the varying impedance generated by the electromagnetic eddy current signal, j is an imaginary unit, and ω is the excitation angular frequency;
and 4, obtaining the radius, the material characteristic and the thickness information of the metal shell of the spherical metal conductor of the sample to be detected through the linear relationship of the peak frequency value obtained in the step 3 and the negative correlation of the lift-off distance and the slope information in a pre-stored database.
2. The method for measuring the characteristic parameters of the non-contact spherical metal conductor based on the electromagnetic eddy current testing as claimed in claim 1, wherein the step 2 specifically comprises the following steps:
2.1, the data processing terminal (1) receives data from the impedance analyzer (2) and reads the corrected sampling data; the corrected sampled data includes the receive coil impedance Z; by the self-impedance Z of the receiving coil (3)0Adding the variable impedance delta Z generated by the electromagnetic eddy current signal to obtain the impedance Z of the receiving coil:
Z＝Z0+ΔZ
in the above formula, Z is the impedance of the receiving coil, Z0To receiveThe self impedance of the coil, and delta Z is the variable impedance generated by the electromagnetic eddy current signal;
2.2, for the spherical metal conductor of the sample to be detected, expressing the variable impedance delta Z generated by the electromagnetic eddy current signal as follows:
Figure FDA0003050155400000021
in the above formula, Δ Z is the varying impedance generated by the electromagnetic eddy current signal, Δ R is the variation of the real part of the impedance, j is the imaginary unit, Δ X is the variation of the imaginary part, Z1The distance between the lower plane of the excitation coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of2The distance of the upper plane of the excitation coil from the horizontal axis of the spherical metal conductor of the sample to be tested; z is a radical of3The distance between the lower plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of4The distance between the upper plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; x is the number of1Is the inside radius of the receive coil; x is the number of2The outside radius of the receiving coil; x is the number of3Is the inside radius of the field coil, x4The outside radius of the excitation coil; omega is the excitation angular frequency; n is a radical of1The number of exciting coil turns is set; n is a radical of2The number of turns of the receiving coil is; the gap between the adjacent metal layers t and t +1 is bt，bt 2n+1Is b istThe metal layer is positioned on the spherical metal conductor (5) of the sample to be detected to the power of 2n + 1; n is the number of layers of the multi-layer metal surface, tthContaining electrical conductivity σtAnd relative magnetic permeability mut；VijNRepresenting the ith in the matrixthLine, jthA column element; pn，SIs a double integral which is simplified into polynomial integral and comprises a coil rectangular section; wherein:
NOMI＝in(aNbN)[(n+1)μN-1]-aNbNin(aNbN)
NOMK＝kn(aNbN)[(n+1)μN-1]-aNbNkn(aNbN)
DENI＝in(aNbN)(nμN+1)+aNbNin(aNbN)
DENK＝kn(aNbN)(nμN+1)+aNbNkn(aNbN)
in the above formula, in(aNbN) And kn(aNbN) Respectively representing a first Bessel function and a second Bessel function of the spherical metal conductor of the sample to be detected; mu.sNThe magnetic permeability of the outermost metal shell; i'n(aNbN) And k'n(aNbN) Respectively obtaining the derivation results of the first Bezier function and the second Bezier function;
combining data from an impedance analyzer with a skin effect formula to obtain impedance change caused by the spherical metal conductor of the sample to be detected, wherein the skin effect formula is as follows:
Figure FDA0003050155400000022
in the above formula, j is an imaginary unit, ω is an excitation angular frequency, μ0Is the permeability of the gap air, mutIs the relative permeability, σ, of the object to be measuredtIs the measured object conductivity;
obtaining the surface depth of the spherical metal conductor of the sample to be detected:
Figure FDA0003050155400000023
in the above formula, f0For the frequency of the excitation signal, mutIs the relative permeability of the measured object, mu0Permeability of the air being spaced, σtIs the measured object conductivity; j is an imaginary unit, atIs a skin effect formula;
comprising a rectangular section of coilDouble integral P of a surface reduced to polynomial integraln,SComprises the following steps:
Figure FDA0003050155400000031
in the above formula, θ21、θ12Is the boundary angle of the coil cross-section, ro2(θo)、ro1(θo) Is the distance from the center of the metal ball to the boundary of the lowest end of the electromagnetic sensor;
Figure FDA00030501554000000311
is a first order Legendre function;
the second order matrix V (N) is:
y(N)＝T(N，N-1)T(N-1，N-2)...T(2，1)
Figure FDA0003050155400000032
in the above formula, T is a second-order matrix between adjacent metal layers T and T +1, T11、T12、T21、T22Four parameters of the second order matrix T are respectively.
3. The method for measuring the characteristic parameters of the non-contact spherical metal conductor based on the electromagnetic eddy current inspection as claimed in claim 2, wherein the second-order matrix T between the adjacent metal layers T and T +1 in the step 2.2 has the following conditions:
when sigma ist+1Not equal to 0 and σtWhen not equal to 0:
Figure FDA0003050155400000033
Figure FDA0003050155400000034
Figure FDA0003050155400000035
Figure FDA0003050155400000036
when sigma ist+1Not equal to 0 and σtWhen the value is 0:
Figure FDA0003050155400000037
Figure FDA0003050155400000038
Figure FDA0003050155400000039
Figure FDA00030501554000000310
when sigma ist+10 and σtWhen not equal to 0:
Figure FDA0003050155400000041
Figure FDA0003050155400000042
Figure FDA0003050155400000043
Figure FDA0003050155400000044
in the above formula, DEN is:
Figure FDA0003050155400000045
T11、T12、T21、T22four parameters of a second-order matrix T are respectively set; t is the number of metal layers; the gap between the adjacent metal layers t and t +1 is bt；μtRelative magnetic permeability of the measured object; i.e. in(aNbN) And kn(aNbN) Respectively representing a first Bessel function and a second Bessel function of the spherical metal conductor of the sample to be detected; i'n(aNbN) And k'n(aNbN) Respectively are the derivation results of the Bessel function of the first kind and the Bessel function of the second kind.
4. The method for measuring the characteristic parameters of the non-contact spherical metal conductor based on the electromagnetic eddy current testing as claimed in claim 2, wherein the double integral P in step 2.2n,SThe simplified process of (A) is as follows:
when n ≠ 2:
Figure FDA0003050155400000046
when n is 2:
Figure FDA0003050155400000047
in the above formula, θij＝arctan(xi/zi)，i＝1、2；z1The distance between the lower plane of the magnet exciting coil and the horizontal axis of the spherical metal conductor of the sample to be measuredSeparating; z is a radical of2The distance of the upper plane of the excitation coil from the horizontal axis of the spherical metal conductor of the sample to be tested; z is a radical of3The distance between the lower plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; z is a radical of4The distance between the upper plane of the receiving coil and the horizontal axis of the spherical metal conductor of the sample to be detected is the distance; x is the number of1Is the inside radius of the receive coil; x is the number of2The outside radius of the receiving coil; x is the number of3Is the inside radius of the field coil, x4The outside radius of the excitation coil; thetaijThe boundary angle of the coil cross-sectional view.
5. The method for measuring the characteristic parameters of the non-contact spherical metal conductor based on the electromagnetic eddy current testing as claimed in claim 1, wherein: the frequency of the alternating current generated by the output port of the impedance analyzer (2) is 200 Hz-20 kHz.
6. The method for measuring the characteristic parameters of the non-contact spherical metal conductor based on the electromagnetic eddy current testing as claimed in claim 1, wherein: the database stored in advance in the step 4 is a database simulated by simulation, and the database comprises the relationship between the peak frequency generated by the output port of the impedance analyzer (2) and the lift-off distance under the conditions of different radiuses and metal materials.
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