Method and device for measuring low-frequency distribution of effective permeability of a bar-shaped magnetic core

Abstract

The application provides a kind of bar type magnetic core effective permeability low frequency distribution measurement method and device, it is related to low frequency fluctuation detection and application technical field.The method comprises: winding test coil on coil framework, the winding length of test coil is measured and the number of turns is recorded;Test magnetic core is inserted into different positions of test coil, and the inductance of test coil is measured when test magnetic core is in different positions;According to the relationship between permeability and inductance, the area average effective permeability of test magnetic core in different positions is calculated;Based on the preset algorithm, the effective permeability distribution function of test magnetic core is fitted;According to the effective permeability distribution function of test magnetic core, the effective permeability distribution function of the bar type iron-based nanocrystalline alloy magnetic core to be measured is obtained.The application can reduce the measurement error of magnetic core effective permeability, improve the modeling reliability, and obtain the effective permeability distribution function, so as to reduce repeated experiments and improve the modeling efficiency.

Description

Technical Field

[0001] This invention relates to the field of low-frequency fluctuation detection and application technology, specifically to a method and apparatus for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core. Background Technology

[0002] Inductive search coils, based on Faraday's law of electromagnetic induction, possess advantages such as high sensitivity, good stability, and rapid response, and have been widely applied in various fields including magnetotelluric sounding, space physics, and biomedicine. In geological resource exploration, electromagnetic methods can determine the distribution and composition of underground rocks by detecting changes in the electromagnetic properties of rock strata. In space science, inductive coils serve as important equipment for observing changes in the geomagnetic field, supporting space environment monitoring and research on space physical processes. As the most commonly used magnetic field receiver in frequency-domain electromagnetic exploration, the performance level of inductive magnetic sensors determines the width of the usable frequency band and the accuracy of the detection results, playing a crucial role in the overall system's signal response capability and application depth.

[0003] In these types of magnetic sensors, the effective permeability of the magnetic core is one of the core parameters affecting sensor performance. The effective permeability determines the DC inductance of the induction coil, which can typically be simplified as an RLC series circuit, where the inductance L is directly influenced by the core permeability. The spatial distribution of permeability within the core structure not only affects the overall value of the inductive inductance but also determines key technical indicators such as the sensor's operating frequency band, sensing sensitivity, and minimum resolvable magnetic field change. This dependence on core performance is particularly pronounced in low-frequency applications. Because the initial permeability of iron-based nanocrystalline materials changes relatively little at low frequencies, the effective permeability is primarily determined by the core's structural dimensions and geometric distribution. This means that the effective permeability measured at low frequencies is not only highly representative but can also be directly used for sensor modeling, parameter optimization, and performance prediction.

[0004] However, current research on the effective permeability distribution of magnetic cores largely relies on empirical formulas or simplified models. Whether these empirical formulas are applicable to the actual material properties of specific iron-based nanocrystalline magnetic cores remains uncertain. Simplified models often fail to accurately reflect the permeability gradient changes in different regions of the magnetic core, thus affecting the magnetic field response and the accuracy of system simulations. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core. This method addresses the problems in the prior art, such as large deviations in permeability estimation and poor model adaptability when using empirical formulas or simplified models, which prevent the accurate acquisition of the effective permeability of the magnetic core. This invention can reduce the measurement error of the effective permeability of the magnetic core, improve the reliability of modeling, and obtain the effective permeability distribution function, thereby reducing repeated experiments and improving modeling efficiency.

[0006] To achieve the above objectives, the present invention provides a method for measuring the low-frequency distribution of the effective permeability of a rod-shaped magnetic core, comprising:

[0007] A test coil is wound on a coil bobbin, and the winding length and number of turns of the test coil are measured and recorded.

[0008] The test core was inserted into different positions of the test coil, and the inductance of the test coil was measured when the test core was in different positions; the test core was a rod-shaped iron-based nanocrystalline alloy core.

[0009] The average effective permeability of the test core at different locations was calculated based on the permeability-inductance relationship.

[0010] The effective permeability distribution function of the test magnetic core is fitted based on a preset algorithm;

[0011] The effective permeability distribution function of the test rod-shaped iron-based nanocrystalline alloy core is obtained based on the effective permeability distribution function of the test core. The test rod-shaped iron-based nanocrystalline alloy core has the same cross-sectional area as the test core, but different lengths.

[0012] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided, wherein the winding length of the test coil is 10% ± 5% of the length of the test magnetic core, and the number of turns is greater than 200.

[0013] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided, wherein the coil frame is made of non-ferromagnetic, non-metallic material.

[0014] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core includes inserting the test magnetic core into different positions of a test coil and measuring the inductance of the test coil at different positions of the test magnetic core, comprising:

[0015] After inserting the test core into the test coil, connect the test coil to the impedance analyzer using the four-terminal wiring method.

[0016] A coordinate system is established with the axial direction of the test core as the horizontal axis and the center of the test core as the origin;

[0017] Values ​​to the left of the origin are recorded as negative, and values ​​to the right of the origin are recorded as positive. Within the interval... Inside, the test coil is gradually moved from left to right at equal intervals. The initial horizontal coordinate and inductance of the test coil are measured after each movement, forming an inductance data set. x n L n}, n=1,2,3,…,M, where M is the number of measurements. x nLet L be the x-coordinate of the starting position of the test coil in the nth measurement. n Let n be the inductance of the test coil in the nth measurement. To test the length of the magnetic core.

[0018] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided, wherein the permeability-inductance relationship is:

[0019]

[0020] in, The region-average effective permeability is given by the nth measurement. The permeability of free space, To test the number of turns of the coil, To test the cross-sectional area of ​​the magnetic core, l core To test the core length, This is to test the winding length of the coil.

[0021] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided, wherein the expression for the region-average effective permeability is:

[0022]

[0023] In the formula, The region-average effective permeability is given by the nth measurement. This is used to test the effective permeability distribution function of the magnetic core.

[0024] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided, which fits the effective permeability distribution function of the test magnetic core based on a preset algorithm, including:

[0025] According to the inductance data group { x n L n The permeability data set is obtained from the permeability-inductance relationship. x n , };

[0026] The effective permeability distribution function of the test magnetic core is written as:

[0027]

[0028] In the formula, To test the maximum effective permeability of the magnetic core, It is a constant;

[0029] Based on magnetic permeability data set { , The maximum effective permeability of the test core was obtained using the Levenberg-Marquardt (LM) algorithm. and constant This allows us to determine the effective permeability distribution function of the test core. The expression.

[0030] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided. In the LM algorithm, the termination condition is that the rate of change of the correlation coefficient is less than 0.001 or the number of iterations is greater than 200.

[0031] According to the present invention, a method for measuring the low-frequency distribution of effective permeability of a rod-shaped magnetic core is provided, which derives the effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core under test based on the effective permeability distribution function of the tested magnetic core, including:

[0032] The formula for calculating the average effective permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core under test is as follows:

[0033]

[0034] In the formula, The initial permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested; As a demagnetizing factor,

[0035]

[0036] In the formula, The aspect ratio of the rod-shaped iron-based nanocrystalline alloy magnetic core under test.

[0037]

[0038] In the formula, The length of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested. d core The equivalent diameter of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested;

[0039] If the cross-section of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested is circular, then d core It is equal to the diameter of the circle; if the cross-section of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested is square, then

[0040]

[0041] In the formula, A is the cross-sectional area of ​​the square.

[0042] The average effective permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core under test is written as:

[0043]

[0044] Based on the initial permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested ,length equivalent diameter d core and constants k The maximum effective permeability of the tested rod-shaped iron-based nanocrystalline alloy magnetic core was obtained by solving the problem. Therefore, the expression for the effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core under test is obtained as follows:

[0045] .

[0046] Secondly, the present invention provides a measuring device for the low-frequency distribution of the effective permeability of a rod-shaped magnetic core, comprising:

[0047] The recording unit is used to wind a test coil on a coil bobbin, measure the winding length of the test coil, and record the number of turns.

[0048] The measurement unit is used to insert the test core into different positions of the test coil and measure the inductance of the test coil when the test core is in different positions; the test core is a rod-shaped iron-based nanocrystalline alloy core.

[0049] The calculation unit is used to calculate the average effective permeability of the test core at different locations based on the permeability-inductance relationship.

[0050] The fitting unit is used to fit the effective permeability distribution function of the test magnetic core based on a preset algorithm.

[0051] The determination unit is used to derive the effective permeability distribution function of the test rod-shaped iron-based nanocrystalline alloy core based on the effective permeability distribution function of the test core; the test rod-shaped iron-based nanocrystalline alloy core has the same cross-sectional area but a different length from the test core.

[0052] This invention has at least the following technical effects:

[0053] This invention provides a method and apparatus for measuring the low-frequency distribution of effective permeability in rod-shaped magnetic cores. Combining low-frequency inductance measurement technology, the average inductance at different locations within the core is measured, and the regional average effective permeability is calculated using the functional relationship between inductance and permeability. Based on this, the LM algorithm is used to dynamically and adaptively fit the quadratic function distribution model of permeability. The iteration termination condition is set by the rate of change of the correlation coefficient and the number of iterations. Combined with the demagnetization factor theory, the permeability distribution across dimensions of magnetic cores with the same cross-section but different lengths can be calculated. This invention constructs a three-level error control system centered on hardware calibration, coil winding specifications, and the fitting algorithm, effectively controlling the overall measurement error within a low range. Compared with traditional methods that rely on extensive experimental measurements or empirical formulas, this method only requires test data from a single-size magnetic core to derive the spatial effective permeability distribution of a series of magnetic cores made of the same material, significantly reducing experimental costs and improving modeling efficiency. This invention can provide high-precision permeability parameter support for the design of inductive search coils in low-frequency electromagnetic detection fields such as geological exploration and space physics, effectively solving the technical problems of low permeability estimation accuracy and poor adaptability in traditional methods. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0055] In the attached diagram:

[0056] Figure 1 This is a flowchart of the method for measuring the low-frequency distribution of the effective permeability of the rod-shaped magnetic core of the present invention;

[0057] Figure 2a , Figure 2b The images shown are a model diagram and a physical diagram of the test coil according to an embodiment of the present invention.

[0058] Figure 3 The figures show the fitting results of the magnetic permeability of the 25cm magnetic core in this embodiment of the invention and the residual distribution.

[0059] Figure 4 The graphs show the permeability distribution curve and estimation error curve of a 20cm magnetic core according to an embodiment of the present invention.

[0060] Figure 5 The graphs show the permeability distribution curve and estimation error curve of the 30cm magnetic core in this embodiment of the invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0062] The following detailed description of some embodiments of the present invention will be provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0063] This invention constructs a measurement and modeling method that can accurately reflect the effective permeability distribution inside a magnetic core, which is of great significance for improving the design accuracy and practical application effect of inductive sensors. This not only helps solve technical problems such as large permeability estimation errors and poor model adaptability, but also provides solid data support and theoretical basis for inductive search coils in a wider range of application scenarios.

[0064] Please see Figure 1 This invention provides a method for measuring the low-frequency distribution of effective permeability of a rod-shaped iron-based nanocrystalline alloy magnetic core, which addresses the problem of large estimation errors in the effective permeability distribution of iron-based nanocrystalline alloy magnetic cores. The method includes the following steps:

[0065] S1. Wind the test coil on the coil frame, measure the winding length of the test coil and record the number of turns.

[0066] Specifically, the winding length of the test coil is 10% ± 5% of the test core length, with more than 200 turns. The coil bobbin is made of non-ferromagnetic, non-metallic materials, typically nylon or phenolic resin, which possess high temperature stability and low dielectric constant. The test coil is tightly wound with enameled wire onto the coil bobbin, and the winding length of the test coil is... The number of turns wound is N.

[0067] S2, Insert the test core into different positions of the test coil and measure the inductance of the test coil when the test core is in different positions; the test core is a rod-shaped iron-based nanocrystalline alloy core;

[0068] Specifically, the test core length is l core The cross-sectional area of ​​the tested magnetic core is After inserting the test core into the test coil, connect the test coil to the impedance analyzer using the four-terminal wiring method. The impedance analyzer needs to be calibrated with an open circuit / short circuit before use to eliminate parasitic parameters. The test coil after inserting the test core has certain electrical characteristics and can be equivalent to an RLC circuit, where R is the DC resistance of the test coil, L is the DC inductance of the test coil, and C is the parasitic capacitance of the test coil. Since the capacitive reactance of the parasitic capacitance will affect the measured equivalent inductance to some extent, the lower the measurement frequency, the closer the measured equivalent inductance will be to the DC inductance of the test coil, and the smaller the influence of the parasitic capacitance of the test coil on the result, thus the more accurate the measurement result will be. The higher the measurement frequency, the greater the measurement error will be.

[0069] With the axial direction of the test core as the horizontal axis ( x (Axis), with the origin at the exact center of the test core, establish a coordinate system; in this coordinate system, x The positive axis points to the right, with the origin at the exact center of the test core. Values ​​to the left of the origin are recorded as negative, and values ​​to the right are recorded as positive. The interval is... Inside, the test coil is gradually moved from left to right at equal intervals, and the distance between the starting position of the test coil and the origin (i.e., the midpoint of the magnetic core) is measured. This involves measuring the x-coordinate of the starting position of the test coil and its inductance after each movement, forming an inductance data set. x n L n}, n=1,2,3,…,M, where M is the number of measurements. x n Let L be the x-coordinate of the starting position of the test coil in the nth measurement. n Let n be the inductance of the test coil in the nth measurement. l core To test the length of the magnetic core.

[0070] S3, calculate the average effective permeability of the test core at different locations based on the permeability-inductance relationship;

[0071] Specifically, Let n be the region-average effective permeability under the nth measurement. The permeability-inductance relationship can be expressed as follows:

[0072]

[0073] in, The region-average effective permeability is given by the nth measurement. The value of free permeability is . , To test the number of turns of the coil, To test the cross-sectional area of ​​the magnetic core, l core To test the core length, This is to test the winding length of the coil.

[0074] Specifically, data group and The following relationship exists between them:

[0075]

[0076] in, Let x be the x-coordinate of the starting position of the measuring coil in the nth measurement. The effective permeability distribution function of the test core needs to be determined.

[0077] S4, Fit the effective permeability distribution function of the test core based on a preset algorithm;

[0078] In some embodiments, the LM algorithm is used to fit the effective permeability distribution function of the test magnetic core. S4 specifically includes:

[0079] After the above formula conversion, that is, based on the inductance data group { x n L n The permeability data set is obtained from the permeability-inductance relationship. x n , };

[0080] The effective permeability distribution function of the test core is a parabolic function where the effective permeability is greatest at the center of the test core and gradually decreases towards both sides. Therefore, the distribution function can be written as follows:

[0081]

[0082] in, To test the maximum effective permeability of the magnetic core, and since the effective permeability is greatest in the central region of the magnetic core, the origin of the above distribution function is located at the midpoint of the tested magnetic core. k The length of the magnetic core is considered a constant. Some studies suggest this constant is independent of the core material and size. However, to ensure the accuracy of the research, this invention keeps other conditions constant and only changes the length of the magnetic core. In this case, the length of the magnetic core is considered a constant. constant.

[0083] For the test core, the parameter to be fitted can be expressed as: Based on magnetic permeability data set { , The maximum effective permeability of the test core can be obtained using the LM algorithm. and constant This allows us to determine the effective permeability distribution function of the test core. The expression.

[0084] Specifically, the LM algorithm can be expressed as follows:

[0085]

[0086] Since the LM algorithm is an iterative algorithm, the parameters to be fitted need to be estimated before fitting the effective permeability distribution function of the magnetic core using the LM algorithm. , This is an estimate of the maximum effective permeability of the magnetic core under test. For constants The estimated value, research shows that it is a constant. Typically not exceeding 4, therefore for constants The estimate can be considered as .

[0087] Specific The average effective permeability of the region obtained by measurement can be estimated using the following formula. Replace the estimated value.

[0088]

[0089] So, As an increment, in solving the th Increment calculated after the next iteration The updated parameters are expressed as follows:

[0090]

[0091] So, Let be the residual vector, the th The residual vector in the next iteration can be expressed as follows: To measure magnetic permeability, Fit the permeability to the model.

[0092]

[0093] Specifically, For Jacobian matrices, Given the transpose of the Jacobian matrix, under the measurement method of this invention, the elements of the Jacobian matrix can be represented as follows: . diag This is to extract the diagonal elements of the matrix. This is the damping factor (controlling the step size). The initial value needs to be preset before the iterative algorithm begins. Generally, The initial value can be set to 0.001.

[0094] So, the first Damping factor in the next iteration calculation The following strategies can be used for adaptive adjustment, where

[0095]

[0096] Specifically, R 2 The coefficient of determination can be expressed as follows:

[0097]

[0098] Specifically, the termination condition for the LM algorithm can be expressed as the correlation coefficient change rate being less than 0.001 or the number of iterations being greater than 200. After the iteration terminates, the parameter to be optimized can be solved. After confirming the parameters, the effective permeability distribution function of the test core can be obtained. The expression.

[0099] S5. The effective permeability distribution function of the test rod-shaped iron-based nanocrystalline alloy core is obtained from the effective permeability distribution function of the test core. The cross-sectional area of ​​the test rod-shaped iron-based nanocrystalline alloy core is the same as that of the test core, but the lengths are different.

[0100] Specifically, the formula for calculating the average effective permeability of the tested rod-shaped iron-based nanocrystalline alloy magnetic core is as follows:

[0101]

[0102] In the formula, This represents the initial permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core under test. For iron-based nanocrystalline alloy magnetic cores, the initial permeability at the test frequency needs to be determined based on the distribution of the initial permeability as a function of frequency. This parameter is usually provided by the manufacturer and is related to the process, materials, and structure. The demagnetizing factor can be specifically expressed as follows:

[0103]

[0104] in The aspect ratio of the rod-shaped iron-based nanocrystalline alloy magnetic core under test.

[0105]

[0106] in The length of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested. d core This is the equivalent diameter of the rod-shaped iron-based nanocrystalline alloy magnetic core under test. If the cross-section of the rod-shaped iron-based nanocrystalline alloy magnetic core under test is circular, then... d coreThe value is equal to the diameter of the circle; for a magnetic core with a square cross-section, it needs to be calculated as an equivalent cylindrical magnetic core, as shown in the following equivalent formula, where A is the cross-sectional area of ​​the square core.

[0107]

[0108] The average effective permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core under test can be written as:

[0109]

[0110] Based on the initial permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core obtained through the above measurements... ,length equivalent diameter d core and the constants obtained by data fitting. k The maximum effective permeability of the tested rod-shaped iron-based nanocrystalline alloy magnetic core was obtained by solving the problem. Therefore, the expression for the effective permeability distribution function of the tested rod-shaped iron-based nanocrystalline alloy magnetic core with the same cross-sectional area but different lengths is obtained as follows:

[0111] .

[0112] Based on the same inventive concept, another embodiment of the present invention provides a measuring device for the low-frequency distribution of effective permeability of a rod-shaped magnetic core. This device corresponds to the method of the aforementioned embodiment and includes:

[0113] The recording unit is used to wind a test coil on a coil bobbin, measure the winding length of the test coil, and record the number of turns.

[0114] The measurement unit is used to insert the test core into different positions of the test coil and measure the inductance of the test coil when the test core is in different positions; the test core is a rod-shaped iron-based nanocrystalline alloy core.

[0115] The calculation unit is used to calculate the average effective permeability of the test core at different locations based on the permeability-inductance relationship.

[0116] The fitting unit is used to fit the effective permeability distribution function of the test magnetic core based on a preset algorithm.

[0117] The determination unit is used to derive the effective permeability distribution function of the test rod-shaped iron-based nanocrystalline alloy core based on the effective permeability distribution function of the test core; the test rod-shaped iron-based nanocrystalline alloy core has the same cross-sectional area but a different length from the test core.

[0118] The following is a specific embodiment of the present invention.

[0119] The first step of this experiment, in order to determine the effective permeability distribution of a square iron-based nanocrystalline alloy magnetic core with a length of 25cm and a cross-section with a side length of 0.5cm, involved designing a length l using enameled wire with a diameter of 0.3mm. coil A three-layer test coil with a diameter of 2.8 cm and 228 turns. Figure 2a , Figure 2b The images shown are a model diagram and a physical diagram of the test coil.

[0120] Since enameled wire cannot be directly wound onto a magnetic core, a coil bobbin made of a specific material is needed to solve this problem. The bobbin is made of a non-ferromagnetic, non-metallic material with high temperature stability (i.e., a low coefficient of thermal expansion) and the lowest possible dielectric constant; nylon and phenolic resin are typically chosen as the materials. When winding the test coil, the enameled wire needs to be wound tightly against the coil bobbin to ensure accurate inductance measurements.

[0121] The second step involves calibrating the E4980AL impedance analyzer using open / short circuit calibration to avoid the influence of parasitic parameters on the experiment. The circuit mode of the E4980AL impedance analyzer is adjusted to series mode. Since lower measurement frequencies yield more accurate DC inductance measurements, the excitation signal frequency of the E4980AL impedance analyzer is adjusted to 20Hz, which is also the lowest measurement frequency that the analyzer can be set to. The magnetic core under test is inserted into the test coil, ensuring that one end of the test coil coincides with one end of the magnetic core. The coordinates of the test coil endpoints are recorded with the center of the magnetic core as the origin. The E4980AL impedance analyzer is connected using the four-terminal method, and the inductance data is recorded. The test coil is then moved, and the coordinates and inductance are recorded at 1cm intervals until the endpoint of the test coil coincides with the other end of the magnetic core. This process is repeated three times. While ensuring accuracy, the average of the three inductance measurements is taken. This yields M sets of inductance data. x n L n}

[0122] The third step is to calculate the average effective permeability of the magnetic core in different coordinate ranges based on the functional relationship between the inductance, the test coil, and the relevant parameters of the magnetic core. By substituting the relevant known parameters, the relationship between the average effective permeability and the coordinates in different regions of the magnetic core can be established.

[0123] Fourth, based on the average effective permeability distribution values ​​of different regions obtained in the third step, assume that the effective permeability distribution function of the iron-based nanocrystalline alloy core is... , Let x be the x-coordinate of the starting position of the measuring coil in the nth measurement, then the average effective permeability of the region in the nth measurement is... It can be written as:

[0124]

[0125] The effective permeability distribution function of an iron-based nanocrystalline alloy magnetic core is a parabolic function with the highest effective permeability at the center of the core, gradually decreasing towards both sides. Therefore, the distribution function can be written as:

[0126]

[0127] in If the effective permeability of the magnetic core is the maximum value, and the effective permeability is greatest in the central region of the magnetic core, then the origin of the above distribution function is at the midpoint of the magnetic core. It is a constant. Let be the length of the magnetic core. Specifically, for the magnetic core under test, the parameter to be fitted can be expressed as: Then the function to be fitted can be written as:

[0128]

[0129] Based on the LM algorithm, the above function is fitted using measurement data. The LM algorithm can be expressed as follows.

[0130]

[0131] The initial step in fitting the core distribution function using the LM algorithm requires estimating the parameters to be fitted, i.e. , This is an estimate of the maximum effective permeability of the magnetic core under test. For parameters The estimated value, of which The following calculation method is used to obtain the average effective permeability. These are estimated values.

[0132]

[0133] As an increment, in solving the th Increment calculated after the next iteration The updated parameters are expressed as follows:

[0134]

[0135] in r For the residual vector, To measure magnetic permeability, Fit the permeability to the model. The residual vector in the next iteration can be expressed as follows:

[0136]

[0137] For Jacobian matrices, Let be the transpose of the Jacobian matrix. Under this measurement method, the elements of the Jacobian matrix can be expressed as: . diag This is to extract the diagonal elements of the matrix. This is the damping factor (controlling the step size), and its initial value needs to be preset before the iterative algorithm begins. The initial value is set to 0.01.

[0138] Specifically, the first Damping factor in the next iteration calculation The following strategies can be used for adaptive adjustment, where

[0139]

[0140] in The coefficient of determination can be expressed as follows:

[0141]

[0142] In this fitting process, after iterations, the iteration stopped because the rate of change of the correlation coefficient was less than 0.001, and the obtained fitting parameters were... So, if Figure 3 As shown, for a square iron-based nanocrystalline alloy magnetic core with a length of 25 cm and a cross-section of 0.5 cm, the spatial distribution function of its effective permeability is:

[0143]

[0144] Fifth, to ensure the rigor and accuracy of the model, the cross-sectional area of ​​the magnetic core is kept constant, and only the length of the magnetic core is changed. The effective permeability distribution of iron-based nanocrystalline alloy magnetic cores with lengths of 20cm and 30cm under the same area is estimated.

[0145] For a magnetic core of a given size and shape, its average effective permeability is mainly related to its demagnetization factor and initial permeability, and can be expressed as follows:

[0146]

[0147] In the formula The initial permeability of the magnetic core is mainly related to the material of the core. For iron-based nanocrystalline alloys, the initial permeability of the core at 20Hz is... , The demagnetizing factor can be specifically expressed as follows:

[0148]

[0149] in The aspect ratio of the magnetic core. For a square magnetic core, it can be calculated as an equivalent cylindrical magnetic core, then the equivalent diameter is... , Given the cross-sectional area of ​​the magnetic core, the aspect ratio for 20cm and 30cm magnetic cores can be calculated as follows: , Therefore, the effective permeability of 20cm and 30cm magnetic cores can be calculated as follows. , .

[0150] Similarly, assume that the effective permeability distribution function of the magnetic core to be estimated is...

[0151]

[0152] Therefore, for magnetic cores of the same area and length (20cm and 30cm), the overall average effective permeability can be expressed as follows:

[0153]

[0154]

[0155] Solving the above equation yields... , .

[0156] For iron-based nanocrystalline alloy magnetic cores with square cross-sections of 0.5 cm and lengths of 20 cm and 30 cm respectively, their effective permeability distribution functions are as follows:

[0157]

[0158]

[0159] To verify the accuracy of the method of the present invention, the inductance at different positions of magnetic cores with aspect ratios of 35.44 and 53.18 (i.e., lengths of 20 cm and 30 cm, respectively) were measured using test coils, and the effective average permeability of different regions was calculated. Subsequently, the permeability distribution function obtained by fitting was compared with the effective permeability estimated in the fifth step using the LM algorithm.

[0160] Based on the above steps, the effective distribution of the 20cm and 30cm iron-based nanocrystalline alloy magnetic cores obtained by measurement is as follows:

[0161]

[0162]

[0163] The relative error between the predicted and measured values ​​is compared using the following formula.

[0164]

[0165]

[0166] Figure 4 The image shows the estimated and measured values ​​of the effective permeability distribution of a magnetic core with an aspect ratio of 35.5, as well as the error between the two values, which ranges from 4.94% to 5.24%.

[0167] Figure 5 The image shows the estimated and measured values ​​of the effective permeability distribution of a magnetic core with an aspect ratio of 53.18, as well as the error between the two values, which ranges from 1.83% to 1.92%.

[0168] from Figure 4 and Figure 5 As can be seen from the present invention, there is a certain error between the estimated value of magnetic permeability distribution of the magnetic core obtained by the method of the present invention and the measured value. The error is larger in the central region of the magnetic core, but the maximum error does not exceed 5.5%. Therefore, it can be considered that the method can estimate the effective permeability distribution of iron-based nanocrystalline alloy magnetic cores of different lengths with the same cross-sectional area.

[0169] In summary, this invention proposes a method and apparatus for measuring the low-frequency distribution of effective permeability in rod-shaped magnetic cores, aiming to solve the problems of insufficient accuracy, high experimental costs, and inaccurate distribution estimation in traditional measurement methods. By optimizing the test coil structure design and combining low-frequency, high-precision inductance measurement technology, the inductance of the magnetic core at different locations is obtained. Using the functional relationship between inductance and permeability, the average effective permeability of each local region is calculated. Furthermore, a dynamic adaptive nonlinear fitting model based on the LM algorithm is employed to construct the spatial distribution function of permeability in the magnetic core, achieving high-resolution local permeability measurement and accurate estimation of permeability distribution across dimensions. This method introduces a three-level error control system, including hardware calibration, coil winding specifications, and fitting algorithm verification, significantly reducing measurement errors and improving modeling reliability. Using this technology, the effective permeability distribution function of iron-based nanocrystalline alloy magnetic cores of different lengths with the same cross-sectional area can be calculated using measured magnetic core data, thereby reducing repeated experiments and improving modeling efficiency.

[0170] In the development of inductive search coils, understanding the precise distribution of effective permeability on the magnetic core is of great significance. Effective permeability is primarily determined by the aspect ratio and initial permeability of the magnetic core. In inductive search coils, the aspect ratio of the magnetic core is typically between 20 and 60. When the initial permeability is greater than 10,000, its variation has a relatively small impact on the effective permeability; at this point, the variation in effective permeability is more dominated by the aspect ratio. Iron-based nanocrystalline alloys possess high initial permeability and remain stable within the commonly used operating frequency range of inductive search coils. This allows the effective permeability measured at low frequencies to not only reflect the characteristics of the magnetic core itself but also to be used for modeling, performance evaluation, and sensitivity analysis across the entire operating frequency range. Furthermore, the lower the measurement frequency, the closer the spatial distribution of the obtained effective permeability is to the true value, resulting in more accurate modeling results.

[0171] The method provided by this invention can reduce the number of processing steps and experimental procedures for iron-based nanocrystalline alloy magnetic core samples while ensuring measurement accuracy, thereby significantly reducing R&D costs and time. Simultaneously, this method provides key parameter support for the modeling, design, and performance optimization of inductive search coils, and has broad engineering application value in fields such as geological exploration, space physics, and electromagnetic environment monitoring. By accurately characterizing the effective permeability distribution of the magnetic core, it effectively solves the problems of large estimation errors and model mismatches in traditional methods, providing a solid data foundation and theoretical basis for the development of high-performance inductive magnetic sensors.

[0172] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the embodiments disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. It should be understood that the invention is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method of measuring the low frequency distribution of the effective permeability of a bar core, characterized in that, The method comprises the following steps: winding a test coil on a coil former, measuring the winding length of the test coil and recording the number of winding turns; inserting a test magnetic core into different positions of the test coil and measuring the inductance of the test coil when the test magnetic core is in different positions; the test magnetic core is a rod-shaped iron-based nanocrystalline alloy magnetic core; calculating the area average effective permeability of the test magnetic core in different positions according to a permeability-inductance relationship; fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm; obtaining the effective permeability distribution function of a to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core according to the effective permeability distribution function of the test magnetic core; the to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core has the same cross-sectional area as the test magnetic core but a different length; the step of inserting the test magnetic core into different positions of the test coil and measuring the inductance of the test coil when the test magnetic core is in different positions comprises: after the test magnetic core is inserted into the test coil, connecting the test coil and an impedance analyzer by a four-terminal connection method; establishing a coordinate system with the axial direction of the test magnetic core as the transverse axis and the middle of the test magnetic core as the origin; The left of the origin is recorded as a negative value, and the right of the origin is recorded as a positive value, and the test coil is gradually moved at equal intervals from left to right in the interval , and the starting position horizontal coordinate and the inductance of the test coil after each movement are measured to form an inductance data set x n , L n}, n=1, 2, 3, …, M, M is the number of measurements, x n is the starting position horizontal coordinate of the test coil for the nth measurement, L n is the inductance of the test coil for the nth measurement, l core is the test magnetic core length; the permeability-inductance relationship is: wherein, is the area average effective permeability for the nth measurement, is the permeability of vacuum, is the number of turns of the test coil, is the cross-sectional area of the test core, l core is the length of the test core, is the length of the test coil; the expression of the area average effective permeability is: wherein is the area-averaged effective permeability for the nth measurement, is the effective permeability distribution function of the test core.

2. The method of measuring the low-frequency distribution of the effective permeability of a bar core according to claim 1, characterized in that, the winding length of the test coil is 10%±5% of the length of the test magnetic core, and the number of winding turns is greater than 200 turns.

3. The method of measuring the low-frequency distribution of the effective permeability of a bar core according to claim 1, characterized in that, the coil former is made of a non-ferromagnetic and non-metallic material.

4. The method of measuring the low-frequency distribution of the effective permeability of a rod-shaped core according to claim 1, characterized in that, the step of fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm comprises: from the inductance data set { x n , L n} and the permeability-inductance relationship { x n , } a permeability data set is derived the effective permeability distribution function of the test magnetic core is written as: wherein is the maximum value of the effective permeability of the magnetic core, is a constant; Based on the permeability data set , } using the Levenberg-Marquardt algorithm to obtain the maximum value of the effective permeability of the test magnetic core and the constant , thereby determining the expression of the effective permeability distribution function of the test magnetic core .

5. The method of measuring the low-frequency distribution of the effective permeability of a bar core according to claim 4, characterized in that, in the Levenberg-Marquardt algorithm, the termination condition is that the correlation coefficient change rate is less than 0.001 or the iteration number is greater than 200.

6. The method of measuring the low-frequency distribution of the effective permeability of a bar core according to claim 4, characterized in that, the step of obtaining the effective permeability distribution function of the to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core according to the effective permeability distribution function of the test magnetic core comprises: the calculation formula of the area average effective permeability of the to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core is: wherein is the initial permeability of the rod-shaped iron-based nanocrystalline alloy magnetic core to be measured; is the demagnetization factor, In the formula, L / D is the length-diameter ratio of the rod-shaped iron-based nanocrystalline alloy magnetic core to be measured, In the formula, The length of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested. d core The equivalent diameter of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested; If the cross section of the rod-shaped iron-based nanocrystalline alloy magnetic core to be measured is circular, then d core is equal to the diameter of the circle; if the cross section of the rod-shaped iron-based nanocrystalline alloy magnetic core to be measured is square, then wherein A is the cross-sectional area of the square; the area average effective permeability of the to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core is written as: According to the initial permeability of the to-be-tested rod-shaped iron-based nanocrystalline alloy magnetic core , length , equivalent diameter d core , and the constant k , the maximum effective permeability of the to-be-tested rod-shaped iron-based nanocrystalline alloy magnetic core is solved , and the expression of the effective permeability distribution function of the to-be-tested rod-shaped iron-based nanocrystalline alloy magnetic core is obtained. 。 7. A measuring device for the low frequency distribution of the effective permeability of a bar core, characterized in that The device for realizing the measurement method of the low-frequency distribution of the effective permeability of the rod-shaped magnetic core according to any one of claims 1-6 comprises: a recording unit for winding a test coil on a coil former, measuring the winding length of the test coil and recording the number of winding turns; a measuring unit for inserting a test magnetic core into different positions of the test coil and measuring the inductance of the test coil when the test magnetic core is in different positions; the test magnetic core is a rod-shaped iron-based nanocrystalline alloy magnetic core; a calculation unit for calculating the area average effective permeability of the test magnetic core in different positions according to a permeability-inductance relationship; a fitting unit for fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm; a determination unit for obtaining the effective permeability distribution function of a to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core according to the effective permeability distribution function of the test magnetic core; the to-be-measured rod-shaped iron-based nanocrystalline alloy magnetic core has the same cross-sectional area as the test magnetic core but a different length.

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