Method and device for measuring low-frequency distribution of effective magnetic conductivity of rod-shaped magnetic core

Abstract

The invention provides a method and a device for measuring low-frequency distribution of effective magnetic conductivity of a rod-shaped magnetic core, and relates to the technical field of low-frequency fluctuation detection and application. The method comprises the following steps: winding a test coil on a coil framework, measuring the winding length of the test coil and recording the number of winding turns; inserting the test magnetic core into different positions of the test coil, and measuring the inductance of the test coil at the different positions of the test magnetic core; according to the magnetic conductivity-inductance relational expression, calculating the regional average effective magnetic conductivity of the test magnetic core at different positions; fitting an effective magnetic conductivity distribution function of the test magnetic core based on a preset algorithm; and obtaining the effective magnetic conductivity distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested according to the effective magnetic conductivity distribution function of the test magnetic core. According to the method, the effective magnetic conductivity measurement error of the magnetic core can be reduced, the modeling reliability is improved, and the effective magnetic conductivity distribution function is obtained, so that repeated experiments are reduced, and the modeling efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the field of low-frequency fluctuation detection and application technology, and in particular to a method and device for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core. Background Art

[0002] Inductive search coils are based on Faraday's law of electromagnetic induction and have the advantages of high sensitivity, good stability, and fast response. They have been widely used in many fields such as magnetotelluric sounding, space physics, and biomedicine. In geological resource exploration, electromagnetic methods can determine the distribution status and basement composition of underground rocks by detecting changes in the electromagnetic properties of rock formations. In the field of space science, inductive coils can serve as important equipment for observing changes in the geomagnetic field, serving space environment monitoring and space physical process research. 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 available frequency band for electromagnetic exploration and the accuracy of detection results, and plays a key role in the signal response capability and application depth of the overall system.

[0003] In this type of magnetic sensor, the effective permeability of the magnetic core is one of the key 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 affected by the core's permeability. The spatial distribution of permeability within the core structure not only affects the overall value of the inductance but also determines key technical specifications such as the sensor's operating frequency band, sensitivity, and minimum resolvable magnetic field change. In low-frequency applications, inductive sensors are particularly dependent on the core's performance. Because the initial permeability of iron-based nanocrystalline materials changes 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 relies heavily on empirical formulas or simplified models. The applicability of these formulas to the actual material properties of specific iron-based nanocrystalline cores remains uncertain. Simplified models often struggle to accurately reflect the permeability gradient variations across different regions of the core, which in turn affects the magnetic field response and system simulation accuracy. Summary of the Invention

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

[0006] In order to achieve the above object, the present invention provides a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core, comprising: Wind the test coil on the coil frame, measure the winding length of the test coil and record the number of winding turns; 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; Calculate the average effective permeability of the test core at different locations based on the permeability-inductance relationship; Fit the effective permeability distribution function of the test core based on a preset algorithm; The effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy core to be tested is obtained according to the effective permeability distribution function of the test core; the rod-shaped iron-based nanocrystalline alloy core to be tested and the test core have the same cross-sectional area but different lengths.

[0007] According to a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core provided by the present invention, 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.

[0008] According to a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core provided by the present invention, the coil skeleton is made of a non-ferromagnetic, non-metallic material.

[0009] According to a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core provided by the present invention, a test core is inserted into different positions of a test coil, and the inductance of the test coil is measured when the test core is at different positions, including: After inserting the test core into the test coil, connect the test coil to the impedance analyzer using the four-terminal wiring method; Establish a coordinate system with the axial direction of the test core as the horizontal axis and the center of the test core as the origin; The left side of the origin is recorded as a negative value, the right side of the origin is recorded as a positive value, and in the interval The test coil is gradually moved from left to right at equal intervals, and the starting position abscissa and inductance of the test coil are measured after each movement to form an inductance data set { x n , L n}, n=1,2,3,…, M, M is the number of measurements, x n L is the starting position abscissa of the test coil for the nth measurement, n is the inductance of the test coil measured for the nth time, To test the core length.

[0010] According to a method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core provided by the present invention, the magnetic permeability-inductance relationship is:

[0011] in, is the regional average effective permeability under the nth measurement, is the vacuum permeability, is the number of turns of the test coil, To test the core cross-sectional area, l core To test the core length, is the winding length of the test coil.

[0012] According to a method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core provided by the present invention, the expression of the regional average effective magnetic permeability is:

[0013] Where, is the regional average effective permeability under the nth measurement, is the effective permeability distribution function of the test core.

[0014] According to the present invention, a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core is provided. The method fits the effective magnetic permeability distribution function of the test magnetic core based on a preset algorithm, comprising: According to the inductance data set { x n , L n} and the permeability-inductance relationship to obtain the permeability data set { x n , }; The effective permeability distribution function of the test core is written as:

[0015] Where, To test the maximum effective magnetic permeability of the core, is a constant; Based on the magnetic permeability data set { , The Levenberg-Marquardt algorithm (LM algorithm) is used to obtain the maximum effective permeability of the test core. and constant , thereby determining the effective permeability distribution function of the test core expression.

[0016] According to a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core provided by the present invention, in the LM algorithm, the termination condition is that the correlation coefficient change rate is less than 0.001 or the number of iterations is greater than 200.

[0017] According to a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core provided by the present invention, the effective magnetic permeability distribution function of the rod-type iron-based nanocrystalline alloy magnetic core to be tested is obtained according to the effective magnetic permeability distribution function of the test magnetic core, including: The calculation formula for the average effective magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested is:

[0018] Where, is the initial magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested; is the demagnetization factor,

[0019] Where, is the aspect ratio of the rod-shaped Fe-based nanocrystalline alloy core to be tested,

[0020] Where, is the length of the rod-shaped Fe-based nanocrystalline alloy core to be tested, d core is the equivalent diameter of the rod-shaped Fe-based nanocrystalline alloy core to be tested; If the cross section of the rod-shaped Fe-based nanocrystalline alloy core to be tested is circular, then d core is equal to the diameter of the circle; if the cross section of the rod-shaped Fe-based nanocrystalline alloy core to be tested is square, then

[0021] Where A is the cross-sectional area of ​​the square.

[0022] The average effective magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested is written as:

[0023] According to the initial magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested ,length , equivalent diameter d core , and the constant k , solve and get the maximum effective permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested , and then the expression of the effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy core to be tested is obtained as follows: .

[0024] In a second aspect, the present invention provides a device for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core, comprising: a recording unit, used for winding a test coil on a coil bobbin, measuring the winding length of the test coil and recording the number of winding turns; A measuring unit is used to insert a test core into different positions of a 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; A calculation unit, used for calculating the average effective magnetic permeability of the test core at different positions according to the magnetic permeability-inductance relationship; A fitting unit, used for fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm; The determination unit is used to obtain the effective magnetic permeability distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested according to the effective magnetic permeability distribution function of the test magnetic core; the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested and the test magnetic core have the same cross-sectional area but different lengths.

[0025] The present invention has at least the following technical effects: The present invention provides a method and device for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core. In combination with low-frequency inductance measurement technology, the average inductance at different positions of the magnetic core is measured, and the functional relationship between inductance and magnetic permeability is used to calculate the regional average effective magnetic permeability. On this basis, the LM algorithm is used to perform dynamic adaptive nonlinear fitting on the quadratic function distribution model of magnetic permeability. The iteration termination condition is set by the correlation coefficient change rate and the number of iterations. Combined with the demagnetization factor theory, the cross-size magnetic permeability distribution of magnetic cores with the same cross-section and different lengths is calculated. The present invention constructs a three-level error control system with hardware calibration, coil winding specifications and fitting algorithms as the core, which effectively controls the overall measurement error within a low range. Compared with traditional methods that rely on a large number of actual measurements or empirical formulas for estimation, this method can deduce the spatial effective magnetic permeability distribution of magnetic cores of the same material series based only on test data of magnetic cores of a single size, significantly reducing experimental costs and improving modeling efficiency. The present invention can provide high-precision magnetic 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 magnetic permeability estimation accuracy and poor adaptability in traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0027] In the attached figure: Figure 1 This is a flow chart of a method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to the present invention; Figure 2a 、 Figure 2b They are respectively a model diagram and a physical diagram of a test coil according to an embodiment of the present invention; Figure 3 The permeability fitting result diagram and residual distribution diagram of the 25 cm magnetic core of the embodiment of the present invention are shown in FIG. Figure 4 The permeability distribution curve and estimated error curve of a 20 cm magnetic core according to an embodiment of the present invention are shown; Figure 5 Graph showing the magnetic permeability distribution curve and estimated error curve of a 30 cm magnetic core according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0029] The following will describe some embodiments of the present invention in detail with reference to the accompanying drawings. In the absence of conflict, the following embodiments and features in the embodiments may be combined with each other.

[0030] This invention establishes a measurement and modeling method that accurately reflects the effective permeability distribution within a magnetic core. This method is of great significance for improving the design accuracy and practical application of inductive sensors. This method not only helps to address technical challenges such as large permeability estimation errors and poor model adaptability, but also provides solid data support and theoretical basis for the application of inductive search coils in a wider range of scenarios.

[0031] See also Figure 1 The embodiment of the present invention provides a method for measuring the low-frequency distribution of the effective magnetic permeability of a rod-shaped iron-based nanocrystalline alloy magnetic core, which is used to solve the problem of large deviation in the estimation of the effective magnetic permeability distribution of the iron-based nanocrystalline alloy magnetic core, including the following steps: S1. Wind the test coil on the coil frame, measure the winding length of the test coil and record the number of winding turns.

[0032] Specifically, the winding length of the test coil is 10% ± 5% of the length of the test core, and the number of turns is greater than 200. The coil frame is made of non-ferromagnetic, non-metallic materials, usually nylon or phenolic resin materials, which have high temperature stability and low dielectric constant. The test coil is tightly wound on the coil frame with enameled wire. The winding length of the test coil is , the number of winding turns is N.

[0033] S2, inserting the test core into different positions of the test coil and measuring 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; Specifically, the test core length is l core , the cross-sectional area of ​​the test 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 for 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 a certain extent, the lower the measured frequency, the closer the measured equivalent inductance will be to the DC inductance of the test coil, and the smaller the impact of the parasitic capacitance of the test coil on the result will be, so the measurement result will be more accurate; the higher the measured frequency, the greater the measurement error will be.

[0034] The horizontal axis is the axial direction of the test core ( x axis), the center of the test core is taken as the origin, and a coordinate system is established; in this coordinate system, x The positive direction of the axis points to the right, the origin is the center of the test core, the left side of the origin is recorded as a negative value, the right side of the origin is recorded as a positive value, in the interval Move the test coil gradually from left to right at equal intervals, and measure the distance between the starting position of the test coil and the origin (i.e., the middle point of the magnetic core). That is, measure the starting position abscissa and inductance of the test coil after each movement to form an inductance data set { x n , L n}, n=1,2,3,…, M, M is the number of measurements, x n L is the starting position abscissa of the test coil for the nth measurement, n is the inductance of the test coil measured for the nth time, l core To test the core length.

[0035] S3, calculate the average effective permeability of the test core at different locations based on the permeability-inductance relationship; Specifically, is the average effective permeability of the region under the nth measurement. The permeability-inductance relationship can be expressed as follows:

[0036] in, is the regional average effective permeability under the nth measurement, is the vacuum permeability, which is , is the number of turns of the test coil, To test the core cross-sectional area, l core To test the core length, is the winding length of the test coil.

[0037] Specifically, the data set and The following relationship is satisfied:

[0038] in, is the abscissa of the starting position of the measuring coil in the nth measurement; The effective permeability distribution function of the test core is to be determined.

[0039] S4, fitting the effective permeability distribution function of the test core based on a preset algorithm; In some embodiments, the effective permeability distribution function of the test magnetic core is fitted using the LM algorithm. S4 specifically includes: After the above formula conversion, that is, according to the inductance data set { x n , L n} and the permeability-inductance relationship to obtain the permeability data set { x n , }; The effective permeability distribution function of the test core is a parabolic function with the maximum effective permeability at the center of the test core and gradually decreasing on both sides. The distribution function can be written as follows:

[0040] in, The maximum effective permeability of the test core is obtained, and the effective permeability of the core center area is the largest. The origin of the above distribution function is at the midpoint of the test core. kis a constant. Some studies have shown that this constant has nothing to do with the core material and size. However, in order to ensure the accuracy of the research, the present invention controls other conditions unchanged and only changes the length of the core. In this case, the constant is considered to be constant.

[0041] For the test core, the parameters to be fitted can be expressed as Based on the magnetic permeability data set { , The maximum effective permeability of the test core can be obtained using the LM algorithm. and constant , thereby determining the effective permeability distribution function of the test core expression.

[0042] Specifically, the LM algorithm can be expressed as follows:

[0043] Since the LM algorithm is an iterative algorithm, it is necessary to estimate the parameters to be fitted before fitting the effective permeability distribution function of the core using the LM algorithm, that is, , is the estimated value of the maximum effective permeability of the core to be tested, For constant The estimated value of Usually no more than 4, so for the constant It can be estimated that .

[0044] Specific It can be estimated according to the following formula, using the average value of the measured regional average effective permeability Instead of an estimate.

[0045]

[0046] So, As the increment, in solving the The increment after the iteration The updated parameters are expressed as follows:

[0047] So, is the residual vector, The residual vector in the iterative calculation can be expressed as follows: To measure magnetic permeability, Fit the magnetic permeability to the model.

[0048]

[0049] Specifically, is the Jacobian matrix, is the transposed matrix of the Jacobian matrix. Under the measurement method of the present invention, the Jacobian matrix elements can be expressed as . diag To get the diagonal elements of the matrix. is the damping factor (control step size), and the initial value needs to be preset before the iterative algorithm is performed. Generally, The initial value can be set to 0.001.

[0050] Then, Damping factor in the iterative calculation Adaptive adjustment can be performed according to the following strategy:

[0051] Specifically, R 2 is the coefficient of determination, which can be expressed as follows

[0052] Specifically, the iteration termination condition of the LM algorithm can be expressed as the correlation coefficient change rate < 0.001 or the number of iterations is greater than 200 times. When the iteration is terminated, the parameter to be optimized can be obtained. After confirming the parameters, the effective permeability distribution function of the test core can be obtained. expression. S5, obtaining an effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested according to the effective permeability distribution function of the test magnetic core; the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested and the test magnetic core have the same cross-sectional area but different lengths.

[0053] Specifically, the calculation formula for the average effective magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested is:

[0054] Where, is the initial magnetic permeability of the rod-type iron-based nanocrystalline alloy core to be tested. For the iron-based nanocrystalline alloy core, it is necessary to find the initial magnetic permeability at the test frequency based on the distribution relationship between the initial magnetic permeability of the iron-based nanocrystalline alloy core and the frequency. This parameter is generally provided by the manufacturer and is related to the process, material and structure. is the demagnetization factor, which can be expressed as follows:

[0055] in is the aspect ratio of the rod-shaped Fe-based nanocrystalline alloy core to be tested,

[0056] in is the length of the rod-shaped Fe-based nanocrystalline alloy core to be tested, d core is the equivalent diameter of the rod-shaped Fe-based nanocrystalline alloy core to be tested. If the cross section of the rod-shaped Fe-based nanocrystalline alloy core to be tested is circular, then d core Equal to the diameter of the circle; for a magnetic core with a square cross section, it needs to be equivalent to a cylindrical magnetic core for calculation. The equivalent calculation formula is as follows, where A is the cross-sectional area of ​​the square,

[0057] The average effective magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested can be written as:

[0058] According to the initial magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested obtained by the above measurement ,length , equivalent diameter d core , and the constants obtained by fitting the data k , solve and get the maximum effective permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested , and then the expression of the effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy core to be tested with the same cross-sectional area and different lengths is obtained: .

[0059] Based on the same inventive concept, another embodiment of the present invention provides a device for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core. The device corresponds to the method of the aforementioned embodiment, and includes: a recording unit, used for winding a test coil on a coil bobbin, measuring the winding length of the test coil and recording the number of winding turns; A measuring unit is used to insert a test core into different positions of a 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; A calculation unit, used for calculating the average effective magnetic permeability of the test core at different positions according to the magnetic permeability-inductance relationship; A fitting unit, used for fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm; The determination unit is used to obtain the effective magnetic permeability distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested according to the effective magnetic permeability distribution function of the test magnetic core; the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested and the test magnetic core have the same cross-sectional area but different lengths.

[0060] The following is a specific embodiment of the present invention.

[0061] In the first step, in order to obtain the effective permeability distribution of a square iron-based nanocrystalline alloy core with a length of 25 cm and a cross-section of 0.5 cm, an enameled wire with a diameter of 0.3 mm was used to design a length l coil The three-layer test coil is 2.8 cm long and has 228 turns. Figure 2a 、 Figure 2b These are the model and actual pictures of the test coil respectively.

[0062] Because enameled wire cannot be wound directly onto a magnetic core, a coil bobbin made of a specific material is required to solve this problem. The coil bobbin must be made of a non-ferromagnetic, non-metallic material with high temperature stability (i.e., a low coefficient of expansion) and the lowest possible dielectric constant. Typical materials used are nylon and phenolic resin. When winding the test coil, the enameled wire must fit snugly around the coil bobbin to ensure accurate inductance measurements.

[0063] The second step is to use open circuit / short circuit calibration of the E4980AL impedance analyzer to avoid the influence of parasitic parameters on the experiment. The circuit mode of the E4980AL impedance analyzer is adjusted to series mode. Since the lower the measurement frequency, the more accurate the measurement result of DC inductance, the excitation signal frequency of the E4980AL impedance analyzer is adjusted to 20Hz, which is also the lowest measurement frequency that the impedance analyzer can be set to. Insert the magnetic core to be measured into the test coil and ensure that one end of the test coil coincides with one end of the magnetic core to be measured. With the center position of the magnetic core to be measured as the origin, record the endpoint coordinates of the test coil at this time. Use the four-terminal method to connect the E4980AL impedance analyzer and record the inductance data. Then move the test coil and record the coordinates and inductance at this time at intervals of 1cm each time until the endpoint of the test coil coincides with the other end of the magnetic core to be measured. Then repeat the above operation three times. Under the premise of ensuring the accuracy of the operation, take the average value of the inductance data of the three measurements. Get M groups of inductance data sets { x n , L n}.

[0064] The third step is to calculate the average effective magnetic permeability within different coordinate ranges of the magnetic core based on the functional relationship between the inductance and the test coil and core-related parameters. Substituting the relevant known parameters, the relationship between the average effective magnetic permeability and coordinates in different areas of the magnetic core can be established.

[0065] The fourth step is to assume that the effective permeability distribution function of the iron-based nanocrystalline alloy core is: , is the horizontal coordinate of the starting position of the measuring coil under the nth measurement, then the average effective permeability of the region under the nth measurement is It can be written as:

[0066] The effective permeability distribution function of the iron-based nanocrystalline alloy core is a parabolic function with the maximum effective permeability at the center of the core and gradually decreasing towards both sides. The distribution function can be written as:

[0067] in is the maximum value of the effective magnetic permeability of the core, and the effective magnetic permeability in the center area of ​​the core is the largest, then the origin of the above distribution function is at the midpoint of the core, is a constant, is the core length. Specifically, for the core to be tested, the parameter to be fitted can be expressed as , then the function to be fitted can be written as:

[0068] Based on the LM algorithm, the above function is fitted using the measured data. The LM algorithm can be expressed as the following formula.

[0069]

[0070] When fitting the core distribution function using the LM algorithm, it is necessary to estimate the parameters to be fitted, namely , is the estimated value of the maximum effective permeability of the core to be tested, For the parameters The estimated value of It is calculated by the following method, that is, the average value of the measured effective permeability is an estimated value.

[0071]

[0072] As the increment, in solving the The increment after the iteration The updated parameters are expressed as follows:

[0073] in r is the residual vector, To measure magnetic permeability, Fit the magnetic permeability to the model. The residual vector in the iterative calculation can be expressed as follows:

[0074] is the Jacobian matrix, is the transposed matrix of the Jacobian matrix. Under this measurement method, the Jacobian matrix elements can be expressed as . diag To get the diagonal elements of the matrix. is the damping factor (control step size), and the initial value needs to be preset before the iterative algorithm is performed. The initial value is set to 0.01.

[0075] Specifically, then Damping factor in the iterative calculation Adaptive adjustment can be performed according to the following strategy:

[0076] in is the coefficient of determination, which can be expressed as follows

[0077] In this fitting, after iteration, the rate of change of the correlation coefficient is less than 0.001, so the iteration stops and the fitting parameters are obtained. , then if Figure 3 As shown in the figure, for a square iron-based nanocrystalline alloy core with a length of 25 cm and a cross section of 0.5 cm, the spatial distribution function of its effective magnetic permeability is:

[0078] In the fifth step, to ensure the rigor and accuracy of the model, the cross-sectional area of ​​the core is kept constant and only the core length is changed. The effective permeability distribution of the iron-based nanocrystalline alloy core with a length of 20 cm and 30 cm under the same area is estimated.

[0079] For a core of a given size and shape, its average effective permeability is mainly related to its demagnetization factor and initial permeability, which can be expressed as follows:

[0080] In the formula is the initial magnetic permeability of the core, which is mainly related to the material of the core. For iron-based nanocrystalline alloys, at 20Hz, the initial magnetic permeability of the core is , is the demagnetization factor, which can be expressed as follows:

[0081] in is the aspect ratio of the core, For a square core, it can be calculated as a cylindrical core, then the equivalent diameter is , is the cross-sectional area of ​​the core, then the aspect ratio of the core of 20cm and 30cm can be obtained by calculation , Then the effective magnetic permeability of the 20cm and 30cm cores can be calculated to be , .

[0082] Similarly, assuming that the effective permeability distribution function of the core to be estimated is

[0083] Then, for the same area, the overall average effective permeability of the 20cm and 30cm length cores can be written as follows

[0084]

[0085] According to the above equation, we can get , .

[0086] Then for the iron-based nanocrystalline alloy cores with a square cross section of 0.5 cm and lengths of 20 cm and 30 cm respectively, their effective permeability distribution functions are

[0087]

[0088] In order to verify the accuracy of the method of the present invention, the first to third steps are used to measure the inductance at different positions of the magnetic cores with aspect ratios of 35.44 and 53.18, that is, the lengths of the magnetic cores are 20 cm and 30 cm respectively, using a test coil, and the effective average magnetic permeability of different areas is calculated. Then, the LM algorithm is used to compare the fitted magnetic permeability distribution function with the effective magnetic permeability estimated in the fifth step.

[0089] Then according to the above steps, the effective distribution of the 20cm and 30cm iron-based nanocrystalline alloy cores is measured as follows:

[0090]

[0091] The relative error between the predicted value and the measured value is compared by the following formula

[0092]

[0093] Figure 4 The figure shows the estimated and measured effective permeability distribution of a core with an aspect ratio of 35.5, as well as the error between the two, which ranges from 4.94% to 5.24%.

[0094] Figure 5 The figure shows the estimated and measured effective permeability distribution of a core with an aspect ratio of 53.18, as well as the error between the two, which ranges from 1.83% to 1.92%.

[0095] from Figure 4 and Figure 5 It can be seen that there is a certain error between the estimated value of the magnetic permeability distribution of the magnetic core obtained by the method of the present invention and the measured value, and the error is larger in the center area of ​​the magnetic core, but the maximum error does not exceed 5.5%. Therefore, it can be considered that this method can better estimate the effective permeability distribution value of the iron-based nanocrystalline alloy magnetic core with different lengths under the same cross-sectional area.

[0096] In summary, the present invention proposes a method and device for measuring the low-frequency distribution of the effective magnetic permeability of a rod-type magnetic core, aiming to address the problems of insufficient precision, high experimental cost, 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 positions is obtained. The functional relationship between inductance and magnetic permeability is used to calculate the average effective magnetic permeability of each local area. A dynamic adaptive nonlinear fitting model based on the LM algorithm is further adopted to construct the spatial distribution function of magnetic permeability in the magnetic core, achieving high-resolution local magnetic permeability measurement and accurate estimation of cross-dimensional magnetic permeability distribution. This method introduces a three-level error control system, including hardware calibration, coil winding specifications, and fitting algorithm verification, which significantly reduces measurement errors and improves modeling reliability. Through this technology, the measured magnetic core data can be used to infer the effective magnetic permeability distribution function of iron-based nanocrystalline alloy magnetic cores with the same cross-sectional area and different lengths, thereby reducing repeated experiments and improving modeling efficiency.

[0097] In the development of inductive search coils, understanding the precise distribution of effective permeability across the magnetic core is crucial. Effective permeability is primarily determined by the core's aspect ratio and initial permeability. In inductive search coils, the core aspect ratio typically ranges from 20 to 60. When the initial permeability is greater than 10,000, its effect on the effective permeability is relatively small; at this point, the variation in effective permeability is more strongly influenced by the aspect ratio. Iron-based nanocrystalline alloys possess high initial permeabilities and remain stable within the operating frequency range commonly used in inductive search coils. This allows the effective permeability measured at low frequencies to not only reflect the core's intrinsic properties but also 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 effective permeability is to the true value, resulting in more accurate modeling results.

[0098] The method provided by the present invention can reduce the number of processing steps and experimental steps required for iron-based nanocrystalline alloy core samples while ensuring measurement accuracy, thereby significantly reducing R&D costs and time expenditures. At the same time, the method provides key parameter support for the modeling, design, and performance optimization of inductive search coils, and has broad engineering application value in geological exploration, space physics, electromagnetic environment monitoring, and other fields. By accurately characterizing the effective permeability distribution of the magnetic core, it can effectively solve the problems of large effective permeability estimation errors and model mismatch in traditional methods, providing a solid data foundation and theoretical basis for the development of high-performance inductive magnetic sensors.

[0099] Those skilled in the art will readily appreciate other embodiments of the present invention after considering the specification and practicing the embodiments disclosed herein. The present invention is intended to cover any variations, uses, or adaptations of the present invention that follow the general principles of the present invention and include common knowledge or customary techniques in the art not disclosed herein. It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and variations can be made without departing from the scope thereof. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core, characterized in that: include: Wind the test coil on the coil frame, measure the winding length of the test coil and record the number of winding turns; Inserting a test core into different positions of the test coil and measuring the inductance of the test coil at different positions of the test core; the test core is a rod-shaped iron-based nanocrystalline alloy core; Calculating the average effective magnetic permeability of the test core at different locations according to the magnetic permeability-inductance relationship; Fit the effective permeability distribution function of the test core based on a preset algorithm; The effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy core to be tested is obtained according to the effective permeability distribution function of the test core; the rod-shaped iron-based nanocrystalline alloy core to be tested and the test core have the same cross-sectional area but different lengths.

2. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic 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 for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 1, characterized in that: The coil frame is made of non-ferromagnetic and non-metallic materials.

4. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 1, characterized in that: Inserting the test core into different positions of the test coil and measuring the inductance of the test coil when the test core is at different positions includes: After inserting the test core into the test coil, the test coil is connected to an impedance analyzer using a four-terminal wiring method; Establish a coordinate system with the axial direction of the test core as the horizontal axis and the center of the test core as the origin; The left side of the origin is recorded as a negative value, the right side of the origin is recorded as a positive value, and in the interval The test coil is gradually moved from left to right at equal intervals, and the starting position abscissa and inductance of the test coil are measured after each movement to form an inductance data set { x n , L n }, n=1,2,3,…, M, M is the number of measurements, x n L is the starting position abscissa of the test coil for the nth measurement, n is the inductance of the test coil measured for the nth time, l core To test the core length.

5. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 4, characterized in that: The permeability-inductance relationship is: in, is the regional average effective permeability under the nth measurement, is the vacuum permeability, is the number of turns of the test coil, To test the core cross-sectional area, l core To test the core length, is the winding length of the test coil.

6. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 5, characterized in that: The expression of the average effective permeability of the region is: Where, is the regional average effective permeability under the nth measurement, is the effective permeability distribution function of the test core.

7. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 6, characterized in that: The method of fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm includes: According to the inductance data set { x n , L n } and the permeability-inductance relationship to obtain the permeability data set { x n , }; The effective permeability distribution function of the test core is written as: Where, To test the maximum effective magnetic permeability of the core, is a constant; Based on the magnetic permeability data set { , }Use the Levenberg-Marquardt algorithm to obtain the maximum effective permeability of the test core and constant , thereby determining the effective permeability distribution function of the test core expression.

8. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 7, 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 number of iterations is greater than 200.

9. The method for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core according to claim 7, characterized in that: The method of obtaining the effective magnetic permeability distribution function of the rod-shaped iron-based nanocrystalline alloy magnetic core to be tested according to the effective magnetic permeability distribution function of the test magnetic core includes: The calculation formula for the average effective magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested is: Where, is the initial magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested; is the demagnetization factor, Where, is the aspect ratio of the rod-shaped Fe-based nanocrystalline alloy core to be tested, Where, is the length of the rod-shaped Fe-based nanocrystalline alloy core to be tested, d core is the equivalent diameter of the rod-shaped Fe-based nanocrystalline alloy core to be tested; If the cross section of the rod-shaped Fe-based nanocrystalline alloy core to be tested is circular, then d core is equal to the diameter of the circle; if the cross section of the rod-shaped Fe-based nanocrystalline alloy core to be tested is square, then Where A is the cross-sectional area of ​​the square. The average effective magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested is written as: According to the initial magnetic permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested ,length , equivalent diameter d core , and the constant k , solve and get the maximum effective permeability of the rod-shaped iron-based nanocrystalline alloy core to be tested , and then the expression of the effective permeability distribution function of the rod-shaped iron-based nanocrystalline alloy core to be tested is obtained as follows: 。 10. A device for measuring the low-frequency distribution of effective magnetic permeability of a rod-type magnetic core, characterized in that: include: a recording unit, used for winding a test coil on a coil bobbin, measuring the winding length of the test coil and recording the number of winding turns; a measuring unit, configured to insert a test core into different positions of the test coil and measure the inductance of the test coil at different positions of the test core; the test core is a rod-shaped iron-based nanocrystalline alloy core; a calculation unit, configured to calculate the average effective magnetic permeability of the regions of the test magnetic core at different positions according to a magnetic permeability-inductance relationship; A fitting unit, used for fitting the effective permeability distribution function of the test magnetic core based on a preset algorithm; The determination unit is used to obtain the effective magnetic permeability distribution function of the rod-type iron-based nanocrystalline alloy magnetic core to be tested according to the effective magnetic permeability distribution function of the test magnetic core; the rod-type iron-based nanocrystalline alloy magnetic core to be tested and the test magnetic core have the same cross-sectional area and different lengths.

Images