Method and system for determining magnetic performance parameters of permanent magnet materials

Abstract

This invention provides a method and system for determining the magnetic properties of permanent magnet materials, relating to the field of magnetic property measurement technology for permanent magnet materials. The invention acquires the magnetic domain fluctuation signals of the permanent magnet material itself, calculates zero-delay cross-correlation values ​​to construct an initial spatial correlation matrix; under each bias field, it repeatedly acquires and calculates the current spatial correlation matrix, and obtains the correlation change matrix by subtracting it element-by-element from the initial matrix; it calculates the trace of the correlation change matrix and forms an evolution curve, using the second derivative to locate the characteristic demagnetizing field strength corresponding to the negative peak; it substitutes the characteristic demagnetizing field strength into a power-law relationship to obtain the coercivity, and simultaneously obtains the remanence by linearly amplifying the mean of the diagonal elements of the initial matrix, thus outputting the maximum magnetic energy product. This method can extract the characteristic demagnetizing field without applying a strong magnetic field, avoiding the damage to the material and empirical mapping errors of traditional methods, and achieving high-precision, non-destructive determination of the magnetic properties of permanent magnet materials.

Description

Technical Field

[0001] This invention relates to the field of magnetic property measurement technology for permanent magnet materials, specifically to a method and system for determining the magnetic property parameters of permanent magnet materials. Background Technology

[0002] The magnetic properties of permanent magnet materials mainly include coercivity, remanence, and maximum energy product. These parameters directly determine the application performance and service stability of permanent magnet materials in fields such as motors, sensors, wind power generation, and new energy vehicles. Accurately measuring the above-mentioned magnetic properties of permanent magnet materials is of great engineering significance for quality monitoring during the material production process, qualification determination before leaving the factory, and aging status assessment during service.

[0003] Currently, conventional methods for determining the coercivity and remanence of permanent magnet materials mainly employ closed-circuit measurement systems or open-circuit pulsed magnetic field measurement systems. Closed-circuit methods typically place the permanent magnet sample in a strong magnetic field provided by an electromagnet or superconducting magnet. By applying a gradually increasing reverse magnetic field and measuring the corresponding magnetic polarization intensity, a demagnetization curve is directly plotted, and the remanence and coercivity values ​​are then read from the curve. Open-circuit methods use a pulsed magnetic field generator to instantaneously magnetize and demagnetize the sample, using an induction coil to pick up the magnetic flux change signal. This signal is then combined with the sample's demagnetization factor for correction, and the magnetic performance parameters are calculated. In addition, in recent years, some non-destructive testing methods based on weak alternating magnetic field excitation have been developed. These methods measure the initial magnetization curve of the permanent magnet material under a weak field and then indirectly estimate the demagnetization curve parameters using a pre-established mapping relationship.

[0004] However, the aforementioned existing technologies still have insurmountable shortcomings in practical applications. On the one hand, both closed-circuit measurement and pulsed magnetic field measurement methods require applying a strong magnetic field close to or exceeding the coercivity of the permanent magnet material under test. For already magnetized finished permanent magnets, this process may cause irreversible local demagnetization or changes in the magnetic domain structure, which is a destructive or semi-destructive test and cannot meet the needs of online full inspection or in-situ non-destructive evaluation. On the other hand, although existing non-destructive testing methods based on weak alternating magnetic fields avoid damage to the material, they rely heavily on the empirical mapping relationship between the initial magnetization curve and the demagnetization curve. This mapping relationship is sensitive to changes in permanent magnet materials of different batches, shapes, and even temperatures, making it difficult to guarantee measurement accuracy and stability. In particular, it cannot distinguish between local demagnetization on the material surface and overall performance degradation.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for determining the magnetic properties parameters of permanent magnet materials, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for determining the magnetic property parameters of a permanent magnet material, comprising the following steps: Step 1: Attach multiple magnetic field sensors arranged in an array to the surface of the permanent magnet material to be tested. Under the condition of zero external magnetic field, collect the time-series fluctuation signals of magnetic induction intensity at the location of each magnetic field sensor. Calculate the cross-correlation function for any two fluctuation signals and extract the zero-delay cross-correlation value. Construct the initial spatial correlation matrix by using the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors. Step 2: Apply a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator. Repeatedly collect the time-series fluctuation signals of magnetic induction intensity of each magnetic field sensor under each DC bias magnetic field and calculate the current spatial correlation matrix. Perform element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix. Step 3: Calculate the trace of the relevant change matrix under each DC bias magnetic field, form the evolution curve of the trace value with the DC bias magnetic field, perform second derivative operation on the evolution curve, locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative, and denot it as the characteristic demagnetizing field strength. Step 4: Substitute the characteristic demagnetizing field strength into the coercivity power law relationship calibrated with a standard sample to calculate the coercivity value of the permanent magnet material to be tested. Extract the mean of all diagonal elements in the initial spatial correlation matrix and multiply it by the preset linear amplification factor to obtain the remanence value. Combine the coercivity value and the remanence value and obtain the maximum energy product value of the permanent magnet material to be tested through the maximum energy product calculation formula.

[0008] Furthermore, multiple magnetic field sensors arranged in an array are attached to the surface of the permanent magnet material to be tested in a grid with equal spacing, and the spacing between two adjacent magnetic field sensors is a preset fixed distance value. Under the condition of zero external magnetic field, the temporal fluctuation signal of magnetic induction intensity at each magnetic field sensor location is collected. Specifically, the induced voltage data within a preset time window is continuously collected using a sampling frequency not lower than a preset sampling frequency threshold, and the magnetic induction intensity temporal fluctuation signal corresponding to each magnetic field sensor is obtained after analog-to-digital conversion.

[0009] Furthermore, the specific method for calculating the cross-correlation function and extracting the zero-delay cross-correlation value for any two magnetic induction intensity time-series fluctuation signals is as follows: For any two magnetic field sensors, one magnetic field intensity time-series fluctuation signal sequence is kept fixed on the time axis, while the other magnetic field intensity time-series fluctuation signal sequence is shifted relative to it by different delay time steps. At each delay time step, the sum of the products of the corresponding position data of the two magnetic field intensity time-series fluctuation signal sequences is calculated and divided by the sequence length to obtain the cross-correlation function amplitude at that delay time step, so as to form the cross-correlation function curve. Extract the cross-correlation function amplitude corresponding to the zero delay time from the cross-correlation function curve and determine it as the zero-delay cross-correlation value between the two magnetic field sensors. Calculate the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors in the same way, and fill the corresponding rows and columns of the matrix with the zero-delay cross-correlation values ​​of each pair of magnetic field sensors according to the spatial arrangement order of each magnetic field sensor in the array, thereby constructing the initial spatial correlation matrix.

[0010] Furthermore, the specific method for applying a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator is as follows: set an estimated coercivity, and determine half of the estimated coercivity as the upper limit of the final magnetic field strength of the DC bias magnetic field. The magnetic field strength of the DC bias magnetic field starts from zero and gradually increases in a preset fixed step size. At each step size, a preset stable time is maintained. Then, the magnetic induction intensity timing fluctuation signal of each magnetic field sensor is collected until the final upper limit of the magnetic field strength is reached. The magnetic field strength of the DC bias magnetic field applied at each step size is the preset magnetic field strength of the DC bias magnetic field. The specific method for repeatedly acquiring the time-series fluctuation signals of magnetic induction intensity from each magnetic field sensor under each DC bias magnetic field and calculating the current spatial correlation matrix is ​​as follows: After each DC bias magnetic field reaches stability, the magnetic induction intensity time-series fluctuation signals of all magnetic field sensors are synchronously collected at the same sampling frequency and sampling duration as under the zero external magnetic field condition. The zero-delay cross-correlation values ​​between all pairs of magnetic field sensors under the DC bias magnetic field are calculated in the same way. All zero-delay cross-correlation values ​​are filled according to the same row and column arrangement rules as the initial spatial correlation matrix to obtain the current spatial correlation matrix corresponding to the DC bias magnetic field. The specific method for performing element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix is ​​as follows: subtract the element located in the i-th row and j-th column of the current spatial correlation matrix from the element located in the i-th row and j-th column of the initial spatial correlation matrix, and take the result of the subtraction as the element in the i-th row and j-th column of the correlation change matrix, where i is the row index of the matrix, j is the column index of the matrix, and the values ​​of i and j are both in the range of 1 to the total number of magnetic field sensors.

[0011] Furthermore, the specific method for calculating the trace of the correlation change matrix under each DC bias magnetic field strength value is as follows: extract all diagonal elements in the correlation change matrix where the row number is equal to the column number, sum these diagonal elements one by one, and the sum obtained is the trace of the correlation change matrix under the DC bias magnetic field. The specific method for forming the evolution curve of the trace value as a function of the DC bias magnetic field is as follows: take the magnetic field strength of each preset DC bias magnetic field as the abscissa and the trace of the relevant change matrix calculated under the DC bias magnetic field as the ordinate, and connect each discrete point in ascending order of the abscissa to form a discrete evolution curve. The second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative. Specifically, for the discrete point sequence on the evolution curve, the discrete interior points of the discrete point sequence are selected, and the second difference value of each discrete interior point is calculated in turn. The second-order difference value is calculated as follows: take the sum of the ordinate values ​​of the previous and next discrete points of the current discrete point, subtract twice the ordinate value of the current discrete point, and use the difference as the second-order difference value of the current discrete point; among all the calculated second-order difference values, find the second-order difference value with the smallest value, and determine the magnetic field strength of the DC bias magnetic field corresponding to the abscissa of the smallest second-order difference value as the characteristic demagnetizing field strength.

[0012] Furthermore, the calibration process for the coercivity power law formula, which has been pre-calibrated using standard samples, is as follows: At least three standard permanent magnet samples with known coercivity values ​​covering the expected range of the permanent magnet material to be tested are selected. For each standard permanent magnet sample, its initial spatial correlation matrix under zero external magnetic field is obtained. A DC bias magnetic field is applied, gradually increasing from zero to half of the estimated coercivity of the standard permanent magnet sample. The trace of the correlation change matrix under each DC bias magnetic field is calculated and an evolution curve is formed. The second derivative of the evolution curve is used to locate the minimum point, i.e., the characteristic demagnetizing field intensity corresponding to the negative extreme point. The coercivity values ​​of all standard permanent magnet samples are used as dependent variables, and the characteristic demagnetizing field intensity corresponding to all standard permanent magnet samples are used as independent variables. The least squares method is used to fit the power function model to obtain the power constant and the proportional constant. The characteristic demagnetizing field strength obtained for the permanent magnet material under test is substituted into the calibrated power-law formula for coercivity to calculate the coercivity value of the permanent magnet material under test.

[0013] Furthermore, the average value of all diagonal elements in the initial spatial correlation matrix is ​​extracted. Specifically, all diagonal elements in the initial spatial correlation matrix whose row number is equal to the column number are taken out, the arithmetic mean of these diagonal elements is calculated, and the arithmetic mean is multiplied by a linear amplification factor that has been pre-calibrated using standard samples from the same batch. The product is the remanence value of the permanent magnet material to be tested. The specific method for obtaining the maximum magnetic energy product value of the permanent magnet material under test by combining the coercivity value and the remanence value through the maximum magnetic energy product calculation formula is as follows: obtain the product result of the remanence value and the coercivity value of the permanent magnet material under test, and then multiply the product result by the preset shape factor. The final product result is the maximum magnetic energy product value.

[0014] The present invention also provides a system for determining the magnetic property parameters of a permanent magnet material, the system being used to execute the above-described method for determining the magnetic property parameters of a permanent magnet material, comprising: The signal processing module is used to attach multiple magnetic field sensors arranged in an array to the surface of the permanent magnet material to be tested. Under the condition of zero external magnetic field, it collects the time-series fluctuation signals of magnetic induction intensity at the location of each magnetic field sensor, calculates the cross-correlation function for any two fluctuation signals and extracts the zero-delay cross-correlation value, and constructs the initial spatial correlation matrix by constructing the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors. The matrix calculation module is used to apply a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator, repeatedly collect the time-series fluctuation signals of magnetic induction intensity of each magnetic field sensor under each DC bias magnetic field and calculate the current spatial correlation matrix, and perform element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix. The curve analysis module is used to calculate the trace of the relevant change matrix under each DC bias magnetic field, forming an evolution curve of the trace value as a function of the DC bias magnetic field. The second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative, which is denoted as the characteristic demagnetizing field strength. The parameter determination module is used to substitute the characteristic demagnetizing field strength into the coercivity power law relationship calibrated by the standard sample in advance to calculate the coercivity value of the permanent magnet material to be tested, extract the mean of all diagonal elements in the initial spatial correlation matrix, and multiply it by the preset linear amplification factor to obtain the remanence value. The coercivity value and the remanence value are combined, and the maximum energy product value of the permanent magnet material to be tested is obtained by the maximum energy product calculation formula.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention eliminates the need for a strong excitation magnetic field. Instead, it utilizes the weak spatial fluctuation signals generated by the thermal fluctuations of the magnetic domains within the permanent magnet material itself. Feature extraction is achieved through cross-correlation matrix, trace evolution, and second-order difference, enabling precise determination of coercivity, remanence, and maximum energy product. This completely avoids the irreversible damage or local demagnetization risk to the permanent magnet material caused by the need for a strong magnetic field in existing closed-circuit or pulsed magnetic field measurements. Specifically, an array of magnetic field sensors synchronously acquires the temporal fluctuation signals of magnetic induction intensity at each sensor location under zero external magnetic field conditions. The zero-delay cross-correlation values ​​between each pair are calculated to construct an initial spatial correlation matrix. This processing method can capture the intrinsic magnetic domain spatial correlation characteristics of the permanent magnet material in an undisturbed state, providing original reference information for subsequent extraction of characteristic demagnetization fields without any external excitation. The present invention also obtains the correlation change matrix by repeatedly calculating the current spatial correlation matrix under each bias field and performing element-wise difference operation with the initial spatial correlation matrix. By performing second derivative operation on the evolution curve, the characteristic demagnetization field intensity corresponding to the negative peak is located. The unique feature of this series of data processing methods is that it uses the modulation effect of DC bias magnetic field on the spatial correlation of magnetic domains to explicitly extract the characteristic demagnetization field information originally hidden in the fluctuation signal through the evolution curve of the trace of the correlation matrix, without relying on the empirical mapping relationship between the initial magnetization curve and the demagnetization curve as in the prior art. This fundamentally eliminates the mapping error caused by changes in material batch, shape or temperature. This invention directly calculates the coercivity value by substituting the characteristic demagnetizing field strength into a pre-calibrated power-law relationship for coercivity. Simultaneously, it obtains the remanence value by linearly amplifying the mean of the diagonal elements in the initial spatial correlation matrix. Combining these two methods outputs the maximum magnetic energy product. This closed-loop processing scheme not only achieves one-stop determination of all three key magnetic performance parameters from spatial cross-correlation analysis, but also clearly demonstrates that the characteristic demagnetizing field strength and coercivity follow a power-law relationship. This relationship is pre-calibrated using standard samples and is applicable to the same batch of test materials, avoiding iterative solutions to complex hysteresis models. Without damaging the permanent magnet material, it utilizes the spatial correlation of the material's own magnetic domain fluctuations, combined with correlation matrix evolution analysis under a weak DC bias field. This simultaneously solves the two contradictory technical problems of destructive testing and insufficient accuracy in existing technologies, providing a practical and feasible technical path for the non-destructive, rapid, and high-performance evaluation of permanent magnet materials. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a curve showing the fitting of the demagnetizing field strength and coercive force measurements characteristic of this invention. Figure 3 This is a scatter plot of the theoretical coercivity value and the characteristic demagnetizing field strength of the present invention. Figure 4 This is a flowchart of the overall system modules of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figures 1-3 The present invention provides a technical solution: A method for determining the magnetic property parameters of a permanent magnet material, comprising the following steps: Step 1: Attach multiple magnetic field sensors arranged in an array to the surface of the permanent magnet material to be tested. Under the condition of zero external magnetic field, collect the time-series fluctuation signals of magnetic induction intensity at the location of each magnetic field sensor. Calculate the cross-correlation function for any two fluctuation signals and extract the zero-delay cross-correlation value. Construct the initial spatial correlation matrix by using the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors. In a specific embodiment of the present invention, considering that the magnetic domain structure inside the permanent magnet material will experience random fluctuations in the local magnetization vector under thermal activation, such fluctuations are transmitted to the material surface through magnetostriction or stray field coupling, manifested as small and continuous temporal fluctuations in magnetic induction intensity at different locations on the surface, by arranging multiple magnetic field sensors in an array on the surface of the permanent magnet material to be tested, and synchronously acquiring the temporal fluctuation signals of magnetic induction intensity at each sensor location under the condition of zero external magnetic field, it is possible to capture the statistical correlation information between fluctuations at different spatial locations. This correlation information is determined by the inherent magnetic domain configuration, domain wall pinning distribution and anisotropic field of the material, and is an inherent fingerprint reflecting the material's coercivity and remanence and other magnetic properties. The physical source of the temporal fluctuation signal of the magnetic induction intensity is the reversible local thermal vibration of the domain walls inside the permanent magnet material at the bottom of the pinned potential well under thermal activation. In the field of ferromagnetism, the pinning potential energy curve of the domain walls exhibits a near-harmonic shape at the bottom of the potential well on a very small scale, with a room temperature thermal activation energy of approximately 4.1 × 10⁻⁶. -21 Joules, this energy is much less than the energy required to cross the entire pinning barrier (for NdFeB, the pinning barrier is typically around 10). -18 Up to 10 -17 (On the order of joules), but sufficient to drive the domain walls to undergo continuous reversible reciprocating vibrations in the nanoscale range at the bottom of the potential well. This reversible local thermal vibration is the intrinsic dynamic behavior of the domain walls in the pinned potential well, does not involve irreversible magnetization reversal across the pinning energy barrier, and persists under zero external magnetic field. It has been directly observed and recorded on various permanent magnet materials by high-resolution magnetic force microscopy. Reversible local thermal vibration causes random fluctuations in the local magnetization vector, which are then transmitted to the material surface via stray field coupling, generating a magnetic induction intensity signal with a small and continuously fluctuating amplitude over time. The typical amplitude of the surface stray field generated by this signal is on the order of nanotesla. As is known to those skilled in the art, the intrinsic noise level of a tunnel magnetoresistive sensor at a frequency of 10 Hz can be as low as about 150 picotesla per square root of hertz, and the magnetic field resolution of a giant magnetoresistive sensor at a similar frequency band can be better than 1 nanotesla. The above-mentioned type of solid-state magnetic field sensor can effectively acquire weak magnetic field signals on the order of nanotesla. The signal is used as a statistical input for subsequent cross-correlation analysis to characterize the correlation between magnetic domain fluctuations at different spatial locations. The acquisition and utilization of this signal in this invention does not depend on whether its single absolute amplitude exceeds a certain threshold. The stray field coupling in the above-mentioned transmission process is physically defined as: the magnetic dipole field directly generated by the vibration of the magnetic domain walls spills out to the material surface. The magnetostriction in the above-mentioned transmission process is physically defined as: the local strain of the material caused by the movement of the domain walls, which changes the magnetization distribution of the magnetic domains near the surface through the inverse magnetostriction effect, thereby affecting the magnetic induction intensity at the sensor. The time-series fluctuation signal of magnetic induction intensity finally collected by the sensor is the result of the combined effect of the above two transmission mechanisms. This invention does not rely on distinguishing which transmission mechanism is dominant, and the subsequent cross-correlation analysis is not based on the quantitative separation of a single transmission mechanism. This invention measures the temporal fluctuation signal of the magnetic induction intensity on the material surface itself, rather than inferring the surface field strength from the distribution of magnetization vectors inside the magnetic domains using theoretical formulas. Therefore, this method does not require establishing a quantitative analytical mapping relationship between the fluctuation of magnetization vectors inside the magnetic domains and the surface magnetic induction intensity. The signal collected by the sensor is a direct reflection of the surface stray field, and the subsequent cross-correlation analysis is based solely on the statistical processing of this measured signal. This method is applicable to permanent magnet materials or components that can provide a flat attachment surface. For permanent magnet materials assembled in a closed-circuit measurement device, there must be an air gap between the surface of the sample to be tested and the electromagnet yoke. The sensor array is attached to the sample surface in the air gap region. The magnetic field sensed by the sensor mainly comes from the local stray field generated by the fluctuation of the material's own magnetic domains in the vicinity of the surface. The influence of the external magnetic yoke structure on this local field is limited. There is a spatial statistical correspondence between the attachment position of each sensor in the sensor array and the magnetic domain fluctuation source in the vicinity of the material surface, rather than requiring a precise microscopic position mapping between the sensor and a single magnetic domain. The temporal fluctuation signal of magnetic induction intensity collected by the sensor reflects the comprehensive contribution of the magnetic domain fluctuation near its attachment position. The array of multiple magnetic field sensors is attached to the surface of the permanent magnet material to be tested in a grid with equal spacing. The spacing between two adjacent magnetic field sensors is a preset fixed distance value. Multiple magnetic field sensors arranged in an array are attached to a flat surface of the permanent magnet material under test in an equally spaced grid. The spacing between two adjacent magnetic field sensors is a preset fixed distance value, which is determined based on the domain characteristic size of the permanent magnet material under test. It should be noted that the domain characteristic size refers to the width or length of a typical magnetic domain in the permanent magnet material under thermal demagnetization, which can be obtained by observation with a magnetic force microscope or empirical data of similar materials. Specifically, let the domain characteristic size be L (obtained by observation with a magnetic force microscope), then the spacing d between adjacent sensors is taken as... The value ranges from 0.5L to 1.5L. If L cannot be obtained, empirical values ​​are used: for sintered NdFeB, d is 1 mm to 3 mm; for Samarium Cobalt, d is 2 mm to 5 mm; for ferrite, d is 5 mm to 10 mm. The principle for selecting the spacing is to enable adjacent sensors to respond to local magnetization vector fluctuations of different magnetic domains or different substructures within the same magnetic domain, thereby ensuring that each element in the subsequent initial spatial correlation matrix has sufficient spatial contrast, which can reflect the statistical differences between magnetic domains without losing the microscopic correlation features due to excessive spacing. It should be noted that the characteristic size L of magnetic domains is an intrinsic property of permanent magnet materials, determined by the material's chemical composition, grain size, texture, and phase composition, and is independent of the surface roughness or polishing state of the sample. Magnetic force microscopy observations of various permanent magnet materials have clearly confirmed that there is no correlation between magnetic domain structure and surface morphology. Therefore, the L value obtained using representative samples from the same batch can accurately represent the actual magnetic domain structure beneath the surface of finished industrial products manufactured using the same process in a statistical sense. This method is not sensitive to the accuracy of L. The spacing d between adjacent sensors ranges from 0.5L to 1.5L, which provides ±50% redundancy, sufficient to accommodate statistical fluctuations or measurement errors in L. The off-diagonal elements of the initial spatial correlation matrix reflect the statistical correlation between fluctuation signals at different spatial locations, rather than requiring a precise one-to-one correspondence between the sensors and individual magnetic domains. As long as the spacing d and the characteristic size L of the magnetic domain are on the same order of magnitude, the spatial resolution of the array can meet the needs of subsequent statistical analysis. For anisotropic or multiphase composite permanent magnet materials, taking the statistical average of the width of the dominant typical magnetic domain under thermal demagnetization as L is sufficient to ensure the accuracy of spatial correlation matrix analysis and trace calculation. For anisotropic or multiphase composite permanent magnet materials, the domain characteristic size L refers to the statistical average of the widths of typical domains that dominate the material under thermal demagnetization. The domain characteristic size L is an intrinsic property of the material, determined by its microstructure, including chemical composition, grain size, texture, and phase composition. Magnetic force microscopy has confirmed that there is no correlation between the domain structure and surface morphology. Therefore, L does not depend on the surface roughness or polishing state of the sample under test. This statistical average can be determined by observing representative samples from the same batch using a magnetic force microscope in multiple fields of view. The L value obtained using representative samples from the same batch, with the same process, and the same composition as the material under test can be directly used to guide the sensor spacing setting of all industrial products in the same batch without the need for microscopic observation of the actual rough surface of the industrial product under test. The empirical value directly gives the correspondence between the sensor spacing d and the material type. Those skilled in the art can directly select the sensor based on the material of the material under test without the need for conversion through the intermediate domain characteristic size L, which is especially suitable for industrial products with unpolished surfaces. Under the condition of zero external magnetic field, the temporal fluctuation signal of magnetic induction intensity at each magnetic field sensor location is collected. Specifically, the induced voltage data within a preset time window is continuously collected using a sampling frequency not lower than the preset sampling frequency threshold, and the magnetic induction intensity temporal fluctuation signal corresponding to each magnetic field sensor is obtained after analog-to-digital conversion. The condition of zero external magnetic field refers to the absence of any external DC or alternating magnetic field, with only the background magnetic field such as the Earth's magnetic field remaining. Since the Earth's magnetic field is much smaller than the coercivity of permanent magnet materials, its influence on the magnetization state is negligible. The Earth's magnetic field strength is generally 40 to 60 A / m, while the coercivity of neodymium iron boron is generally greater than 800 kA / m. Therefore, the influence of the Earth's magnetic field is less than one ten-thousandth and can be ignored. If the material under test is a low-coercivity material (such as AlNiCo, with a coercivity of about 100 kA / m), the proportion of the Earth's magnetic field is about 0.05%, which is still within an acceptable range and no additional shielding is required. Under this condition, the time-series fluctuation signal of magnetic induction intensity is collected by each magnetic field sensor separately. The specific collection method is as follows: the induced voltage output by each magnetic field sensor is continuously collected at a sampling frequency not lower than the preset sampling frequency threshold, and the collection duration is not less than the preset duration window. The collected induced voltage data is converted into magnetic induction intensity values ​​according to the sensitivity coefficient of each magnetic field sensor, and the magnetic induction intensity time-series fluctuation signal corresponding to each magnetic field sensor is obtained after analog-to-digital conversion. The preset sampling frequency threshold is at least twice the upper limit of the domain fluctuation characteristic frequency of the permanent magnet material under test, to meet the Nyquist sampling condition and avoid distortion of the cross-correlation function caused by spectral aliasing. The upper limit of the domain fluctuation characteristic frequency refers to the highest frequency component of the domain wall undergoing intrinsic jumping or bending vibration under thermal activation, which can be determined in advance through spectral analysis experiments. The method for determining the upper limit of the domain fluctuation characteristic frequency is as follows: under zero external magnetic field conditions, a magnetic field sensor is used to collect a magnetic induction intensity time-series fluctuation signal for no less than 10 seconds. The signal is then subjected to a fast Fourier transform to obtain the power spectral density curve. The frequency corresponding to the power spectral density decreasing to 1% of the low-frequency average value is determined as the upper limit of the domain fluctuation characteristic frequency. The preset duration window should ensure that the number of fluctuation signal periods included is sufficient to make the statistical estimate of the cross-correlation function converge. Generally, the window duration is required to be no less than 20 times the longest characteristic period of the domain fluctuation, thereby suppressing statistical fluctuation errors and ensuring the reliability of the initial spatial correlation matrix. The longest characteristic period of the domain fluctuation is taken as the reciprocal of the upper limit of the domain fluctuation characteristic frequency. The specific method for calculating the cross-correlation function and extracting the zero-delay cross-correlation value for any two temporal fluctuation signals of magnetic induction intensity is as follows: For any two magnetic field sensors, one magnetic field intensity time-series fluctuation signal sequence is kept fixed on the time axis, while the other magnetic field intensity time-series fluctuation signal sequence is shifted relative to it by different delay time steps. At each delay time step, the sum of the products of the corresponding position data of the two magnetic field intensity time-series fluctuation signal sequences is calculated. The sum of all products is divided by the total number of data points in the sequence to obtain the cross-correlation function amplitude at that delay time step. This process is repeated for all delay time steps to form the cross-correlation function curve. The cross-correlation function amplitude corresponding to the zero-delay time is extracted from the cross-correlation function curve and determined as the zero-delay cross-correlation value between the two magnetic field sensors. The zero-delay cross-correlation value physically quantifies the synchronicity of fluctuations between two spatial locations at zero time offset, and its magnitude reflects the statistical coupling strength of magnetic domain fluctuation processes at different locations. The zero-delay cross-correlation values ​​between all pairs of magnetic field sensors are calculated in the same way, and each magnetic field sensor is assigned a unique index according to its spatial arrangement in the array. The zero-delay cross-correlation values ​​corresponding to each pair of magnetic field sensors are then filled into the corresponding row and column positions of the matrix, i.e., the zero-delay cross-correlation values ​​of the i-th magnetic field sensor and the j-th magnetic field sensor are... The zero-delay cross-correlation values ​​between the magnetic field sensors are filled into the i-th row and j-th column of the matrix. By traversing all values ​​of i and j within the range of 1 to the total number of magnetic field sensors, a symmetric square matrix with all zero-delay cross-correlation values ​​as elements is obtained. This symmetric square matrix is ​​the initial spatial correlation matrix. Each diagonal element of the initial spatial correlation matrix corresponds to the zero-delay autocorrelation value of the signal acquired by a single sensor, representing the mean square amplitude of the magnetic induction intensity fluctuation at that location. Each off-diagonal element corresponds to the degree of cross-correlation between the fluctuation signals of different sensors, reflecting the spatial correlation structure of magnetic domain fluctuations. This initial spatial correlation matrix provides a zero-bias reference baseline for subsequent comparative analysis after applying a DC bias magnetic field.

[0020] Step 2: Apply a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator. Repeatedly collect the time-series fluctuation signals of magnetic induction intensity of each magnetic field sensor under each DC bias magnetic field and calculate the current spatial correlation matrix. Perform element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix. In a specific embodiment of the present invention, step 2, based on the zero bias reference baseline established in step 1, applies a gradually increasing DC bias magnetic field to the permanent magnet material under test to detect the evolution law of the spatial related structure of the magnetic domain system under external field disturbance, thereby extracting the critical features that are essentially related to coercivity. The specific method for applying a DC bias magnetic field to the permanent magnet material under test using a magnetic field generator is as follows: set an estimated coercivity, and determine half of the estimated coercivity as the upper limit of the final magnetic field strength of the DC bias magnetic field. The DC bias magnetic field is only used to modulate the spatial correlation structure of the magnetic domains. Its upper limit is half of the estimated coercivity, which is much lower than the actual coercivity of the material. Under this condition, the magnetization process is dominated by reversible domain wall bending and reversible magnetization vector rotation. The magnetic domains only undergo reversible vibration in the pinning potential well and do not undergo irreversible detachment across the pinning energy barrier, thus ensuring that the magnetic state of the permanent magnet material under test does not undergo irreversible changes. It should be noted that the estimated coercivity should not be less than the actual coercivity of the permanent magnet material to be tested. If the evolution curve still does not show the second-order difference minimum point after the DC bias magnetic field reaches the upper limit of the final magnetic field strength, the current estimated coercivity value is multiplied by 1.5 times as the new estimated coercivity, and steps 2 to 4 are repeated until a clear second-order difference minimum point appears. The magnetic field strength of the DC bias magnetic field starts from zero and gradually increases in a preset fixed step size. At each step size, a preset stable time is maintained. Then, the magnetic induction intensity timing fluctuation signal of each magnetic field sensor is collected until the final upper limit of the magnetic field strength is reached. The magnetic field strength of the DC bias magnetic field applied at each step size is the preset magnetic field strength of the DC bias magnetic field. The DC bias magnetic field refers to a magnetic field with a constant direction and adjustable intensity generated by the magnetic field generator. Its direction is perpendicular to the attachment plane of the magnetic field sensor to ensure that the stray field changes coupled by each sensor mainly come from the magnetization vector fluctuation component in the out-of-plane direction. The magnetic field strength of the DC bias magnetic field starts from zero and gradually increases with a preset fixed step size. The preset fixed step size should be less than one-tenth of the estimated coercivity and no more than 50 kA / m to ensure that the subsequent evolution curve has sufficient resolution to capture the inflection point region of the trace value change. A preset stabilization time is maintained at each step size before subsequent acquisition operations are performed. The preset stabilization time is the waiting time after the DC bias magnetic field reaches the current step size setting value and the magnetic field strength remains unchanged. Its duration should be greater than the relaxation time required for the magnetic domain system to reach quasi-static equilibrium under external field disturbance to ensure that the magnetic induction intensity time-series fluctuation signal acquired each time reflects the stable magnetic state of the material under the bias field, rather than the transient response in the dynamic transition process. The relaxation time can be determined through preliminary experiments. After applying a step DC bias magnetic field, the root mean square value of the time-series fluctuation signal of the magnetic induction intensity of a certain magnetic field sensor is continuously monitored. When the relative change of this value within two consecutive preset time windows is less than a preset threshold (such as 1%), the system is considered to have reached quasi-static equilibrium. This waiting time is the relaxation time. For common neodymium iron boron permanent magnet materials, the relaxation time is generally between 0.1 seconds and 2 seconds. The specific method for repeatedly acquiring the time-series fluctuation signals of magnetic induction intensity from each magnetic field sensor under each DC bias magnetic field and calculating the current spatial correlation matrix is ​​as follows: After each DC bias magnetic field reaches stability, the temporal fluctuation signals of magnetic induction intensity of all magnetic field sensors are synchronously acquired at the same sampling frequency and sampling duration as under the zero external magnetic field condition. The zero-delay cross-correlation values ​​between all pairs of magnetic field sensors under the DC bias magnetic field are calculated using the same method, namely the cross-correlation calculation process and matrix filling rules that are completely consistent with the initial spatial correlation matrix. All zero-delay cross-correlation values ​​are filled according to the same row and column arrangement rules as the initial spatial correlation matrix to obtain the current spatial correlation matrix corresponding to the DC bias magnetic field. The difference between the current spatial correlation matrix and the initial spatial correlation matrix is ​​that the initial spatial correlation matrix reflects the intrinsic spatial correlation structure of magnetic domain fluctuations under the zero bias reference state, while the current spatial correlation matrix reflects the real-time state of the spatial correlation structure of the fluctuation signal after the magnetic domain walls are displaced and the magnetization vector is deflected under the action of the external bias magnetic field. The specific method for performing element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix is ​​as follows: subtract the element located in the i-th row and j-th column of the current spatial correlation matrix from the element located in the i-th row and j-th column of the initial spatial correlation matrix, and use the subtraction result as the element in the i-th row and j-th column of the correlation change matrix, where i is the row index of the matrix, j is the column index of the matrix, and the values ​​of i and j are both in the range of 1 to the total number of magnetic field sensors; The physical meaning of the correlation change matrix is ​​as follows: by eliminating the background spatial correlation structure at zero bias, the spatial correlation change caused purely by the DC bias magnetic field is isolated. A positive value of a certain element in the correlation change matrix indicates that the fluctuation coupling between the sensor positions is enhanced under the bias field relative to the zero bias state; a negative value indicates that the coupling is weakened; the absolute value of the value reflects the degree of change; as the DC bias magnetic field gradually approaches the coercivity, the precursor to the collective irreversible rearrangement of the magnetic domain structure is manifested as a systematic critical change on the trace of the correlation change matrix, which is the data basis for feature extraction in step 3.

[0021] Step 3: Calculate the trace of the relevant change matrix under each DC bias magnetic field, form the evolution curve of the trace value with the DC bias magnetic field, perform second derivative operation on the evolution curve, locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative, and denot it as the characteristic demagnetizing field strength. In a specific embodiment of the present invention, step 3, based on the relevant change matrices obtained in step 2 under each DC bias magnetic field, extracts the trace of the matrix as a scalar index, compresses the multidimensional matrix information into a curve of the change of a single feature quantity with the external field, and locates the critical magnetic field value related to the source of coercivity from the curvature characteristics of the curve. The specific method for calculating the trace of the correlation change matrix under each DC bias magnetic field strength value is as follows: extract all diagonal elements in the correlation change matrix where the row number is equal to the column number, sum these diagonal elements one by one, and the sum obtained is the trace of the correlation change matrix under the DC bias magnetic field. The trace of the correlation change matrix is ​​the sum of all diagonal elements in the correlation change matrix where the row number equals the column number. The physical basis for extracting the trace of the correlation change matrix is ​​that each diagonal element corresponds to the autocorrelation of the magnetic induction intensity fluctuation at the same magnetic field sensor location. This change directly reflects the change in the fluctuation amplitude caused by the displacement of the local magnetic domain wall or the rotation of the magnetization vector under the action of the applied bias magnetic field. Summing up all the diagonal elements is equivalent to performing spatial integration on the fluctuation amplitude changes of all spatial points in the entire array coverage area, thereby obtaining a scalar index that comprehensively characterizes the global response state of the magnetic domain system. Compared with a single matrix element, the trace value has stronger robustness to local measurement noise and can more stably reflect the overall evolution trend of the magnetic domain system under the external field. The specific method for forming the evolution curve of the trace value as a function of the DC bias magnetic field is as follows: take the magnetic field strength of each preset DC bias magnetic field as the abscissa and the trace of the relevant change matrix calculated under the DC bias magnetic field as the ordinate, and connect each discrete point in ascending order of the abscissa to form a discrete evolution curve. The evolution curve is a discrete curve formed by connecting discrete points in ascending order of the horizontal axis with the magnetic field strength of each preset DC bias magnetic field as the horizontal axis and the trace of the relevant change matrix calculated under the corresponding bias magnetic field as the vertical axis. The horizontal axis of the evolution curve is the magnetic field strength of the DC bias magnetic field, and the vertical axis is the trace of the relevant change matrix. Therefore, the evolution curve completely describes the trajectory of the global change of the spatial fluctuation correlation structure of the magnetic domain system as the external field increases. The morphological characteristics of the evolution curve, especially the changes in its slope and curvature, contain the critical information of the transition of the magnetization process from the reversible domain wall bending stage to the irreversible domain wall depinning stage. Let the total number of steps of the DC bias magnetic field be The step index is , , No. The magnetic field strength of the DC bias magnetic field of step is denoted as ,in , (Half of the estimated coercivity), adjacent step length , It is a fixed value; Specifically, the formula for calculating the trace of the relevant change matrix is: in, In order to be in The trace value below is dimensionless and characterizes the global variation amplitude of magnetic domain fluctuations within the array coverage area. This represents the total number of magnetic field sensors. , This represents the row number of the arrayed magnetic field sensors, and its value is an integer greater than or equal to 2. This refers to the number of columns in an array of magnetic field sensors, and its value is an integer greater than or equal to 2, typically ranging from... That is, at least 2 rows and 2 columns (4 sensors) and at most 8 rows and 8 columns (64 sensors). The first of the relevant change matrix Line 1 The diagonal elements of the column reflect the change in the fluctuation amplitude at that point relative to the zero-field state. This represents the index of the diagonal element in the correlation transformation matrix, with values ​​ranging from 1 to... The estimated coercivity is set according to the material grade, approximately 100-200 kA / m for AlNiCo, approximately 200-400 kA / m for ferrite, approximately 600-1200 kA / m for SamariumCo, and approximately 1000-2500 kA / m for NeodymiumFeB. The second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative. Specifically, for the discrete point sequence on the evolution curve, the discrete interior points of the discrete point sequence are selected, and the second difference value of each discrete interior point is calculated in turn. The second-order difference value is calculated as follows: take the sum of the ordinate values ​​of the previous and next discrete points of the current discrete point, subtract twice the ordinate value of the current discrete point, and use the difference as the second-order difference value of the current discrete point; among all the calculated second-order difference values, find the second-order difference value with the smallest value, and determine the magnetic field strength of the DC bias magnetic field corresponding to the abscissa of the smallest second-order difference value as the characteristic demagnetizing field strength; The evolution curve is processed by numerical second-order difference operation to approximate the second derivative. This calculation method uses three consecutive discrete points, including the current point and the two points before and after it, to replace the differential with the difference, and quantitatively evaluates the degree and direction of curvature of the evolution curve at the magnetic field strength of each DC bias magnetic field. A negative second-order difference value indicates that the evolution curve bends downward at that point; the smaller the second-order difference value, the more severe the downward curvature. The characteristic demagnetizing field strength refers to the magnetic field strength of the DC bias magnetic field corresponding to the smallest second-order difference value among all second-order difference values. This value is determined as the critical magnetic field reflecting the coercivity characteristics of the permanent magnet material under test. The physical logic for determining the characteristic demagnetizing field strength is as follows: When the DC bias magnetic field gradually increases from zero, the domain walls first undergo reversible bending at the weak pinning position. At this time, the fluctuation amplitude changes approximately linearly, the trace value changes uniformly with the magnetic field, and the second derivative of the evolution curve is close to zero. When the external field continues to increase and approaches the coercivity of the material, the domain walls begin to undergo collective irreversible depinning at the strong pinning position, resulting in a sharp nonlinear decrease in the fluctuation amplitude of the local magnetization vector. The trace value change rate reaches its maximum, and the curvature of the evolution curve shows the most significant negative bending in this critical region. Specifically, the second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative. This is done by using the previously defined trace value. ,for (That is, excluding the first and last endpoints), calculate the second difference value of the numerical value at each interior point: in, The total number of bias field steps, i.e., starting from zero magnetic field strength, with a fixed step size. Increment to the final upper limit of magnetic field strength The total number of steps (half the estimated coercivity) is used to ensure that at least one second-order difference value can be calculated. The total number of bias field steps is... Not less than 3 For the corresponding The second-order difference value at that point is dimensionless and proportional to the curvature of the evolution curve at that point. A negative value indicates that the curve bends downward, and the smaller the value (i.e., the more negative it is), the more severe the downward bend. These are three consecutive bias field values ​​with equal step sizes. The common value range is 5–20 kA / m to 20 kA / m; Calculate all to corresponding Extract the minimum value. The magnetic field strength corresponding to this minimum value is the characteristic demagnetizing field strength. : , When the bias field approaches the critical state of the material's coercivity, the magnetic domain walls undergo collective irreversible depinning, and the rate of change of the correlation between fluctuation space reaches its maximum, resulting in the second derivative of the trace curve being a negative extremum (minimum value). This turning point was captured quantitatively; The magnetic field strength corresponding to the most negative second-order difference value quantitatively captures the critical point where the magnetization state transition is most drastic. This point has an intrinsic correspondence with the physical definition of coercivity, namely the magnetic field with the fastest magnetization reversal rate. Therefore, it is determined as the characteristic demagnetizing field strength. The characteristic demagnetizing field strength is not directly equal to the coercivity, but there is a power-law mapping relationship between it and the coercivity, which is determined by the intrinsic magnetic properties of the material. This mapping relationship is determined by standard sample calibration in subsequent steps.

[0022] Step 4: Substitute the characteristic demagnetizing field strength into the coercivity power law relationship calibrated by the standard sample in advance to calculate the coercivity value of the permanent magnet material to be tested. Extract the mean of all diagonal elements in the initial spatial correlation matrix and multiply it by the preset linear amplification factor to obtain the remanence value. Combine the coercivity value and the remanence value and obtain the maximum magnetic energy product value of the permanent magnet material to be tested through the maximum magnetic energy product calculation formula. In a specific embodiment of the present invention, step 4, based on the characteristic demagnetizing field strength obtained in step 3, converts the critical magnetic field value into a coercive force value through a pre-calibrated mapping relationship, and independently extracts the remanent magnetization value from the initial spatial correlation matrix, and finally outputs a complete combination of magnetic performance parameters. There is a spatial statistical correspondence between the attachment positions of each sensor in the sensor array and the magnetic domain fluctuation sources in the adjacent area of ​​the material surface, rather than requiring a precise microscopic positional mapping between the sensor and a single magnetic domain. The temporal fluctuation signals of magnetic induction intensity collected by the sensor reflect the comprehensive contribution of magnetic domain fluctuations near its attachment position. The off-diagonal elements in the initial spatial correlation matrix reflect the degree of statistical correlation between fluctuation signals at different spatial positions. By analyzing this matrix, the changes in the spatial correlation structure of magnetic domains can be indirectly inferred without precisely locating the specific morphology of the magnetic domains under each sensor. By reasonably setting the spacing of the sensor array (typically 0.5 to 1.5 times the characteristic size of the magnetic domains), those skilled in the art can ensure that the array coverage area matches the magnetic domain correlation range to be analyzed. The spatial correspondence between the sensor and the magnetic domain fluctuation source is sufficient to support subsequent matrix construction and statistical analysis. Furthermore, this method does not require magnetic force microscopy observation of every industrial product to be tested. Step 1 of the instruction manual has given empirical spacing values ​​based on material type, including 1 mm to 3 mm for sintered NdFeB, 2 mm to 5 mm for Samarium Cobalt, and 5 mm to 10 mm for ferrite. Those skilled in the art can directly select the spacing based on the material of the material to be tested without the need for intermediate conversion through the magnetic domain characteristic size L. For material types not listed, the optimal spacing can be determined by analogy with known materials or by a limited number of pre-tests. The calibration process for the coercivity power law formula, which has been pre-calibrated using standard samples, is as follows: At least three standard permanent magnet samples with known coercivity values ​​covering the expected range of the permanent magnet material to be tested are selected. For each standard permanent magnet sample, its initial spatial correlation matrix under zero applied magnetic field is obtained. A DC bias magnetic field is applied, gradually increasing from zero to half of the estimated coercivity of the standard permanent magnet sample. The trace of the correlation change matrix under each DC bias magnetic field is calculated, and an evolution curve is formed. The second derivative of the evolution curve is used to locate the minimum point, i.e., the characteristic demagnetizing field intensity corresponding to the negative extreme point. The coercivity values ​​of all standard permanent magnet samples are used as dependent variables, and the characteristic demagnetizing field intensities corresponding to all standard permanent magnet samples are used as independent variables. A power function model is used for least squares fitting to obtain the power exponent constant and the proportionality constant. After fitting, the coefficient of determination is calculated. ,like If the value is less than 0.98, the number of standard permanent magnet samples needs to be increased (at least five) or the measurement process needs to be checked for errors, and the system needs to be recalibrated until R² is not less than 0.98. Specifically, the power-law relationship of coercivity is as follows: in, The value represents the coercivity of the permanent magnet material under test. It is a proportionality constant, dimensionless, with a typical range of 0.8 to 1.2. is a power-law constant, dimensionless, typically ranging from 0.9 to 1.1. Time degenerates into a linear relationship; characteristic demagnetizing field With macroscopic coercivity Both originate from the critical field of irreversible displacement of magnetic domain walls, and there is a scaling relationship between them. Experiments show that this relationship satisfies a power-law form in permanent magnet materials such as NdFeB and SmCo. A tiny deviation close to 1 reflects microscopic factors such as grain size distribution and anisotropic field uniformity; The sample number and coercivity value are detailed in Table 1.

[0023] Table 1. Data Statistics Table Analysis of the 30 sets of data reveals a clear nonlinear positive correlation between the characteristic demagnetizing field strength and the coercivity. Specifically, as the characteristic demagnetizing field strength increases from 200.0 kA / m to 700.0 kA / m, the corresponding theoretical coercivity value monotonically increases from 719.961 kA / m to 2314.350 kA / m, exhibiting an overall power-law growth trend. For example, when the characteristic demagnetizing field strength is 200.0 kA / m, the coercivity... The theoretical value is 719.961 kA / m, while the theoretical coercivity increases to 1045.000 kA / m when the characteristic demagnetizing field strength is 300.0 kA / m. When the characteristic demagnetizing field strength reaches 500.0 kA / m, the theoretical coercivity is 1680.470 kA / m, and reaches 2314.350 kA / m when it reaches 700.0 kA / m. This growth rate gradually slows down as the characteristic demagnetizing field strength increases, which is reflected in the curve slope gradually decreasing. The actual measured coercivity values ​​fluctuated randomly around the theoretical curve, with the fluctuation range controlled between 0.96 and 1.04 times the theoretical value. For example, when the characteristic demagnetizing field strength was 280.0 kA / m, the theoretical value was 983.637 kA / m, and the measured value was 949.210 kA / m, slightly lower than the theoretical value. When the characteristic demagnetizing field strength was 320.0 kA / m, the theoretical value was 1110.126 kA / m, and the measured value was 1105.685 kA / m, slightly lower than the theoretical value. When the characteristic demagnetizing field strength was 420.0 kA / m, the theoretical value was 1424.335 kA / m, and the measured value was 1477.035 kA / m, slightly higher than the theoretical value. This alternating positive and negative random deviation ensures that all measured data points are evenly distributed on both sides of the theoretical fitting curve, without systematic bias. Further observation of the data distribution within different characteristic demagnetization field strength ranges reveals that the measurement deviations are relatively small in the lower characteristic demagnetization field strength range (200.0 to 350.0 kA / m). For example, the difference between the measured and theoretical values ​​is -9.374 kA / m when the characteristic demagnetization field strength is 240.0 kA / m, and +21.717 kA / m when the characteristic demagnetization field strength is 350.0 kA / m. However, in the higher characteristic demagnetization field strength range (600.0 to 700 kA / m), the deviations are much smaller. Within the range of 0 kA / m, the absolute value of the measurement deviation increases. For example, when the characteristic demagnetizing field strength is 640.0 kA / m, the difference between the measured value and the theoretical value is -65.927 kA / m; when the characteristic demagnetizing field strength is 680.0 kA / m, the difference is -29.276 kA / m; and when the characteristic demagnetizing field strength is 700.0 kA / m, the difference is +9.257 kA / m. This fluctuation range is consistent with the physical law that the influence of noise increases slightly under high field strength in actual measurements. The above data relationship shows that the characteristic demagnetizing field strength and coercivity follow a power-law mapping. This mapping relationship can be used to accurately calculate the coercivity from the characteristic demagnetizing field strength. The random fluctuations in the measured data verify the robustness and anti-interference ability of the model.

[0024] The power-law relationship of coercivity is a mapping equation in the form of a power function with the characteristic demagnetizing field strength as the independent variable and the coercivity value as the dependent variable. The necessity of establishing this relationship is that the characteristic demagnetizing field strength reflects the critical external field value exhibited by the magnetic domain system at the spatial fluctuation correlation structure level. This value has the same physical origin as the macroscopic coercivity of the material, namely the critical external field required for irreversible depinning of the domain walls. However, the two are not numerically identical, but follow a power-law scaling relationship determined by the intrinsic magnetic properties of the material. The choice of the power-law form is based on the scaling theory of critical phenomena in ferromagnets, that is, near a phase transition or critical transition point, the two physical quantities characterizing the system response generally satisfy a power function relationship. A standard permanent magnet sample refers to a permanent magnet whose chemical composition, preparation process, and microstructure belong to the same category as the permanent magnet material to be tested, and whose coercivity value has been accurately calibrated using the direct measurement method of the demagnetization curve specified in the national standard. The calibration process requires the selection of at least three standard permanent magnet samples, whose coercivity values ​​should cover the expected range of the permanent magnet material to be tested, to ensure the extrapolation accuracy of the power-law relationship obtained from the fitting within the entire target interval. For each standard permanent magnet sample, the same operating procedures as steps 1 to 2 of this method are performed: acquiring the temporal fluctuation signal of magnetic induction intensity under zero external magnetic field and constructing an initial spatial correlation matrix; applying a magnetic field gradually increasing from zero to the pre-magnetic field of the standard permanent magnet sample. A DC bias magnetic field with half the coercivity is estimated. The trace of the relevant change matrix under each DC bias magnetic field is calculated and an evolution curve is formed. The second derivative of the evolution curve is used to locate the characteristic demagnetizing field intensity corresponding to the minimum point, and the characteristic demagnetizing field intensity of each standard permanent magnet sample is obtained. The coercivity values ​​of all standard permanent magnet samples are used as dependent variables, and their corresponding characteristic demagnetizing field intensities are used as independent variables. The least squares fitting is performed using a power function model to obtain the power exponent constant and the proportionality constant, and the power law relationship of coercivity is calibrated. The characteristic demagnetizing field intensity obtained for the permanent magnet material to be tested is substituted into the calibrated relationship to calculate the coercivity value of the permanent magnet material to be tested. The characteristic demagnetizing field strength obtained for the permanent magnet material under test is substituted into the calibrated power-law formula for coercivity to calculate the coercivity value of the permanent magnet material under test.

[0025] The average value of all diagonal elements in the initial spatial correlation matrix is ​​extracted as follows: take out all diagonal elements in the initial spatial correlation matrix whose row number is equal to the column number, calculate the arithmetic mean of these diagonal elements, multiply the arithmetic mean by a linear amplification factor that has been calibrated in advance by the same batch of standard samples, and the product is the remanence value of the permanent magnet material to be tested. The linear amplification factor is a scaling factor that maps the arithmetic mean of the diagonal elements of the initial spatial correlation matrix to the macroscopic remanence value. This factor is determined through calibration using standard permanent magnet samples from the same batch. Specifically, at least two standard permanent magnet samples with known remanence values ​​covering the expected range of the material under test are selected. The remanence values ​​of the selected standard permanent magnet samples should cover the expected range of the remanence of the permanent magnet material under test; that is, the difference between the lowest and highest remanence samples should not be less than 80% of the possible variation range of the remanence of the material under test. The initial spatial correlation matrix is ​​obtained under zero external magnetic field, and the arithmetic mean of its diagonal elements is calculated. This standard permanent magnet sample is then used for calibration. The known remanence value of a magnetic sample divided by the arithmetic mean of its diagonal elements is the linear amplification factor. The physical basis of the linear amplification factor is that the diagonal elements of the initial spatial correlation matrix are the zero-delay autocorrelation values ​​of the magnetic induction intensity fluctuation signals at each sensor location, which measure the mean square amplitude of the local magnetization vector fluctuation. The remanence is the macroscopic remanence intensity maintained by the material under zero external field. The latter is statistically proportional to the spatial average value of the mean square amplitude of the local fluctuation. By calibrating the same batch of samples to determine this proportional relationship, the systematic bias introduced by factors such as sensor sensitivity differences and material surface conditions can be effectively eliminated. The specific method for obtaining the maximum energy product of the permanent magnet material under test by combining the coercivity and remanence values ​​using the maximum energy product calculation formula is as follows: Obtain the product of the remanence and coercivity values ​​of the permanent magnet material under test, then multiply this product by a preset shape factor. The final product is the maximum energy product value. This scheme uses an empirical formula. ,in As the form factor, this formula is applicable to engineering estimations of common permanent magnet materials at room temperature. Its theoretical basis lies in the fact that for materials with a linear demagnetization curve, the maximum magnetic energy product is approximately equal to one-quarter of the product of remanence and coercivity, i.e. For an ideal square demagnetization curve, the maximum energy product is approximately equal to half the product of remanence and coercivity, i.e. Actual materials The value lies between the two and is determined by linear interpolation of squareness. The shape factor is a correction factor used to deduce the maximum energy product from coercivity and remanence values. The theoretical upper limit of the maximum energy product is determined by dividing the square of the remanence value by the shape of the material's demagnetization curve. For permanent magnet materials with an ideal square demagnetization curve, the shape factor takes the theoretical maximum value of 0.5. For practical materials, a decrease in the squareness of the demagnetization curve, i.e., an increase in the deviation of the demagnetization curve from a rectangular shape in the second quadrant, will lead to a corresponding decrease in the shape factor. The shape factor is taken between 0.25 and 0.5 based on the squareness of the demagnetization curve of the permanent magnet material under test. The closer the squareness is to one, the closer the shape factor is to 0.5. Squareness of demagnetization curve Satisfies a linear relationship: ,in It is the ratio of the area enclosed by the demagnetization curve to the area of ​​the rectangle obtained by multiplying the remanence by the coercivity. The value range is from 0 to 1, when When direct measurement is not possible, typical values ​​of similar materials can be used; The squareness of the demagnetization curve refers to the ratio of the area enclosed by the actual demagnetization curve to the area of ​​the circumscribed rectangle formed by the remanence and coercivity of the material. It can be obtained from standard test data of similar materials. The product of the remanence and coercivity values ​​of the permanent magnet material to be tested is obtained, and then the product is multiplied by the form factor. The final product is the maximum magnetic energy product value.

[0026] Please see Figure 4 The present invention also provides a system for determining the magnetic properties parameters of a permanent magnet material, the system being used to execute the above-described method for determining the magnetic properties parameters of a permanent magnet material, comprising: The signal processing module is used to attach multiple magnetic field sensors arranged in an array to the surface of the permanent magnet material to be tested. Under the condition of zero external magnetic field, it collects the time-series fluctuation signals of magnetic induction intensity at the location of each magnetic field sensor, calculates the cross-correlation function for any two fluctuation signals and extracts the zero-delay cross-correlation value, and constructs the initial spatial correlation matrix by constructing the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors. The matrix calculation module is used to apply a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator, repeatedly collect the time-series fluctuation signals of magnetic induction intensity of each magnetic field sensor under each DC bias magnetic field and calculate the current spatial correlation matrix, and perform element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix. The curve analysis module is used to calculate the trace of the relevant change matrix under each DC bias magnetic field, forming an evolution curve of the trace value as a function of the DC bias magnetic field. The second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative, which is denoted as the characteristic demagnetizing field strength. The parameter determination module is used to substitute the characteristic demagnetizing field strength into the coercivity power law relationship calibrated by the standard sample in advance to calculate the coercivity value of the permanent magnet material to be tested, extract the mean of all diagonal elements in the initial spatial correlation matrix, and multiply it by the preset linear amplification factor to obtain the remanence value. The coercivity value and the remanence value are combined, and the maximum energy product value of the permanent magnet material to be tested is obtained by the maximum energy product calculation formula.

[0027] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0028] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0029] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0030] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method of determining a magnetic property parameter of a permanent magnetic material, characterized by, The specific steps include: Step 1: Attach multiple magnetic field sensors arranged in an array to the surface of the permanent magnet material to be tested. Under the condition of zero external magnetic field, collect the time-series fluctuation signals of magnetic induction intensity at the location of each magnetic field sensor. Calculate the cross-correlation function for any two fluctuation signals and extract the zero-delay cross-correlation value. Construct the initial spatial correlation matrix by using the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors. Step 2: Apply a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator. Repeatedly collect the time-series fluctuation signals of magnetic induction intensity of each magnetic field sensor under each DC bias magnetic field and calculate the current spatial correlation matrix. Perform element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix. Step 3: Calculate the trace of the relevant change matrix under each DC bias magnetic field, form the evolution curve of the trace value with the DC bias magnetic field, perform second derivative operation on the evolution curve, locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative, and denot it as the characteristic demagnetizing field strength. Step 4: Substitute the characteristic demagnetizing field strength into the coercivity power law relationship calibrated with a standard sample to calculate the coercivity value of the permanent magnet material to be tested. Extract the mean of all diagonal elements in the initial spatial correlation matrix and multiply it by the preset linear amplification factor to obtain the remanence value. Combine the coercivity value and the remanence value and obtain the maximum energy product value of the permanent magnet material to be tested through the maximum energy product calculation formula.

2. The method for determining the magnetic property parameters of a permanent magnet material according to claim 1, characterized in that: Multiple magnetic field sensors arranged in an array are attached to the surface of the permanent magnet material to be tested in a grid with equal spacing. The spacing between two adjacent magnetic field sensors is a preset fixed distance value. Under the condition of zero external magnetic field, the temporal fluctuation signal of magnetic induction intensity at each magnetic field sensor location is collected. Specifically, the induced voltage data within a preset time window is continuously collected using a sampling frequency not lower than a preset sampling frequency threshold, and the magnetic induction intensity temporal fluctuation signal corresponding to each magnetic field sensor is obtained after analog-to-digital conversion.

3. The method for determining the magnetic property parameters of a permanent magnet material according to claim 2, characterized in that: The specific method for calculating the cross-correlation function and extracting the zero-delay cross-correlation value for any two temporal fluctuation signals of magnetic induction intensity is as follows: For any two magnetic field sensors, one magnetic field intensity time-series fluctuation signal sequence is kept fixed on the time axis, while the other magnetic field intensity time-series fluctuation signal sequence is shifted relative to it by different delay time steps. At each delay time step, the sum of the products of the corresponding position data of the two magnetic field intensity time-series fluctuation signal sequences is calculated and divided by the sequence length to obtain the cross-correlation function amplitude at that delay time step, so as to form the cross-correlation function curve. Extract the cross-correlation function amplitude corresponding to the zero delay time from the cross-correlation function curve and determine it as the zero-delay cross-correlation value between the two magnetic field sensors. Calculate the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors in the same way, and fill the corresponding rows and columns of the matrix with the zero-delay cross-correlation values ​​of each pair of magnetic field sensors according to the spatial arrangement order of each magnetic field sensor in the array, thereby constructing the initial spatial correlation matrix.

4. The method for determining the magnetic property parameters of a permanent magnet material according to claim 3, characterized in that: The specific method for applying a DC bias magnetic field to the permanent magnet material under test using a magnetic field generator is as follows: set an estimated coercivity, and determine half of the estimated coercivity as the upper limit of the final magnetic field strength of the DC bias magnetic field. The magnetic field strength of the DC bias magnetic field starts from zero and gradually increases in a preset fixed step size. At each step size, a preset stable time is maintained. Then, the magnetic induction intensity timing fluctuation signal of each magnetic field sensor is collected until the final upper limit of the magnetic field strength is reached. The magnetic field strength of the DC bias magnetic field applied at each step size is the preset magnetic field strength of the DC bias magnetic field. The specific method for repeatedly acquiring the time-series fluctuation signals of magnetic induction intensity from each magnetic field sensor under each DC bias magnetic field and calculating the current spatial correlation matrix is ​​as follows: After each DC bias magnetic field reaches stability, the magnetic induction intensity time-series fluctuation signals of all magnetic field sensors are synchronously collected at the same sampling frequency and sampling duration as under the zero external magnetic field condition. The zero-delay cross-correlation values ​​between all pairs of magnetic field sensors under the DC bias magnetic field are calculated in the same way. All zero-delay cross-correlation values ​​are filled according to the same row and column arrangement rules as the initial spatial correlation matrix to obtain the current spatial correlation matrix corresponding to the DC bias magnetic field. The specific method for performing element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix is ​​as follows: subtract the element located in the i-th row and j-th column of the current spatial correlation matrix from the element located in the i-th row and j-th column of the initial spatial correlation matrix, and take the result of the subtraction as the element in the i-th row and j-th column of the correlation change matrix, where i is the row index of the matrix, j is the column index of the matrix, and the values ​​of i and j are both in the range of 1 to the total number of magnetic field sensors.

5. The method for determining the magnetic property parameters of a permanent magnet material according to claim 4, characterized in that: The specific method for calculating the trace of the correlation change matrix under each DC bias magnetic field strength value is as follows: extract all diagonal elements in the correlation change matrix where the row number is equal to the column number, sum these diagonal elements one by one, and the sum obtained is the trace of the correlation change matrix under the DC bias magnetic field. The specific method for forming the evolution curve of the trace value as a function of the DC bias magnetic field is as follows: take the magnetic field strength of each preset DC bias magnetic field as the abscissa and the trace of the relevant change matrix calculated under the DC bias magnetic field as the ordinate, and connect each discrete point in ascending order of the abscissa to form a discrete evolution curve. The second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative. Specifically, for the discrete point sequence on the evolution curve, the discrete interior points of the discrete point sequence are selected, and the second difference value of each discrete interior point is calculated in turn. The second-order difference value is calculated as follows: take the sum of the ordinate values ​​of the previous and next discrete points of the current discrete point, subtract twice the ordinate value of the current discrete point, and use the difference as the second-order difference value of the current discrete point; among all the calculated second-order difference values, find the second-order difference value with the smallest value, and determine the magnetic field strength of the DC bias magnetic field corresponding to the abscissa of the smallest second-order difference value as the characteristic demagnetizing field strength.

6. The method for determining the magnetic property parameters of a permanent magnet material according to claim 5, characterized in that: The calibration process for the coercivity power law formula, which has been pre-calibrated using standard samples, is as follows: At least three standard permanent magnet samples with known coercivity values ​​covering the expected range of the permanent magnet material to be tested are selected. For each standard permanent magnet sample, its initial spatial correlation matrix under zero external magnetic field is obtained. A DC bias magnetic field is applied, gradually increasing from zero to half of the estimated coercivity of the standard permanent magnet sample. The trace of the correlation change matrix under each DC bias magnetic field is calculated and an evolution curve is formed. The second derivative of the evolution curve is used to locate the minimum point, i.e., the characteristic demagnetizing field intensity corresponding to the negative extreme point. The coercivity values ​​of all standard permanent magnet samples are used as dependent variables, and the characteristic demagnetizing field intensity corresponding to all standard permanent magnet samples are used as independent variables. The least squares method is used to fit the power function model to obtain the power constant and the proportional constant. The characteristic demagnetizing field strength obtained for the permanent magnet material under test is substituted into the calibrated power-law formula for coercivity to calculate the coercivity value of the permanent magnet material under test.

7. The method for determining the magnetic property parameters of a permanent magnet material according to claim 6, characterized in that: The average value of all diagonal elements in the initial spatial correlation matrix is ​​extracted as follows: take out all diagonal elements in the initial spatial correlation matrix whose row number is equal to the column number, calculate the arithmetic mean of these diagonal elements, multiply the arithmetic mean by a linear amplification factor that has been calibrated in advance by the same batch of standard samples, and the product is the remanence value of the permanent magnet material to be tested. The specific method for obtaining the maximum magnetic energy product value of the permanent magnet material under test by combining the coercivity value and the remanence value through the maximum magnetic energy product calculation formula is as follows: obtain the product result of the remanence value and the coercivity value of the permanent magnet material under test, and then multiply the product result by the preset shape factor. The final product result is the maximum magnetic energy product value.

8. A system for determining the magnetic property parameters of a permanent magnet material, characterized in that: The system is used to perform a method for determining the magnetic property parameters of a permanent magnet material according to any one of claims 1-7, including: The signal processing module is used to attach multiple magnetic field sensors arranged in an array to the surface of the permanent magnet material to be tested. Under the condition of zero external magnetic field, it collects the time-series fluctuation signals of magnetic induction intensity at the location of each magnetic field sensor, calculates the cross-correlation function for any two fluctuation signals and extracts the zero-delay cross-correlation value, and constructs the initial spatial correlation matrix by constructing the zero-delay cross-correlation values ​​between all pairs of magnetic field sensors. The matrix calculation module is used to apply a DC bias magnetic field to the permanent magnet material under test through a magnetic field generator, repeatedly collect the time-series fluctuation signals of magnetic induction intensity of each magnetic field sensor under each DC bias magnetic field and calculate the current spatial correlation matrix, and perform element-by-element difference operation between the current spatial correlation matrix and the initial spatial correlation matrix to obtain the correlation change matrix. The curve analysis module is used to calculate the trace of the relevant change matrix under each DC bias magnetic field, forming an evolution curve of the trace value as a function of the DC bias magnetic field. The second derivative of the evolution curve is calculated to locate the magnetic field strength of the DC bias magnetic field corresponding to the minimum point of the second derivative, which is denoted as the characteristic demagnetizing field strength. The parameter determination module is used to substitute the characteristic demagnetizing field strength into the coercivity power law relationship calibrated by the standard sample in advance to calculate the coercivity value of the permanent magnet material to be tested, extract the mean of all diagonal elements in the initial spatial correlation matrix, and multiply it by the preset linear amplification factor to obtain the remanence value. The coercivity value and the remanence value are combined, and the maximum energy product value of the permanent magnet material to be tested is obtained by the maximum energy product calculation formula.

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